Question

A monopolist faces the following demand curve: Q = 260-2P Where Q is the weekly production and P is the price, measured in $/unit. The firm's cost function is given by C= 20 + 10Q+Q2. Assuming the firm maximizes profits, 1. (10 pts) Find the equation describing the marginal revenue (MR) curve. 2. (20 pts) What is the level of production (Q), price (P), and total profit (TT) per week? 3. (20 pts) If the government decides to levy a per-unit tax of 30 $/unit on this product, what will be the new level of production (Q), price (P), and total profit (TT)?

Answer 1

Demand: Q = 260-P P = 860-8 1 Cost Fimetion: 0=20 +10 +02 1. Total Revenue ETR) = P.& TR=1260-0 (260 B MR = 2(TR) = ( 260- 28 Ә& 얹 9 R = 130-8 2. Mc = 10 +23 for Profit max. Monopolist produces at MR = MC 130-B-10+20 120 = 3 S*=40 => from Demand equation P = 260-40 =110 2 Profit (7)= (P-Mc) xa MC: 10+2140) Me=go "T= (110-90) x40 K = 800

(6 sure Now putting per unit tax of 430 Now cost function becomes 20 +100 +R? + 300 MC = 10 +29 430 7 Mc=40+2a, since on onopolet i producing at +R = Mc +9R = Mc for Profit mandel MR = 130-8 130-B- 40 +20 go = 30 Qx=30 p=115 ps 260-30 = 2 MC= 40 +2(30) = 100 poogit (1)= (P-MC)*Q Ta = (US-100) X30 1 =450