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Suppose customers believe that the good they are buying is of high quality with a probability of p, and of low quality with probability 1-p. A high quality good is valued at vH and costs cH to produce, while a low quality good is valued at vL and costs cL to produce.

a) If high-quality firms do nothing to signal their quality, what price would (risk-neutral) consumers be willing to pay for the product?
b) Let cH = 9/10vH and vH = 2vL. For what values of p could consumer beliefs about quality be consistent? (That is, for what values of p is there actually a positive probability that some firms are producing high-quality goods?)

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Joshua Stredder
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28 Sep 2019

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Related questions

The firm A&B produces high-quality widgets with a cost equal to C(qi) = 2qi. The demand for widgets

is QD =100-P.

(a) Suppose the firm A&B is a monopolist. What is the profit-maximizing price and quantity? How much profit does the firm collect?

(b) How much consumer surplus does the firm generate? What is the deadweight loss?

(c) Suppose consumers cannot see the differences between high- and low-quality widgets before purchasing them. What is the quantity sold by firm A&B if the price of low-quality widgets is $1?

(d) Suppose consumers cannot get any utility of low-quality widgets. Therefore, if they were aware and could distinguish between high- and low-quality widgets, they would purchase the high-quality widgets, regardless of the price of the low-quality widgets. How much is the firm A&B willing to pay to inform consumers about the differences between high- and low-quality widgets? How can the firm A&B achieve that?

1. (12 points) Suppose a typical used car buyer is willing to pay $6000 dollars for a low-quality used car (Lemon), and $14,000 for a high-quality car (Plum). Also, suppose the market supply of Plums is given by QP = -60 +.01P and the market supply of Lemons is given by QL = -20 +.01 P. Let the typical buyer’s belief that a car of unknown quality is a Plum = z, so (1-z) is the probability that a car of unknown quality is a Lemon.

Assume that buyers are risk-neutral so that the price a buyer will offer for a car of unknown quality is given by:

P = z($14,000) + (1-z)($6000). Therefore P = $6000 + $8000z.


a) (8 points) State the equilibrium condition in this market.

z = QP/(QP + QL)















b) (4 points) Determine the two values of z that lead to a market equilibrium. .

z = 0

z = .252. (16 pointsSuppose a manufacturer is a monopoly. This manufacturer produces a good at MC = 8 and sells it to a retailer. The retailer is also a monopoly, and it sells the good bought from the manufacturer to consumers. The retailer has no additional costs other than the price they pay to the manufacturer. The retailer faces a demand curve P = 200 –4Q, where Q is the number of units sold.

a) What price will the manufacturer charge to the retailer?

PM = 104






b) What price will the retailer charge to the consumers?

PR = 152







c) If the two firms merged, what would be the price charged?

P = 104







d) If the two firms merged into a single firm, how much profit would the firm make?

Î = 2304







e) How much profit would the two firms make if they do not merge?

Î M = 1152

Î R = 576

Total Î = 1728





3. (8 points) Consider the case of a manufacturer (upstream firm) who sells a product to a retailer (downstream firm). For each of the following four possible situations carefully explain under which circumstances there is an incentive for the firms to vertically integrate. (You may assume the cost of vertical integration is zero).

Both firms are perfectly competitive

NO






Both firms are monopolies

YES






The manufacturer is perfectly competitive and the retailer is a monopoly

NO







The manufacturer is a monopoly and the retailer is perfectly competitive.

YES If the Retailer has a variable proportions production function. Otherwise, NO.



Cell World and Phones R US are two stores in a small town that sell used cell phones. Cell World sells only high-quality used cell phones. Each phone costs Cell World $90 to buy and repair. Phones R US sells low-quality used cell phones and each phone costs them $70 to buy and repair. Consumers are willing to pay $85 for a low-quality used cell phone and $110 for a high-quality used cell phone. However, consumers don't know which store sells high-quality cell phones and which store sells low-quality cell phones. Therefore, they are willing to pay $95 for an used cell phone.

Cell World would like its customers to know that it sells high-quality cell phones. So, to send such a signal, Cell World wants to offer a warranty that covers all necessar repairs for the cell phones. Such a warranty would cost Cell World $5 per year per cell phone (cost of warranty = $5 x years of warranty), while it would cost Phones R US $9 per year per cell phone (cost of warranty = $9 x years of warranty). Consumers will assume that the store offering the longer warranty sells high-quality cell phones. If both stores offer the same warranty, consumers will be willing to pay only $95 per cell phone.

A. Without offering a warranty, Cell World would make a profit of ($5, $9, $10, $15, $20, $25) per cell phone, and Phones R US would make a profit of ($5, $9, $10, $15, $20 $25) per cell phone.

B. Suppose that Cell World commits itself to a two year warranty (Y = 2). Then Phons R US's best response is to (offer no warranty, offer a one-year warranty, offer a two-year warranty, offer a three-year warranty) so Cell World's profit will be (-$10, $0, $5, $10, $15, $20) per cell phone, and Phones R US's profit will be ($7, $10, $13, $15, $16, $22, $25) per cell phone.

C. If Cell World commits itself to a one year warranty (Y = 1), what would maximize Phones R US profit? (offering a one year warranty or offering no warranty)

D. Suppose that Cell World offers a warranty and Phones R US does not. It is then discovered that consumers that bought their cell phones at Cell World mistreat their cell phones compared to owners of Phones R US cell phones. This is a problem of (a lemons market, adverse selection, asymmetric information, moral hazard).

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