
677 P.2d 1215 (1983)
David ALTMAN, Appellant,
v.
ALASKA TRUSS & MANUFACTURING COMPANY, INC., Woods & Rohde, d/b/a Alaska Truss & Millwork Inc., and Roger Woods and Verne Rohde, individually, Appellees.
No. 5775.
Supreme Court of Alaska.
December 16, 1983.
*1216 Kenneth P. Jacobus, Hughes, Thorsness, Gantz, Powell & Brundin, Anchorage, for appellant.
Noel H. Kopperud and Dan W. Burton, Wasilla, for appellee Alaska Truss & Manufacturing Co., Inc.
Roger E. Henderson, Houston & Henderson, Anchorage, for appellees Woods & Rohde and Roger Woods and Verne Rohde.
Before BURKE, C.J., and RABINOWITZ, MATTHEWS, COMPTON and MOORE, JJ.

OPINION
COMPTON, Justice.
The issue presented in this appeal is whether the superior court erred in ruling that the defendants to this action, Alaska *1217 Truss & Manufacturing Co. ("ATM") and Woods & Rohde, Inc. ("W & R"), do not owe the plaintiff, David Altman, any rent in addition to that which they have already paid. For the reasons set forth below, we conclude that the superior court correctly held that ATM and W & R do not owe any additional rent to Altman for the leased premises. We find it necessary, however, to remand the case to the superior court for further consideration of whether ATM and W & R owe additional rent for their use of property that was not included in the lease.

I. FACTUAL AND PROCEDURAL BACKGROUND
Prior to trial, the parties stipulated to many of the facts; accordingly, very few are in dispute. Rail Air Industrial Park, Inc. ("Rail Air") leased approximately four and one-third acres of land from the State of Alaska. On May 22, 1968, Rail Air subleased approximately one and one-half acres of this property to ATM. The sublease term began on January 1, 1969, and ran through December 31, 1973. The annual rent, calculated at four and one-half cents per square foot, amounted to $3,440.00.
The sublease contained a rent escalation clause, which provided that the rent would increase in proportion to any rent increase imposed by the state on the primary lease. The clause specifically stated that the increase would occur during the "term of this lease[,] any hold over tenancy or any renewal of this lease pursuant to the option herein granted."[1]
The renewal option specified that the sublessee could renew the sublease for a period of five years, provided that the sublessee gave the sublessor written notice of its election to do so on or before September 30, 1973. It further specified that the renewal would be upon the same terms and conditions as contained in the sublease, except that the rent "shall be subject to negotiation." If the parties failed to agree upon a renewal rate within forty-five days after the option was exercised, the renewal rate was to be established by arbitration, which was to be completed by December 31, 1973.[2]
In February of 1973, ATM assigned its sublease to W & R, a manufacturer of trusses and other building components. Six months later, in August of 1973, Rail Air transferred to Bayside Land, Inc. its interests in the state lease and the ATM sublease. W & R used property adjacent to the leased property to store supplies and materials. Bayside Land was aware of this, but chose not to demand any additional rent for the use of the extra land.
On September 25, 1973, ATM sent written notice to Rail Air and Bayside Land that it elected to exercise the renewal option. The parties did not seriously discuss a renewal rate within forty-five days of the notice, nor did they submit the issue to arbitration. On December 26, 1973, an *1218 agent for ATM requested Bayside Land to sign a document it prepared, entitled "Renewal of Lease." The renewal specified that the annual rent was to be $4,509.76, which represents an increase from four and one-half cents per square foot to seven cents per square foot. This increase was apparently decided upon unilaterally by ATM.[3] Bayside Land responded by letter on January 27, 1974 that it could not sign the renewal without having a copy of the original sublease between Rail Air and ATM. ATM provided Bayside Land with a copy of the sublease, but the renewal lease was never executed.
No meaningful discussions or negotiations took place regarding the rent to be paid and, beginning in January 1974, ATM and W & R unilaterally paid rent monthly at the annual rate of $4,509.72. Bayside Land accepted each of the payments without expressing any protest or indicating that the rent paid was less than what was due.
On October 7, 1974, Altman succeeded to all of Bayside Land's interests in the state lease and the ATM sublease.[4] Shortly after this, he "walked the property" with Roger Woods of W & R. The parties agreed that at that time Altman noted W & R was using more land than was covered by the lease. Altman did not request W & R to stop using the additional land, but indicated that W & R would or might have to pay "a reasonable amount" for its use. No specific figure was mentioned and the general impression created was that this was a subject for future negotiations.
On November 8, 1974, Altman wrote to W & R and inquired about several matters, including whether the ATM sublease had been renewed, whether anyone was in default on the sublease, and whether it was then possible to submit the matter of the rental rate to arbitration. Altman indicated that he believed a reasonable rental rate for the leased property would be $16,250.00 per year. No mention was made of W & R's use of the extra land.
Woods responded on behalf of W & R by letter dated December 11, 1974. He indicated that the sublease had been renewed. He further indicated that the sublease had provided that the rental rate for the renewal period was to have been established by December 31, 1973. Woods maintained that because no new rental rate had been agreed upon, the renewal was at the same rental rate as under the initial sublease. He stated that there were no defaults under the sublease.
Altman did not respond to this letter in writing. He indicated in a telephone conversation, two to three months later, that he wanted W & R to pay more rent. He did not refer to Woods' letter or take any position on whether the sublease had been renewed, and if so, at what rental rate. W & R indicated to Altman that they were unable to pay more rent. It informed Altman that if the rent were increased, it would have to move because it would not be able to pay a substantial increase.
As will be set forth in greater detail, the parties periodically discussed the issues of whether rent should be paid for the property used by W & R that was not covered by the sublease and whether increased rent should be paid under the sublease. No agreements were ever reached on these issues.
On December 15, 1974, the State of Alaska increased Altman's rent on the four acres it was leasing to him from $2,390.00 per year to $12,180.00 per year. This represents an increase of approximately *1219 500%.[5] Altman did not notify ATM and W & R of this increase until September 1976, at which time he mentioned it in a conversation regarding his desire to receive more rent.
On November 29, 1976, Altman made a written demand, for the first time, that ATM and W & R pay additional rent in the future and pay for their past "rent deficiency." Altman demanded a total of $61,500.00 for past rent and a prospective increase of the rent to a total of $2,000.00 per month. Altman indicated that he arrived at these figures by assuming that the annual fair rental value of the leased property was $16,000.00 and the annual fair rental value of the additional land used by W & R was $8,000.00. Subtracting the $4,500.00 paid annually since 1974, Altman calculated that there was a rent deficiency of $20,500.00 for the years 1974, 1975 and 1976, totalling $61,500.00. (This is mathematically incorrect; $24,000.00 minus $4,500.00 equals $19,500.00 and not $20,500.00, which for three years would total $58,500.00). Altman indicated that the state had increased its rent by approximately 600% (this is also incorrect; it was an increase of 509%) and the sublease had provided that ATM's rent would automatically increase proportionately. Altman, however, did not indicate what a 500% (or 600%) increase in the rental would amount to ($17,200.00 at 500%; $20,640.00 at 600%) and did not suggest that he was relying upon this to determine what the rental rate should have been or should be in the future. Instead, Altman relied exclusively upon what he believed the fair rental value was of the property. He indicated that, using the fair rental value figures he had chosen, rent should be paid prospectively in the amount of $2,000.00 per month ($16,000.00 per year for the leased property, plus $8,000.00 per year for the additional property used, which totals $24,000.00, divided by twelve months). Finally, Altman indicated that all of his figures were for the purpose of settling the matter; if ATM and W & R did not agree to them, he would pursue "the appropriate legal procedures ... prior to December 31, 1976," and he expected he would be awarded more money than what he was demanding.
W & R responded by a letter from its attorney, indicating that it knew of no possible basis for Altman's demand. It requested Altman to forward copies of any documents "that would tend to support [the] position that [W & R] owes you money, not necessarily the $61,500.00 that you have specified, but any money at all." W & R never received any written response from Altman until he filed suit in September 1978.
ATM's attorney responded that his client was out of town until January 1977, but he would then contact Altman. Altman accepted this and indicated that he would be in Chicago during that time. He further indicated that he had turned his files over to his attorneys in Anchorage, but had not yet asked them to commence any proceedings. On January 12, 1977, ATM's attorney received a telephone call from Altman's attorney, who stated that he would confer with Altman and then get back in touch with him. In the spring of 1977, ATM's attorney again spoke with Altman's attorney, who indicated that he had not been able to discuss the matter with Altman. ATM did not hear anything further on the matter until Altman filed his suit in 1978.
In late 1974 or early 1975, W & R had indicated to Altman that it would like to purchase Altman's leasehold interest in two and one-half acres of land for approximately *1220 $250,000.00. On February 6, 1975, Woods wrote to Altman and indicated that he was thus far unable to obtain financing for the purchase. Negotiations between the parties as to the purchase continued throughout the course of the lease term. As late as April 8, 1977, W & R was still considering purchasing part of Altman's leasehold. W & R, however, eventually purchased property from someone else. Altman learned of this in 1978 and was "shocked" that W & R had not purchased his property. W & R suggests that there was a direct connection between Altman's discovery of this and his filing the lawsuit against ATM and W & R. Altman denies that there is any relationship between the two.
In his complaint, Altman alleged that the sublease had been renewed by ATM, that the parties were unable to agree on the rent for the renewal term, that the rent automatically increased when the State of Alaska increased its rent by 500%, that the fair rental value of the leased property was and is $28,000.00 per year, that ATM and W & R are liable in quantum meruit for the reasonable value of the premises, and that there was an implied contract between Altman and ATM and W & R to pay the reasonable rental value of the leased property and the adjacent property used by W & R. ATM and W & R filed answers to the complaint, denying Altman's allegations, except that there was a valid renewal, and alleging waiver and estoppel as affirmative defenses. Altman moved for partial summary judgment but the superior court denied this motion.
The case then proceeded to trial. ATM and W & R retreated from their earlier position and contended that the sublease had not been renewed because the renewal was not accepted by Bayside Land or Altman. The superior court found that there was no renewal of the sublease. The court concluded that a month-to-month tenancy was created on the same terms and conditions as the original sublease. It further concluded that it was an implied or express right of this tenancy that W & R be able to use adjacent property without payment of rent for the storage of its materials unless and until this use interfered with the use of the property by Bayside Land or Altman. The court concluded that Altman waived any right he may have had to additional rent for the use of this adjacent property. The court further concluded that Altman did not have any implied contract right to receive the fair rental value of the leased property or the adjacent property, that Altman did not have any right to receive quantum meruit damages for the use of the property, and that the doctrine of quasi-estoppel applies to preclude Altman from recovering any damages from either ATM or W & R. The court entered judgments in favor of ATM and W & R on all counts.
Altman contends on appeal that: (1) the sublease was renewed and the doctrines of estoppel and quasi-estoppel bar ATM and W & R from asserting otherwise; (2) the rent payable under the sublease was automatically raised when the state raised its rent; (3) if not, he is nonetheless entitled to the fair rental value of the leased property; and (4) W & R is liable for the fair rental value of the property it used that was not covered by the lease.
We note at the outset that Civil Rule 52(a) provides in part that "[f]indings of fact [made by the trial court] shall not be set aside unless clearly erroneous, and due regard shall be given to the opportunity of the trial court to judge ... the credibility of the witnesses." Alaska R.Civ.P. 52(a). A finding of fact is clearly erroneous only if we have a definite and firm conviction on the basis of the entire record that a mistake has been made. Martens v. Metzgar, 591 P.2d 541 (Alaska 1979).

II. LEASE RENEWAL
Altman first argues that the superior court erred in holding that the sublease was not renewed. He contends that ATM unilaterally renewed the lease for five years by sending written notice to Rail Air and Bayside Land of its election to do so, in accordance with the option granted in the sublease. Altman further contends that *1221 the renewal was effective even though the rental rate for the renewal period was not agreed upon within forty-five days or established by arbitration as required by the option provision. We agree.
The general rule is that "[a]n option to extend or renew a lease, in order to be effective, must be exercised in the mode specified by the agreement of the parties, and in accordance with the scope of the privilege conferred." 51C C.J.S. Landlord and Tenant § 57, at 177-78 (1968). The option for renewal in the sublease provided that it could be exercised upon ATM's election to do so "provided that Lessee shall give the Lessor written notice on or before September 30, 1973 of its election to so extend the term of this lease." ATM sent written notice to Rail Air and Bayside Land on September 25, 1973, that it elected to exercise the renewal option. This notice was sufficient to exercise the option. It was not necessary for Bayside Land to sign the Renewal of Lease prepared by ATM:
An election or option to renew or extend a lease must of course be exercised to bring the renewal or extension into effect, and generally, where the tenant seasonably notifies the landlord of his desire to renew the lease, the landlord should execute and deliver to the tenant a new lease, although so far as concerns the right of the lessee to the premises where he has done everything to entitle him to a renewal or an extension, as the case may be, there is no necessity for the execution of a new lease.

50 Am.Jur.2d Landlord and Tenant § 1179, at 64 (1970) (footnotes omitted) (emphasis added).
ATM contends that the sublease was not validly renewed because the parties did not agree upon the rental rate for the renewal period or submit the issue to arbitration as required by the sublease. Although these circumstances obviously have an impact upon the rental owed during the renewal period, they do not invalidate the renewal. As stated in Friedman on Leases, "[t]he amount of the renewal rent is sometimes left for future determination. If the determination is to be made by arbitration or appraisal, the renewal is enforceable." 2 M. Friedman, Friedman on Leases § 14.1, at 561 (1974) (footnote omitted). See also Fun Products Distributors, Inc. v. Martens, 559 P.2d 1054 (Alaska 1977) (renewal option not invalid when, barring mutual agreement, rent to be determined by appraisers); Hammond v. Ringstad, 10 Alaska 543 (D.Alaska 1945) (renewal option providing rent to be agreed upon by the parties valid and enforceable). Cf. Anderson v. Jacobs, 374 P.2d 489 (Alaska 1962) (renewal option upon terms and conditions to be agreed upon by parties not enforceable without new agreement). See generally 51C C.J.S. Landlord and Tenant § 56(3) (1968). We thus conclude that the sublease was properly renewed upon ATM's timely notice of its intent to exercise the option. We accordingly need not address Altman's argument that ATM and W & R are estopped from denying that the sublease was renewed.

III. RENT ESCALATION CLAUSE
The sublease specifically provided that if the state increased its rent on the primary lease, the rent under the sublease would be increased by the same percentage. On December 15, 1974, the state increased its rent approximately 500%. Altman contends that the rent on ATM's sublease accordingly increased 500% automatically on December 15, 1974. We believe that Altman had the right to enforce this provision and could have prospectively demanded a 500% increase in ATM's rent at any time during the leasehold period following December 15, 1974. We conclude, however, that Altman never attempted to enforce the provision prospectively and we agree with the superior court that Altman is estopped by his conduct from now enforcing that right retrospectively.
The first time that Altman asserted to ATM and W & R that the rent under the sublease had automatically increased 500% because of the state's increase in its rent was in his complaint, filed in September 1978. Prior to that time, Altman simply *1222 never stated or acted as though the state's increase in its rent automatically increased the rent payable under the sublease. It was not until September 1976 that Altman even informed ATM and W & R that the state had increased its rent in December of 1974. Even at that time, Altman did not state or imply that he intended to enforce the escalation provision. Instead, Altman relied upon the state's increase in its rent, and the escalation provision in the sublease, as evidence that ATM and W & R should agree to an increase in the rent paid under the sublease.
Altman states that during the September 1976 conversation, he referred to the state's increase in its rent, which he had to pay, as part of the reason he was "outraged" at ATM's and W & R's refusal to recognize that he was owed additional (but unspecified) rent. ATM states that during the conversation Altman said that the rental disagreement had to be "resolved," but he did not demand a specific sum or say "I need this or I need that"; "it was simply an expression of his unhappiness." Altman did not state that ATM and W & R were in default under the sublease because they were not paying increased rent and, until November of 1976, Altman always indicated that he was seeking additional rent prospectively, rather than retrospectively.
In November 1976, Altman sent a written demand for increased rent to ATM and W & R. Altman referred to the state's increase in its rent and noted that ATM and W & R had "totally ignored" the escalation provision of the sublease. Altman, however, did not demand an increase in the rent on the basis of the escalation provision, nor indicate that ATM and W & R were in default under the sublease because they had not paid this amount since December of 1974. Instead, Altman contended that the rental rate for the renewal period was the fair rental value of the premises. He assumed that the fair rental value of the leased property was $16,000.00 a year and demanded that ATM and W & R pay this amount prospectively and pay the "rent deficiency" of the difference between this amount and the $4,500.00 paid annually since 1974.
Altman's non-reliance upon the rent escalation provision is obvious not only from the entire focus of his letter, but from the figures he used as well. Altman demanded the fair rental value of the leased property for 1974, as well as for 1975 and 1976. The state's increase in its rent did not occur until December 15, 1974. Accordingly, the escalation provision would not have resulted in increased rent until that time. Furthermore, a 500% increase in the rent specified in the sublease would have amounted to $17,200.00, which is $1,200.00 more than the $16,000.00 demanded by Altman.[6]
Finally, although W & R responded to Altman's demand by requesting any documents "that would tend to support [the] position that [W & R] owes you ... any money at all," Altman did not supply any such documents. The next written communication from Altman on the subject was his complaint, filed nearly two years later. Similarly, Altman was to discuss the subject further with ATM, but never did so.
During the entire course of negotiations regarding whether the rent should be increased for the renewal period, and if so to what amount, Altman consistently acted as though the escalation provision was not of any force or effect. He never asserted, until filing his complaint, that the provision *1223 was binding upon ATM and W & R during the renewal period; nor did he assert that ATM and W & R were in default under the sublease because they had not paid increased rent under the provision. ATM and W & R paid monthly rent in the amount of $375.81. Altman accepted each of these payments without protest.[7]
We agree with the superior court, on the basis of these facts, that Altman is estopped from now asserting that the rent under the sublease was automatically increased when the state increased its rent on December 15, 1974. As we indicated in Jamison v. Consolidated Utilities, Inc., 576 P.2d 97 (Alaska 1978), "the general elements required for the application of the doctrine of equitable estoppel are the assertion of a position by conduct or word, reasonable reliance thereon by another party, and resulting prejudice." Id. at 102 (footnote omitted), citing Arctic Contractors, Inc. v. State, 564 P.2d 30, 40 (Alaska 1977). By his conduct and words, Altman consistently asserted to ATM and W & R that the escalation provision was of no force or effect during the renewal period. ATM and W & R reasonably relied upon this assertion to their prejudice by remaining on the premises and paying only $375.81 in rent each month, which they believed constituted full payment of rent.[8] Although it is not an element to equitable estoppel, see Jamison v. Consolidated Utilities, Inc., 576 P.2d at 102, there is substantial evidence supporting the superior court's finding that it would be unconscionable to permit Altman to enforce the escalation provision, and thereby collect an additional $50,750.00 in rent, when Altman never indicated any intent to enforce the provision and accepted each month's payment of rent as though it were complete payment.
We also agree with the superior court that Altman impliedly waived his right to enforce the escalation provision of the sublease. As we stated in Milne v. Anderson, 576 P.2d 109, 112 (Alaska 1978), "[a]n implied waiver arises where the course of conduct pursued evidences an intention to waive a right, or is inconsistent with any other intention than a waiver, or where neglect to insist upon the right results in prejudice to another party." Altman's conduct in never insisting upon his right to enforce the escalation provision was inconsistent with any other intention than a waiver of his right; furthermore, his neglect to insist upon his right resulted in prejudice to ATM and W & R. To have preserved his right under the escalation provision, Altman needed only to have notified ATM and W & R that he intended to enforce the provision. Altman did not do this until he filed his suit in 1978. We thus conclude that the superior court properly held that Altman is estopped from enforcing, and has waived his right to enforce, the escalation provision of the sublease.

IV. FAIR RENTAL VALUE OF LEASED PREMISES
Altman contends that if the escalation provision of the sublease is not enforceable, he is nonetheless entitled to recover the fair rental value of the leased premises during the renewal period. The superior court concluded that Altman waived and is *1224 estopped from asserting any rights he may have had to more rent than was paid by ATM and W & R during the renewal period. The court accordingly held that Altman failed to establish that ATM and W & R were liable by implied contract to pay additional rent for the leased premises.[9] We agree.
The sublease provided that if the renewal option were exercised the rent payable during the renewal period was to be subject to negotiation. If the parties failed to agree upon a renewal rate within forty-five days of when the option was exercised, the issue was to be submitted to arbitration and the arbitrators were to render a decision before the primary term ended. There is substantial authority supporting the proposition that when, through no fault of the lessor, the renewal rental rate is not established by arbitration or appraisal as agreed upon in the lease, then the lessee is obligated to pay the fair rental value of the premises for the renewal period. 2 M. Friedman, Friedman on Leases § 14.1, at 564-65 (1974); 50 Am.Jur.2d Landlord and Tenant § 1167, at 52-53 (1970); Annot., 26 A.L.R.2d 744 (1952). It is essential to the application of this rule, however, that the lessor have done everything within his or her power to have the rental rate established by arbitration or appraisal. E.g., Annot., 26 A.L.R.2d at 750. If the lessor has failed to do so, then the remedy left to him or her is to enforce the arbitration or appraisal procedure. Id.
ATM exercised its renewal option on September 25, 1973. ATM and Bayside Land, then lessor, did not agree upon the renewal rate within forty-five days and neither party submitted the issue to arbitration, as required by the sublease. After Altman succeeded to Bayside Land's interests in the lease, Altman inquired of W & R whether it was then possible to submit the issue of the rental rate to arbitration. W & R responded that it believed that because the issue had not been timely submitted to arbitration, the renewal was at the same rental rate as under the initial sublease. Altman's only response to this was to indicate two to three months later that he wanted W & R to pay more rent. He did not specify what amount he wanted. W & R responded that if the rent were increased, it would have to move because it could not afford to pay any substantial increase.
Despite the position taken by W & R, ATM indicated to Altman that it wished to settle the matter of the renewal rental rate and would be willing to then submit the issue to arbitration. Altman did not respond in writing to ATM's request, but testified at the trial that he was certain he telephoned ATM and expressed approval of the idea. Nonetheless, Altman did not do what he could under the terms of the sublease to have the matter submitted to arbitration. The sublease specified that each party was to appoint one arbitrator; Altman never made any attempt to appoint one.
Altman contended at trial that he thought the arbitration clause was "mutually waived" because ATM never appointed an arbitrator. He stated, "[t]hey spoke about arbitration, but they were here and they knew all of the realtors here, and I certainly didn't. I was a stranger. They never appointed an arbitrator." Altman was asked, "[w]hat about you proposing an arbitration?" He responded:
They were both represented by attorneys, and I was unfamiliar with appraisers here. I didn't know one from the other and it would be pointless for me to go to the  search out an appraiser if they weren't interested in appointing  to proceeding because they  they said they  what about the arbitration but they wouldn't appoint an appraiser. So I considered  my impression was that when they suggested arbitration I said *1225 fine, let's go. My impression was that they didn't really care to proceed in that fashion because I said let's go, I'd be willing to arbitrate.
Altman conceded, however, that he was aware of at least one appraiser in Anchorage. Furthermore, in his demand letter of November 1976, Altman stated: "If payment is not made, I will seek Anchorage counsel's advice as to whether I should request that we follow the arbitration procedure specified in the lease." Thus, as late as November 1976, Altman was aware that he could initiate the arbitration proceedings to have the rental rate during the renewal period determined.
ATM indicated that it expected Altman to begin the arbitration process. It believed that no agreement was reached on the renewal rental rate because it was exceedingly difficult to communicate with Altman in a meaningful way. It is apparent that submitting the issue of the renewal rental rate to arbitration would result in a higher rent being owed, which explains ATM's expectation that Altman would begin the process. As Woods of W & R stated, "I did not push it because all I could see, of course, was that it would cost me more money ... I did not evade the discussion but I did not further the discussion."
Rather than initiate the arbitration process, as he could have done, Altman unilaterally decided in the fall of 1976 that the fair rental value of the premises was $16,000.00 per year, which amount he decided ATM and W & R owed him retrospectively from January 1, 1974. This was not a possibility contemplated by the sublease, nor was it agreed to by ATM and W & R. These facts are remarkably similar to the facts of Ruth v. S.Z.B. Corp., 36 Misc.2d 422, 232 N.Y.S.2d 930 (1962). In Ruth, the lessee agreed to pay a specified sum of rent, plus 25% of its gross income in excess of $85,000.00. The lessee and lessor disputed how this amount was to be calculated. The lease provided that in the event of such controversy, the amount was to be determined by agreement or by arbitration. The parties were unable to agree upon the proper means of calculation and the issue was not submitted to arbitration. Instead, the lessor unilaterally determined what amount it believed was correct and demanded payment of this sum by the lessee. The lessee refused to pay this amount and the lessor brought suit. The court held that the lessor was not entitled to unilaterally determine what the correct amount should be, but instead was obligated to submit the issue to arbitration. Thus, the court concluded that the lessee was not in default under the lease because "[t]here could be no default in payment of additional rent until the amount thereof was ascertained in the manner prescribed in the lease, viz., by agreement or by arbitration." 232 N.Y.S.2d at 932. We similarly conclude that Altman was obligated to initiate the arbitration proceedings; his endeavor to unilaterally determine the fair rental value of the premises was without consequence.
In Ruth, the court ordered the parties to commence the arbitration proceedings specified in the lease and further ordered that the lessee pay whatever arrearages were determined by the arbitrators to exist. We must decide whether this remedy is appropriate in this case.
We note that there is no evidence whatsoever that Altman even once rejected the payments of rent tendered by ATM and W & R. Furthermore, there is no evidence that Altman ever informed ATM or W & R that even one of their monthly payments only partially satisfied their rental obligation. This is so even after Altman sent his "demand letter" in November 1976; i.e., Altman continued to accept each of the rental payments made without protesting that they were insufficient. The superior court found, based upon substantial evidence, that ATM and W & R relied upon Altman's acceptance of their monthly payments in remaining on the premises. We hold that these facts constitute a waiver and estop Altman from now asserting any right to enforce the arbitration provision of the sublease.
*1226 Altman suggests that because the parties repeatedly discussed renegotiating the rental rate during the renewal period an implied contract was formed by which ATM and W & R agreed to pay the fair rental value of the premises. The facts simply do not substantiate this. W & R consistently and carefully indicated to Altman that they were unwilling to pay any additional rent for the premises. Altman could not have reasonably believed that W & R had agreed to pay the fair rental value of the premises. Similarly, there is no evidence indicating that Altman could have reasonably believed ATM had impliedly agreed to pay the fair rental value of the premises. ATM expressed sincere interest in settling the matter, but did not imply that it would agree to whatever Altman ultimately decided was fair. Altman conceded as much at trial. He stated, "[a]s nearly as I can make out ... their idea was that why don't I cooperate and agree to the old  carry forward the old figure and that was the only proposal during this entire period... ." Altman further stated that he thought ATM and W & R "deliniat[ed] in an opening way what their understanding of the legal situation was" when they stated that "the rent provisions remain at the same rate as before the renewal." Finally, Altman understood "throughout this whole period of time, '74, 5, 6 and 7, that the rental controversy was still a subject of conversation and discussion and it was still an open item."
An implied-in-fact contract exists only when there is mutual assent between the parties, Martens v. Metzgar, 524 P.2d 666 (Alaska 1974), and a constructive or quasi-contract is created by law for reasons of justice, even though there is no express assent by the parties. B.B. & S. Construction Co. v. Stone, 535 P.2d 271 (Alaska 1975). Obviously, there was no mutual assent between the parties that ATM and W & R would pay the fair rental value of the premises during the renewal period. We agree with the superior court that Altman failed to establish that ATM and W & R incurred any liability for the fair rental value of the premises by the theory of quasi-contract. There simply are no "reasons of justice," id. at 275 n. 8, compelling the conclusion that ATM and W & R should be obligated to pay the fair rental value of the premises. Altman failed to initiate any arbitration proceedings; he failed to protest any payment of rent tendered by ATM and W & R; he indicated a willingness to further discuss the rental issue after his demand letter of November 1976, but he failed to do so; and, after more than nearly two years of continuing to accept rental payments without protest following his demand letter, he then filed his action against ATM and W & R. We conclude that the superior court properly determined that there was no implied contract between the parties that ATM and W & R would pay the fair rental value of the leased premises.

V. FAIR RENTAL VALUE OF ADJACENT PROPERTY
Altman's last contention on appeal is that the superior court erred in holding that he is not entitled to the fair rental value of the land used by W & R adjacent to the leased property. The court concluded that W & R had an implied or express right as part of its tenancy to use this adjacent property without payment of rent unless and until W & R's use interfered with the use of the property by Bayside Land or Altman. The court further concluded that Altman had waived any right he may have had to additional rent for the use of the property and that there was no implied contract between the parties that its fair rental value would be paid.
In the absence of a contrary agreement, the use of property belonging to another person with that person's consent implies an agreement by the tenant to pay the fair rental value of the premises. Carpenter v. United States, 84 U.S. (17 Wall.) 489, 21 L.Ed. 680, 681 (1873); Rich v. Hughes, 9 Ariz. App. 518, 454 P.2d 188, 191 (1969); Ross v. City of Long Beach, 24 Cal.2d 258, 148 P.2d 649, 652 (1944). See generally 52 C.J.S. Landlord and Tenant *1227 § 470 (1968). If, however, the owner permits the tenant to use the property with the agreement that no rent is to be paid, there is, of course, no implied obligation to pay rent. Niagara Falls Bridge Commission v. United States, 76 F. Supp. 1018, 1019 (Ct.Cl. 1948). The owner may subsequently decide to charge rent for the property, but he must give clear notice of this to the tenant. Willis v. Kemp, 130 Ga. App. 758, 204 S.E.2d 486, 490 (1974). See also Compton Advertising, Inc. v. Madison-59th Street Corp., 91 Misc.2d 768, 398 N.Y.S.2d 607, 613 (1977). A tenant who continues to use the property after such notice without protesting the rental charge impliedly agrees to pay the demanded rent. Bates Block Associates, Inc. v. Milady's Shop, Inc., 3 Mass. App. 776, 333 N.E.2d 214, 215 (1975); Robert Werk & Co. v. Shirer, 91 So.2d 110, 113 (La. App. 1956).
The tenant who occupied the premises before W & R used the adjacent property without paying rent for it, in accordance with its agreement with the lessor. W & R subsequently took possession of the leased premises and also used the adjacent property to store its materials and supplies without payment of rent. When Bayside Land became lessor of the property, it was aware of W & R's use of the property and chose not to demand any additional rent for it. Woods believed that W & R was entitled to use the property without paying rent so long as W & R's use did not interfere with Bayside Land's use of the property.
Shortly after Altman succeeded to Bayside Land's interests as lessor, he "walked the property" with Woods. He did not request W & R to stop using the adjacent land, but indicated that W & R would or might have to pay a "reasonable amount" for its use. No specific sum was mentioned. Woods and Altman discussed on various occasions whether additional rent should be paid for the use of the property. Woods testified that the discussions were always "general and not specific." Woods never indicated any willingness on behalf of W & R to pay additional rent for the use of the property; instead, he indicated to Altman that W & R was interested in purchasing Altman's leasehold in approximately two and one-half acres of land for $250,000.00. Altman was receptive to this idea and the parties discussed negotiations throughout the lease term.
The first and only time that Altman made a specific demand for the payment of additional rent for the use of the adjacent property was in his letter of November 1976. Altman indicated that he believed W & R was using approximately fifty percent more property than was covered by the lease and he believed that the fair rental value of the property was $8,000.00 per year. Altman did not demand retrospective payment of rent, but instead only demanded that W & R pay $8,000.00 per year for the use of the property commencing January 2, 1977. W & R protested and requested Altman to specify the basis for his demand. Altman did not respond to this request. As late as April 1977, W & R was still negotiating with Altman for the purchase of his leasehold interests in certain property. Altman learned in 1978 that W & R subsequently purchased land from someone else. He then filed this suit in September 1978.
As indicated, the superior court held that W & R had an implied or express right to use the adjacent property without payment of rent during the entire term of the lease. The court concluded that Altman had waived any right he may have had to additional rent for the use of the property. It further concluded that there was no implied contract between the parties that the fair rental value of the property would be paid to Altman. We do not believe the court's findings of fact are sufficient to support these conclusions. As we have stated, a lessor who has permitted a tenant to use property without payment of rent may demand rent for property if he clearly notifies the tenant that rent will be charged prospectively.
It is apparent from the record that W & R initially used the adjacent property with the lessor's agreement that no rent *1228 would be charged. Although Altman indicated at the time he succeeded to Bayside Land's interest in the sublease that W & R would or might have to pay "a reasonable amount" of rent for the use of the property, Altman did not make a specific demand for the payment of rent until November 1976. We therefore find substantial support in the record for the court's conclusion that Altman waived any right he may have had prior to November 1976 for the payment of additional rent. We believe, however, that Altman's letter was a sufficient notification that he intended to charge rent for the use of the property as of January 1977. W & R's continued use of the property after that time constituted an implied consent to pay rent for the use of the property.
The superior court did not refer to Altman's demand for rent in November 1976 when concluding that Altman had waived any right he may have had to additional rent for the use of the adjacent property. As we have indicated, Altman's demand for additional rent for the use of the property was sufficient and W & R impliedly consented to the demand. Whether W & R's consent extended to the amount demanded by Altman, or only to the fair rental value of the adjacent property, are issues that must be determined. If it is found to be the latter, then the fair rental value of the property will have to be determined also. Accordingly, it is necessary to remand the case to the court for a determination of these issues.
AFFIRMED IN PART, REVERSED IN PART and REMANDED for further proceedings consistent with this opinion.
MATTHEWS, Justice, joined by RABINOWITZ, Justice, dissenting.
The majority concludes, correctly in my opinion, that the lease was renewed, but that no rent for the renewal period was ever agreed upon and the arbitration remedy set forth in the renewal clause was not utilized. The appropriate relief is therefore to require the parties to submit to arbitration, or for the trial court to establish a reasonable rent for them.[1] However, rather than requiring either of these alternatives, the majority concludes that Altman has waived his right to seek these remedies, or is estopped from seeking them, by accepting rent payments tendered before this law suit was filed. I disagree with this conclusion.
Waiver is conduct indicating a purpose to abandon or relinquish a known right, Milne v. Anderson, 576 P.2d 109, 113 (Alaska 1978). Estoppel generally requires the assertion of a position by word or deed, reasonable reliance thereon by another party, and resulting prejudice. Jamison v. Consolidated Utilities, Inc., 576 P.2d 97, 102 (Alaska 1978). The evidence in this case makes it quite clear that from the outset of the renewal the lessees were told that the rental price tendered was not an acceptable renewal rate.[2] This point was repeatedly *1229 made, and was acknowledged by the lessees through their own efforts to negotiate. Thus, there is no evidence that Altman either intended to waive or abandon his right to contend that the renewal rent should be higher, or through word or action misled the lessees into such a conclusion.[3]
Ordinarily the acceptance of rent after a lease having a renewal term has expired amounts to consent by the landlord to renewal for a rental amount in the amount of the rent accepted. Fun Products Distributors, Inc. v. Martens, 559 P.2d 1054 (Alaska 1977) is illustrative of this rule. However, this rule does not apply where there is evidence showing an intent not to consent by the landlord who accepts the rent. See Annot. 45 A.L.R.2d 827, 831 (1951). The cases appear to be unanimous that acceptance of rent during the process of negotiation of renewal terms is not consent to renewal on the old terms. Id. § 6, at 841-842. See also Young v. Bridwell, 20 Utah 2d 332, 437 P.2d 686, 689 (1968). Since there can be no doubt in this case that the tenant was at all times aware that the rental rate paid was not a renewal rental rate acceptable to the landlord, and such payments were made during negotiations as to what the rent should be, there is no basis for concluding that Altman either consented to the rate paid as the appropriate renewal rate, or communicated such consent.[4]
*1230 For these reasons I would reverse the judgment of the superior court and remand for submission to arbitration or for a determination of the appropriate rent during the renewal period by the superior court. Because appellant correctly declines to suggest that he is entitled both to a determination of fair rental value and an increase in rent under the escalation clause, I intimate no opinion as to the correctness of Part III of the majority opinion concerning the escalation clause.[5]
NOTES
[1]  The rent escalation clause provided as follows:

The demised premsies [sic] are State of Alaska leased lands held by the Lessor subject to a right in the State of Alaska to reappraise and thereupon increase the rental owed by the Lessor to the State of Alaska at five (5) year intervales [sic]. When, and if, during the primary term of this lease any hold over tenancy or any renewal of this lease pursuant to the option herein granted, the State of Alaska lease rental is increased the rental due from the Lessee to the Lessor pursuant hereto shall, upon the effective date of the State's increase, be increased by the same percentage.
[2]  The renewal option provided as follows:

The Lessee shall have the option to extend the term of this Lease, upon the expiration of the term hereof, for a period of five (5) years, upon the same terms and conditions as herein contained, excepting the provision as to rent; provided, that Lessee shall give the Lessor written notice on or before September 30, 1973 of its election to so extend the term of this lease.
The rent payable by the Lessee to the Lessor during extended renewal shall be subject to negotiation provided however that if the parties fail to agree upon a renewal rate within 45 days after said written notice is given, the matter shall be subject to binding arbitration pursuant to the Uniform Arbitration Act A.S. 09.43. In the latter event each party shall appoint one arbitrator and they shall choose a third. The arbitrators shall make their award prior to the end of the primary term hereof.
[3]  The sublease provided that the rent was to increase to seven cents per square foot if the lessor provided railroad trackage across the premises and paved the streets. These improvements were not made.
[4]  Altman was formerly a senior partner of a Chicago law firm, specializing in federal tax law. He considers himself "more than semiretired" at this time. Altman succeeded to Bayside Land's interest in the sublease in the course of acquiring a total of approximately 45 acres of land from Bayside Land. Approximately 15 acres of the land were leased from the state. At one point, Altman offered to sell the majority of the 45 acres for $5,000,000.00.
[5]  The proportionate increase under the state's lease for the 1.5 acres subleased to ATM was from $788.00 per year to $4,019.00 per year. The annual rent specified in the sublease ($3,440.00) and the increased rent paid by ATM after it renewed the sublease ($4,509.76) not only paid more than the proportionate share of the state's lease before the 500% increase in rent, but also paid more than the rent owed under the state lease for the entire 4.37 acres before the 500% increase ($2,390.00). Even after the 500% increase in the state's lease, the rent paid by ATM and W & R ($4,509.76) paid more than its proportionate share of rent owed on the state's lease ($4,019.00).
[6]  Altman contends that a 500% increase in the initial rental rate would amount to $22,932.90. This incorrectly assumes that the initial rental rate was $4,500.00 per year. The sublease specified that the rent to be paid was $3,440.00 per year. ATM and W & R unilaterally chose to increase the rent they were paying to $4,500.00 when they exercised the renewal option. Accordingly, the $3,440.00 amount is what should be used as the basis for determining what the rent would be if increased 500%. The increased rent would therefore total $17,200.00 per year, rather than $22,932.90. Altman's calculations, however, make it all the clearer that in demanding that ATM and W & R pay $16,000.00 per year in rent he was not attempting to enforce the escalation provision, inasmuch as the rent demanded by Altman was approximately $7,000.00, or almost 50%, less than what the rent would have been if calculated according to Altman's interpretation of the escalation provision.
[7]  The dissenters' view of estoppel and waiver is in reality a disagreement with the trial court's findings of fact on these issues. This court chooses to accept them as not clearly erroneous. The dissenters obviously do not.
[8]  If ATM and W & R had abandoned the premises, they would have remained liable for the rent during the remainder of the renewal period. The lease specifically provided, however, that "Lessor shall make every reasonable effort to relet the demised premises at not less than the prevailing rental for comparable space in the area." ATM and W & R would be liable to Altman only for any deficiency between their rental obligation and the rental obtained by reletting the premises. The parties agree that the fair rental value of the premises was in considerable excess of the seven cents per square foot paid by ATM and W & R. Thus, ATM and W & R could have, as a practical matter, avoided any obligation to pay Altman additional rent. They indicated that they would have chosen to abandon the premises if Altman demanded a substantial increase in their rent. ATM and W & R were accordingly prejudiced by Altman's failure to assert his right to additional rent.
[9]  Altman asserted in the superior court that he was also entitled to recover in quantum meruit, which argument the court rejected. Altman has not briefed this issue on appeal and we therefore need not consider it. Hitt v. J.B. Coghill, Inc., 641 P.2d 211 (Alaska 1982); Lewis v. State, 469 P.2d 689 (Alaska 1970).
[1]  R. Schoshinski, American Law of Landlord & Tenant § 9.6, at 612 (1980) states:

Where arbitration or appraisal fail either because one party refuses to act or due to circumstances beyond the control of both parties, courts establish a reasonable rent for the renewal period, on the basis that the parties had indicated such intent by employing an arbitration or appraisal provision in their lease.
[2]  Barker, attorney for ATM, in a letter to Altman of April 25, 1975, summarized what had transpired after renewal of the option to exercise:

The option to renew was exercised by a letter from Alaska Truss & Manufacturing, Inc. to Rail Air Industrial Park dated September 25, 1973. Subsequently, Mr. Tyler attempted to negotiate with Mr. Bocek for the amount of the rental for the extended term, but was never successful in completing these negotiations. (Ex. S)
According to Bocek of Bayside Land, he took the position in the negotiations that at the very least the lease payments would have to be in the area of $800 to $950 per month; that Tyler, of ATM, and Thomason, Tyler's agent, were told that the original rate was "absolutely unavailable" and "we [Bayside Land] felt certain that should we go to arbitration as called for in the original sublease that arbitrators would certainly, with today's costs, be up in the area of $1,200 to $1,300 per month on this lease." These negotiations carried on beyond the middle of the summer of 1974. (Exhibit U) In October of 1974 when Altman "walked" the property with Woods shortly after acquiring Bayside Land's interest he requested an increase in rentals, as Woods explained, "in the neighborhood of four times what we were paying." [Tr. 376] Shortly thereafter, on November 8, 1974, Altman wrote W & R suggesting arbitration of the rental rate: "... is there any reason why we should not now proceed to arbitration in accordance with section 18 requiring each party to appoint one arbitrator and then have the two arbitrators chose a third arbitrator?" (Exhibit M) This suggestion was rebuffed by Woods. Thereafter, as the majority opinion makes abundantly clear, the dispute continued: "Altman ... indicated ... two or three months later, that he wanted W & R to pay more rent." Op. at 7; "The parties periodically discussed ... whether increased rent should be paid under the sublease." Op. at 7; "On November 29, 1976 Altman made a written demand ... that ATM and W & R pay additional rent ..." Op. at 8; "during the September 1976 conversation ..." Altman was "`outraged' at ATM's and W & R's refusal to recognize that he was owed additional (but unspecified) rent. ATM states that during the conversation Altman said that the rental disagreement had to be `resolved'... ." Op. at 16-17; "during the entire course of negotiations regarding whether the rent should be increased for the renewal period ..." Op. at 19; "ATM indicated to Altman that it wished to settle the matter of the renewal rental rate and would be willing to then submit the issue to arbitration" Op. at 23; Altman did not respond in writing to ATM's request, [to arbitrate] but testified at the trial that he was certain that he telephoned ATM and expressed approval of the idea." Op. at 23-24; ATM "believed that no agreement was reached on the renewal rate because it was exceedingly difficult to communicate with Altman in a meaningful way." Op. at 25; "It is apparent that submitting the issue of renewal rental rate to arbitration would result in a higher rent being owed, which explains ATM's expectation that Altman would begin the process. As Woods of W & R stated, `I did not push it because I could see, of course, that it would cost me more money.' ..." Op. at 25; "the parties repeatedly discussed renegotiating the rental rate during the renewal period ..." Op. at 27; "Altman understood `throughout this whole period of time, '74, '75, '76 and '77, that the rental controversy was still a subject of conversation and discussion and it was still an open item.'" Op. at 28.
[3]  One of the remarkable aspects of this case is the fact that there is no disagreement but that the proper renewal rate "was in considerable excess" of the rent actually paid. Op. at 20, n. 8.
[4]  Furthermore, the reasoning used by the majority is suspect. If I understand the opinion correctly, it says:

(1) If the arbitration remedy in the renewal clause of a lease is not utilized, the lessee is obligated to pay fair rental value as established by the court.
(2) However, if the lessor has not exhausted his arbitration remedy, the court will remand him to that remedy.
(3) Altman did not exhaust his arbitration remedy because he did not initiate arbitration.
(4) However, Altman should not be remanded to his arbitration remedy because he has waived his right to seek arbitration by continuing to accept the rental payments without protest.
This reasoning process is unusual because if the conclusion expressed in part (4) is correct, the first three premises are unnecessary. This is so because, as explained above, if a lessor accepts rental payments in a renewal context "without protest", that is without indicating nonconsent to renewal at a rate in the amount of rent tendered, renewal is accomplished at that rental rate. If this had occurred the rate of renewal rent would have been established by that fact and there would be no occasion to speak either of the arbitration remedy, or its waiver. However, for the reasons explained above it is clear that this did not take place.
[5]  It would seem unconscionable to upwardly adjust the rents upon renewal to reflect a general increase in land prices and rents and then to raise them again because of the increase in rent in the underlying lease which is reflective of the same general price trends.
