Suppose customers believe that the good they are buying is of high quality with

Question

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?)

Explanation / Answer

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.

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