3. (20 points) There are three identical farmers (A, B and C') that all sell zucchini at the farmers market. Each farmer decides how many zucchini he will bring to the farmers market. The market price for zucchini is then determined by the price consumers are willing to pay for the total amount of zucchini available (Z4 + Zp + Z). The inverse market demand curve for zucchini is given by: . PZ)=6- -7 (4) Each farmer has no fixed costs and constant marginal costs equal to $2. (a) Write down an equation giving farmer A's profits as a function of farmer A's number of zucchini and the number of zucchini brought by farmers B and C (w4(Z4, ZB, Z)). (b) Given your profit function in part (a), find farmer A's optimal number of zucchini as a function of the number of zucchini being brought by farmers B and C (Za(Zg, Z))- (c) Using the best response function you found for farmer A in part (b), find the equilibrium number of zucchini brought by each farmer. (Hint: Recognizing that all three farmers are identical makes this much easier.) (d) What is the efficient number of zucchini? Is this the same as the total number of zucchini provided in equilibrium