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Perfect Competition Assume that the production of corn is a perfectly competitive industry. The market demand, is described by a linear demand function QB: 20 P. There are forty corn farmers, and each farmer has the same production costs, described by the following total cost function of TC(q) - 10g + 5912. Note that q is the individual quantity of a farmer (= rm). The market supply 1s Qg- 1 q,= 2-121 q,. The unit of all quantities is thousands of tons of corn. 1. Calculate the price elasticity of demand. Show that a rm In this industry maximizes prot by setting (1 - maa:{ 1310 10,0} Derive the industry supply curve, and show that it is Q3 = maa:{4(P 10), 0} Plot the demand and supply curves in the (Q, P) plane. Show that, in equilibrium, P = 12 and Q = 8. 939'???\" Calculate consumer surplus, producer surplus and social welfare at the perfectly competitive equilibrium. 7. Now assume the government regulates the corn market, perhaps because it believes the price farmers receive is too low, and sets price P = 15. Calculate the quantity traded under this regulation. Calculate consumer surplus, producer surplus and social welfare