This problem concerns a market for a commodity item in which there are many sellers, all firms that produce the item, and many buyers, who are consumers. Supply of the product depends on the price received by the firms and increases as that price increases. If firms receive p per unit, they will supply

(in total) S(p) = 1000(p−4) units of the good for p " 4. (If the price is less than 4, they will supply none.) Consumerdemanddependson the price that consumers must pay per unit for the good. Calling the price per unit to consumers q , consumer demand is given by the demand function D(q) = 2000(10 − q) for q  10. If the price exceeds 10, consumers demand no units of the good.

(a) Suppose this good is sold in a market where consumers pay an amount that exactly equals the amount (per unit) taken in by producers. That is, suppose that p = q . Where does supply equal demand? (You might want to draw a picture of supply and demand in this market, just to get the practice.)

(b) Suppose that this good is sold in a region where there is a 10% sales tax.

That is, if the posted price per unit of the good is p (which is what the sellers of the good receive, free and clear), then for each unit of the good purchased, a consumer must remit q = 1.1p. What is the equilibrium in this market? How much tax revenue does the government take in?

(c) Suppose that this good is sold in a region where sellers must pay the government 10% of their gross revenues (but no sales tax is imposed on buyers). That is, if purchasers of the good pay q per unit purchased, the seller receives q gross, but only p = 0.9q net of the mandatory payment to the government. What is the equilibrium in this market? How much tax revenue does the government take in?