NYC Economic Assingment Help With Solution
1. Consider a seller auctioning an object via a second-price sealed-bid auction. There are 2 bidders whose valuations are independently drawn from a uniform distribution on [0; 1]. Assume that the seller attaches a value of zero to the object.
(a) What is the equilibrium of the game if the bidders use weakly-dominant strategies?
(b) What is the sellers expected revenue?
(c) Suppose now that the sellers sets a reserve price r equal to 1/2 . Compute the sellers new expected revenue.
(d) Suppose a new bidder arrives. This new bidder is willing to participate in the auction only if the seller removes the reserve price (i.e., r = 0). Should the seller let this third bidder into the auction and remove the reserve price?
2. Consider a third-price sealed-bid auction with n bidders. This is an auction where the highest bidder wins but only pays the third-highest bid. Let the biddersvaluations be independently drawn from a uniform distribution on [0; 1] and assume that bidders use linear strategies of the following form
b (v) = v, with >>0:
(a) Use the Revenue Equivalence Theorem to derive an explicit expression for .
(b) What is the sellers expected revenue for n = 5?
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3. Twenty ve di¤erent stores sell the same product in a given area to a population of two thousand consumers. Consumers are equally likely to rst visit any of the twenty five stores. Half of the consumers have no search costs, are willing to pay up to $45 to buy one unit of the product and purchase at the lowest price. The other half is willing to buy one unit of the product up to a maximum of $70 and must incur a cost of $44 in order to nd out about the prices charged by other stores. Each store can sell up to 90 units and has a unit cost of $25.
(a) Argue that, in equilibrium, there exist at most two di¤erent prices.
(b) Argue that, if there exist two di¤erent equilibrium prices, then the higher price must be 70.
(c) Show that the following is an equilibrium: 5 rms set a price of 70 and the remaining 20 rms set a price of 45.
4. The inverse market demand for widgets in NYC is p = 120 2Q. The manufacturer licenses a single dealer to sell widgets in NYC. Therefore, the dealer acts as a monopolist in the NYC market. The manufacturer sells each widget to the dealer for $d > c, where c = $40 is the cost of producing each widget. In addition, the manufacturer may levy a fixed fee of $ on the dealership.
Consider a two-stage game in which in Stage I the manufacturer sets the per-unit price charged to the dealer d, and the xed fee . In Stage II the dealer determines the quantity to sell in order to maximize its pro ts.
(a) Suppose the unit price the manufacturer charges the dealer d is given (determined in the rst stage of the game). Also, suppose that the manufacturer does not charge the dealership any xed fee, that is = 0: Compute the dealers profit- maximizing sales of widgets as a function of d.
(b) Compute the manufacturers pro t-maximizing price d it charges the dealer for each widget sold.
(c) Compute quantity of widgets sold by the dealer, and the price p charged to buyers.
(d) Compute the pro ts made by the dealer and the manufacturer.
(e) Can you nd a price d and a xed fee such that both the manufacturer and the dealer, make higher profits than the ones you found in (d)?
5. Suppose that the price a monopolist may charge, p, is a function of its output q and advertising level . That is, the inverse demand curve is p = + a bq.
The firms costs are the sum of its production costs, C (q) = cq and its advertising costs, , where $1 of advertising costs $1. That is, its total cost is cq + ..
(a) Determine the optimal levels of advertising and output.
(b) Compare the output you obtained in part (a) with the optimal output without advertising (i.e., = 0). Is the rm producing more or less output with advertising?
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