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7. Product & Cost Curves: Numerical Cobb-Douglas Case > Continue with the general functions from the previous two problems, specifying particular values for input prices w and r and also for the fixed quantity of K, Ko. > Production and cost functions are: Q(L, K) = LK½ C(L, K) = wL + rK > Let input prices be: w = r = 1 Thus total cost is: C(L, K) = L + K a. Write the long run total, average, and marginal cost equations, which are functions of Q (see Problems 4d and 6a): LTC = C = LAC = C/Q = LMC = &C/GQ = b. Suppose that K is fixed in the short run at Ko = 1. Using your earlier results and the fact that Q = TPL, calculate these functions of the variable input L: %3D TPL = %3D APL = = Q/L = MPL = 8Q/8L = c. Write the short run cost functions (see 6b) with input K fixed at Ko = 1: FC = AFC = VC = AVC = TC = SAC = MC = %3D %3D

7. Product & Cost Curves: Numerical Cobb-Douglas Case > Continue with the general functions from the previous two problems, specifying particular values for input prices w and r and also for the fixed quantity of K, Ko. > Production and cost functions are: Q(L, K) = LK½ C(L, K) = wL + rK > Let input prices be: w = r = 1 Thus total cost is: C(L, K) = L + K a. Write the long run total, average, and marginal cost equations, which are functions of Q (see Problems 4d and 6a): LTC = C = LAC = C/Q = LMC = &C/GQ = b. Suppose that K is fixed in the short run at Ko = 1. Using your earlier results and the fact that Q = TPL, calculate these functions of the variable input L: %3D TPL = %3D APL = = Q/L = MPL = 8Q/8L = c. Write the short run cost functions (see 6b) with input K fixed at Ko = 1: FC = AFC = VC = AVC = TC = SAC = MC = %3D %3D

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.3P
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Could I have help deriving these equations
9. 7. Product & Cost Curves: Numerical Cobb-Douglas Case > Continue with the general functions from the previous two problems, specifying particular values for input prices w and r and also for the fixed quantity of K, Ko. > Production and cost functions are: Q(L, K) = L½K½ C(L, K) = wL + rK > Let input prices be: w = r = 1 Thus total cost is: C(L, K) = L + K a. Write the long run total, average, and marginal cost equations, which are functions of Q (see Problems 4d and 6a): LTC = C = and Econom LAC = C/Q = LMC = dC/GQ = b. Suppose that K is fixed in the short run at Ko = 1. Using your earlier results and the fact that Q = TPL, calculate these functions of the variable input L: TPL = APL = Q/L = ehat MPL = ÖQ/ÖL = c. Write the short run cost functions (see 6b) with input K fixed at Ko = 1: FC = fthe r AFC = VC = AVC = TC = SAC = MC =
Transcribed Image Text:9. 7. Product & Cost Curves: Numerical Cobb-Douglas Case > Continue with the general functions from the previous two problems, specifying particular values for input prices w and r and also for the fixed quantity of K, Ko. > Production and cost functions are: Q(L, K) = L½K½ C(L, K) = wL + rK > Let input prices be: w = r = 1 Thus total cost is: C(L, K) = L + K a. Write the long run total, average, and marginal cost equations, which are functions of Q (see Problems 4d and 6a): LTC = C = and Econom LAC = C/Q = LMC = dC/GQ = b. Suppose that K is fixed in the short run at Ko = 1. Using your earlier results and the fact that Q = TPL, calculate these functions of the variable input L: TPL = APL = Q/L = ehat MPL = ÖQ/ÖL = c. Write the short run cost functions (see 6b) with input K fixed at Ko = 1: FC = fthe r AFC = VC = AVC = TC = SAC = MC =
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