Question

3. Suppose consumers believe that the good they are buying is of high quality with probability 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) con- sumers be willing to pay for the product? 


. (b) Let cH = 9 vH , vH = 2vL . For what values of p could consumer beliefs about quality be 10 
consistent? (That is, for what values of p is there actually a positive probability that some firms are producing high-quality goods?)

Answer 1

A) Risk-neutral consumers will be willing to pay the expected value "EV" of the product.

EV = p*vH + (1-p)vL

Let's call "P" the price, which "p" is the probability that the good is high quality.

P=p*vH + (1-p)vL

Consumers do not care how much the product costs to produce.

B)
cH = (9/10)vH
vH = 2vL

Producers will only produce high quality goods if P>cH

P = p*2vL + (1-p)vL > (9/10)*2vL

p*2vL + vL -p*vL > (18/10)*vL

(p+1)vL > (18/10)*vL
(p+1) > (18/10)
p > (18/10)-1
p > 0.8

p must be greater than 0.8 for consumer beliefs about quality to be consistent.