There are two types of electric pencil-sharpener producers. “High-quality” manufacturers produce very good sharpeners that consumers value at $14. “Low-quality” manufacturers produce less good ones that are valued at $8. At the time of purchase, customers cannot distinguish between a high-quality product and a low-quality product; nor can they identify the manufacturer. However, they can determine the quality of the product after purchase. The consumers are risk neutral; if they have probability q of getting a high-quality product and 1 - q of getting a low-quality product, then they value this prospect at 14q + 8(1 - q). Each type of manufacturer can manufacture the product at a constant unit cost of $11.50. All manufacturers behave competitively.

(a) Suppose that the sale of low-quality electric pencil-sharpeners is illegal, so that the only items allowed to appear on the market are of high quality. What will be the equilibrium price?

(b) Suppose that there were no high-quality sellers. How many low-quality sharpeners would you expect to be sold in equilibrium?

(c) Could there be an equilibrium in which equal (positive) quantities of the two types of pencil sharpeners appear in the market?

(d) Now we change our assumptions about the technology. Suppose that each producer can choose to manufacture either a high-quality or a low- quality pencil-sharpener, with a unit cost of $11.50 for the former and $11 for the latter, what would we expect to happen in equilibrium?

(e) Assuming that each producer is able to make the production choice described in the last question, what good would it do if the government banned production of low-quality electric pencil-sharpeners?

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