It appears that this court has never directly addressed the question whether an advertisement can constitute a contractual offer. But see Sutton v. Hawaiian Trust Co., Ltd., 43 Haw. 310 (1959) (announcement that certain property will be sold at auction is not a binding contractual offer to sell but merely a declaration of intention to hold an auction at which bids will be received). There is substantial agreement among the courts that have addressed the question, however, that advertisements by merchants listing goods for sale at a particular price are generally invitations to deal, rather than binding contractual offers that consumers may freely accept. See, e.g., Georgian Co. v. Bloom, 27 Ga. App. 468, 108 S.E. 813, 814 (1921) (holding that newspaper advertisements, " 'stating that the advertiser has a certain quantity of goods which he [or she] wants to dispose of at certain prices, are not offers which become contracts as soon as any person to whose notice they might come signifies his [or her] acceptance by notifying the [seller] that he [or she] will take a certain quantity of them[ ]' "); Steinberg v. Chicago Med. Sch., 69 Ill.2d 320, 13 Ill. Dec. 699, 371 N.E.2d 634, 639 (1977) (noting that advertisements for sale of goods at a fixed price are invitations to deal rather than binding offers); Osage Homestead, Inc. v. Sutphin, 657 S.W.2d 346, 351-52 (Mo. Ct. App. 1983) (holding that an advertisement offering a rig for sale at a specified price was not a contractual offer); Ehrlich v. Willis Music Co., 93 Ohio App. 246, 113 N.E.2d 252 (1952) (noting that an advertisement for sale of a television at a specified price "was no more than an invitation to patronize the store"). See also 1 Williston, A Treatise on the Law of Contracts � 4.7 at 286-87 (4th ed. 1990) ( "if goods are advertised for sale at a certain price, it is generally not an offer, and no contract is formed because of the statement of an intending purchaser that he will take a specified quantity of goods at that price"); Restatement (Second) of Contracts � 26 at 75 (1981) ("[a] manifestation of willingness to enter into a bargain is not an offer if the person to whom it is addressed knows or has reason to know that the person making it does not intend to conclude a bargain until he has made a further manifestation of assent"). Rather than make an offer, advertisements invite offers by prospective purchasers. "Only when the merchant takes the money is there an acceptance of the offer to purchase." Steinberg, 13 Ill. Dec. 699, 371 N.E.2d at 639; see also Osage, 657 S.W.2d at 351-52 (holding that a contract for sale of an advertised item was not complete until the seller accepted the buyer's offer to purchase based on the advertisement).

There is a very narrow, yet well-established, exception to this rule, which arises when an advertisement is "clear, definite, and explicit, and leaves nothing open for negotiation." Lefkowitz v. Great Minneapolis Surplus Store, 251 Minn. 188, 86 N.W.2d 689, 691 (1957); see also R.E. Crummer & Co. v. Nuveen, 147 F.2d 3, 5 (7th Cir. 1945) (holding that advertisement inviting specific bond-holders to send their bonds to a designated bank for surrender pursuant to clearly specified terms constituted a binding contractual offer); Leonard v. Pepsico, Inc., 88 F. Supp. 2d 116, 124 (S.D.N.Y. 1999) (holding that "the absence of any words of limitation [,] such as 'first come, first served,' [rendered] the alleged offer [for a fighter jet in exchange for 'Pepsi-points'] sufficiently indefinite that no contract could be formed[ ] "); Donovan v. RRL Corp., 26 Cal. 4th 261, 109 Cal. Rptr. 2d 807, 27 P.3d 702, 711 (2001) (holding that a licensed automobile dealer's advertisement regarding a particular vehicle at a specific price constituted an offer in light of the California Vehicle Code, which rendered illegal the failure to sell the vehicle at the advertised price to any person while it remained unsold); Izadi v. Machado (Gus) Ford, Inc., 550 So. 2d 1135, 1139 (Fla. Dist. Ct. App. 1989) (holding that car dealer's advertisement offering a minimum $3,000 "allowance" for any vehicle that a consumer traded in, regardless of its actual value, constituted a binding contractual offer); Oliver v. Henley, 21 S.W.2d 576, 578-79 (Tex. Civ. App. 1929) (holding that an advertisement, offering to "ship sacks of 3 bushels each, freight prepaid, to any point in Texas for $4 per sack, said sack tagged according to our state seed laws," constituted a binding contractual offer); Chang v. First Colonial Sav. Bank, 242 Va. 388, 410 S.E.2d 928, 930 (1991) (holding that bank's advertisement promising two free gifts and $20,136.12 upon maturing in 3 1/2 years in exchange for a $14,000 deposit constituted an offer that was accepted when $14,000 was deposited). In such advertisements, "there must ordinarily be some language of commitment or some invitation to take action without further communication." Restatement (Second) of Contracts � 26 at 76 (1981); see also 1 Corbin on Contracts � 2.4 at 116-122 (1993) (noting that advertisements are not presumed to be offers unless they contain unusually clear words to the contrary).

We agree with the foregoing well-established principles. Accordingly, we hold that advertisements are generally not binding contractual offers, unless they invite acceptance without further negotiations in clear, definite, express, and unconditional language.

(a) If the dealer can only make one, take-it-or-leave-it, offer, what offer should he make?
His payoff is the integral from P to 24 of (P-15)f(v)dv, which is (P-15) times the integral of .1 dv, which is (P-15)(.1v) evaluated for v between P and 24, which is (P- 15)(2.4) - (P-15) (.1P) = (P-15)(2.4 - .1P). Maximizing with respect to P yields the first order condition 2.4 - 2*.1 P + 1.5 =0, so P = 3.9/.2 = 19.5. Not uncoincidentally, that is halfway between 15 and 24.

(b) Dealers customarily ask the customer to make the first offer. How could that help the dealer, in this model? How would a wise customer respond?
Suppose the customer said, "I offer 17,000". The dealer would then know the customer's value was at least $V=17$, valuable information. The dealer would raise the price he offers accordingly. (Go through the calculation in part (a) again, substituting a value distribution on [17,24] for one on [14, 24], and you will find that expected dealer profit rises. Does the probability of a failed deal fall? I bet it does--even aside from the [14,15] interval no longer existing-- because now the dealer has more to lose by the deal failing.

The wise customer's response is to make the first offer-- but to offer $6,000. Or something else in the interval [0,14], which is uninformative.

(c) Suppose the law treats a posted price as a first offer. What price should the dealer post?
The dealer should post a first price of $50,000. Or something else in the interval [24, infinity], which does not constrain his ability to get $24,000 from the high-valuing customer.

(d) Suppose the law treats a posted price as a nonbinding indication of where bargaining might start, rather than as an offer. Suppose, too, that the customer mistakenly thinks that the posted price is binding. What price should the dealer post?
This is the most interesting part of the problem. I won't solve it completely here. It actually is a lot more complicated than I thought. But this situation is probably good for the dealer. Suppose he posts a price of $17,000, and a customer says to him, "I accept the price of $17,000" to lock in the price before the dealer realized his mistake. The dealer would then be in the situation of part (b) where, in effect, he has gotten the customer to make the first offer.

But what happens if the customer says, "$17,000 is too high"? If only customers with values in the interval [15, 17] did that, it would be simple enough to carry forward the analysis, and the price would end up lower. But if that were the case, the customers with values in [17,24] would not be so quick to accept 17 as in the last paragraph. They would want to grumble about it being too high, and pretend to be low-valuers. Probably the equilibrium involves mixed strategies. As happens sometimes with homework problems, there might be an idea for a journal article here.

(e) Suppose the dealer can make an infinite sequence of offers, but with a discount rate of 10% between offers. What should be his strategy?
This is a more common sort of problem, akin to Rubinstein (1982), even though this is a setting of incomplete information. I won't try to solve it here, though.