ch5_Q&A

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Jan 9, 2024

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1 Chapter 5: Cost Analysis - Suggested Questions Question 1: A firm's total cost function is given by the equation : TC = 4000 + 5Q + 10Q 2 . 1.1) Write an expression for each of the following cost functions: a. Total Fixed Cost b. Average Fixed Cost c. Total Variable Cost d. Average Variable Cost e. Average Total Cost f. Marginal Cost 1.2) Determine the quantity (Q*) that minimizes the average total cost (ATC). Solution: 1.1) a. TFC = 4000 b. AFC = c. TVC = TC - TFC TVC = 5 Q + 10 d. AVC = = = 5 + 10Q e. ATC = = f. MC = 5 + 20Q 1.2) Q* = 20 units -- > Min. ATC.

2 Question 2: A firm has a fixed cost of $5000 and a constant marginal cost of production of $500 per unit produced. Find the firm’s total cost, average total cost, average fixed cost, average variable cost functions. Solution: TC = TFC + TVC = 5000 + 500Q. ATC = TC/Q = AFC + AVC = 5000/Q + 500. AFC = 5000/Q. AVC = 500. Question 3: A firm’s production function is Q = 500L 0.6 K 0.8 , where Q is the output level, L is the number of labor hours, and K is the number of machines. If the price of labor (P L ) is $15 per hour and the price of a machine (P K ) is $50 per hour, what is the firm’s expansion path? Solution: • The firm’s expansion path is K = 0.4L .

3 Question 4: A firm has the following production function : Q = 4(LK) 0.5 . The price of labor (P L ) = $8 per hour and the price of capital (P K ) = $2 per unit. 4.1) If capital ( K ̅ ) is a fixed input ( K ̅ = 10), derive following functions: a) Short-run total cost: STC = f(Q) = Q 2 /20 + 20. (See Figure 4.1) b) Short-run average total cost: SATC = Q/20 + 20/Q. (See Figure 4.2) c) Short-run average variable cost: SAVC = Q/20. (See Figure 4.2) d) Short-run marginal cost: SMC = Q/10. (See Figure 4.2) e) Short-run average fixed cost: SAFC = 20/Q . (See Figure 4.3) 4.2) If all inputs are variable, derive the following functions: a) Long-run total cost: LTC = f(Q) = 2Q. (See Figure 4.4) b) Long-run average cost: LAC = 2. (See Figure 4.5) c) Long-run marginal cost: LMC = 2. (See Figure 4.5) Figure 4.1: STC = Q 2 /20 + 20. STC = Q 2 /20 + 20.

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4 Figure 4.2: SATC, SAVC, and SMC Figure 4.3: SAFC SMC = Q/10. SATC = Q/20 + 20/Q. SAVC = Q/20. SAFC = 20/Q. Min. SATC = SMC Min. SAVC = SMC

5 Figure 4.4: LTC = 2Q. Figure 4.5: LAC and LMC. LAC = LMC = 2. LTC = 2Q.

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