Chapters 5 and 6 Study Guide

Chapters 5 and 6 Study Guide - Chapters 5 and 6 Study Guide...

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Chapters 5 and 6 Study Guide 1. Assume a firm faces the following TC = 5,000 + 2Q + 4Q 2 . If the price is $122, what quantity the firm should produce? Answer: To maximize profit, the firm should always produce where MR=MC. Assuming that this is a perfectly competitive firm, Price or P=MR , thus the firm should produce where P=MR=MC Thus, find MC from TC function If TC = 5,000 + 2Q + 4Q 2 = MC = 0 + 2Q 1-1 + (4x2)Q 2-1 = 2Q 0 + 8Q = 2 + 8Q Thus, for a perfectly competitive firm, the firm should produce where P=MR=MC If P=122 and P=MC, therefore 122 = 2 + 8Q 122 – 2 = 8Q 120 = 8Q Q = 120/8 = 15 To maximize profit, any firm whether perfectly competitive, monopolist, monopolist competition or oligopoly should produce where MR=MC 2. Example to compute MP Employees (L) Output (Q) MP L AP L 0 0 n/a n/a 1 20 20 20 2 45 25 22.5 3 60 15 20 4 70 10 17.5 5 75 5 15
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- With one employee, the firm produces 20 units. - With 2 employees, the firm produces a total of 45 units. If the first employee produced 20 units, the second employee adds a Marginal Product of Labor (MP L ) of 25=(45 – 20 from the first employee). - With 3 employees, the firm produces a total of 60 units. The third employee adds a MP L of 15 units - With 4 employees, the firm produces a total of 70 units. The fourth employee adds a MP L of 10 units - With 5 employees, the firm produces a total of 75 units. The fifth employee adds a MP L of 5 units Average Product of Labor = AP L = Q/L 3. Assume a firm faces Total Cost function, TC=500 + 100Q + 4Q 2 a. If the firm produces 500 units, what is the firm marginal cost? Answer: From TC function, find MC MC = 0 + 100Q 1-1 + (4x2)Q 2-1 = 100Q 0 + 8Q = 100 + 8Q If Q = 500 Thus, MC = 100 + 8(500) = 100 + 4,000 = $4,100 b. What is the firm average total cost? Answer: From TC function, the firm ATC = TC/Q = [500 + 100(500) + 4(500) 2 ]/500 = $2,101 4. A monopolist firm faces a demand curve of P=5,000 – 4Q and a MC =2,000 + 2Q. To maximize profit, what is price and quantity? Answer: First compute TR = P * Q If P = 5,000 – 4Q TR = (5,000 – 4Q)Q
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TR = 5,000Q – 4Q 2 From TR function, find MR. MR = 5,000Q 1-1 – (4x2)Q 2-1 = 5,000Q 0 – 8Q = 5,000 – 8Q To maximize profit, the monopolist firm must produce where MR = MC Thus, MR=MC 5,000 – 8Q = 2,000 + 2Q 5,000 – 2,000 = 2Q + 8Q 3,000 = 10Q Q = 3,000/10 = 300 To find P, replace Q in the P function P = 5,000 – 4(300) = 5,000 – 1,200 = $3,800 Textbook examples 5–16. Mountain Springs Water Company produces bottled water. Internal consultants estimate the company’s production function to be Q = 300L 2 K, where Q is the number of bottles of water produced each week, L is the hours of labor per week, and K is the number of machine hours per week. Each machine can operate 100 hours a week. Labor costs $20/hour, and each machine costs $1000 per week. a.
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Chapters 5 and 6 Study Guide - Chapters 5 and 6 Study Guide...

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