ch7_Q&A

1 Chapter 7: Monopoly and Monopolistic Competition (Suggested Questions) Question 1: Suppose that the market demand function is Q = 200 – 0.5P where Q is the total output level and P is the price per unit of output. The firm’s total cost function is TC = 10 + 2Q 2 . a) What are the marginal revenue and marginal cost functions? b) What are the profit-maximizing quantity (Q*) and price (P*)? c) What is the Lerner Index (LI) at the profit-maximizing quantity? d) What is the price elasticity of demand (  ) at the profit-maximizing quantity? e) If the price elasticity of demand is -3 and, what is the marginal revenue (MR) at the profit-maximizing price? Solution: a) MR = 400 – 4Q. MC = 4Q b) Q* = 50 units. P* = $300. c) LI = 1/3. d)  = -3. e) MR = $200.

2 Question 2: Suppose that the market demand function for Good X is as follows: Q X = 200 – 0.5P X + 0.2I – 4P Y , where Q X = the total quantity demanded for output, P X = the price per unit of Good X, I = the average income, and P Y = the price per unit of Good Y. There is only one firm producing Good X for the entire market. The firm’s average variable cost function is AVC = 2Q , where Q is the quantity of Good X supplied. Additionally, its total fixed cost is $10. a) What is the firm ’ s total cost function? b) What is the firm’s marginal cost function? c) If I = $1000 and P Y = $50, what is the firm ’ s direct demand function? d) W hat is the firm’s marginal revenue? e) What are the profit-maximizing quantity (Q X *) and price (P X *) of Good X? f) What is the Lerner Index (LI) at the profit-maximizing quantity? g) What is the price elasticity of demand (  X ) at the profit-maximizing quantity? h) If the price elasticity of demand is -3, what is the firm’s marginal revenue (MR) at its profit-maximizing price? Solution: a) TC = 10 + 2Q X 2 . b) MC = 4Q X . c) Q X = 200 – 0.5P X . d) MR = 400 – 4Q X e) Q X * = 50 units. P X * = $300. f) LI = 1/3. g)  X = -3. h) MR = $200.

4 Question 4: A firm is a monopsonist in the labor market. The market demand function for the firm’s output is P = 70 – 0.5Q , where Q is the output level, and P is the price per unit of output. The firm’s production function is Q = L , where L is the amount of labor. The supply for labor function is P L = 10 + L where P L is the price of labor. a) What is the firm's demand for labor function? b) What is the amount of labor at the monopsony equilibrium? c) What is the profit-maximizing price of labor (P L *)? Solution: a) The firm’s demand for labor (MRP L ), P L = 70 – L. b) L* = 20. c) P L * = $30. Question 5: The monopsonist’s demand for labor function is P L = 70 – L, and the supply for labor is P L = 10 + L, where L = the amount of labor and P L = the price of labor. What is the profit-maximizing price of labor (P L *)? Solution: P L * = $30.