Question

Use first order condition and second order condition

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Тип уоu • 7. Perfectly competitive firm faces P(Q) = inverse demand curve and its costs are given by a cost function C(Q), assuming that marginal costs are positive. Firm is also taxed at rate t per unit of output. (a) Write down the firm's profit function. Identify the choice variable, and the parameter if the firm maximizes the profit. (b) Write down the FONC for profit maximization. What does this equa- tion solve for? Can you get it explicitly? Discuss.Under what condi tion does the equilibrium exist? (c) Write down the SOC for profit maximization. Under what condi- tion(s) the profit is indeed maximized? (d) What is the effect of the tax on the equilibrium quantity Support your answer by a graph. (e) What is the effect of the tax on the maximized profit?!

Answer 1

7. (a) T = P(0). & - c(0) - t. (Q.) Profit function (b) die P(g) + P(). 9 - 04(a)-t. FONC. P' (Q) = 0 since P(a) = P. P*P() - c'(@)++ -> dx = 0 explicitly, in perfect competition, price marginal cost + tax. Equilibrium exists under the condition that demand at p*= c'(Q)+t is not zero. Replacing this in demand function will give the equilibrium quantity, &* o soc Negatively sloped demand curre => P'(0) <o, hence if demand carne is negatively sloped, then forofit is maximised. Increased tax will result in higher price and lower equilibrium quantity. (d)

tayt Metta Metti ALA (e) Maximized profit in both eases =o. T = P. 8 - c(8) - t. & x = (c'tt) 8" - clot. 8* There is no effect of tax on maximised profit. U