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production fune on för producing lentils: q = f(K, L) = A (aK/3 + BLV/3) where q is output per acre, K is capital, L is labour, and (A, a, B) are pa- rameters. Denote the wage rate by w, the price of capital by r, and the output price by p. a) Assume that the farmer is operating during a labour shortage, so that labour is fixed at L. Derive the short-run cost function.

production fune on för producing lentils: q = f(K, L) = A (aK/3 + BLV/3) where q is output per acre, K is capital, L is labour, and (A, a, B) are pa- rameters. Denote the wage rate by w, the price of capital by r, and the output price by p. a) Assume that the farmer is operating during a labour shortage, so that labour is fixed at L. Derive the short-run cost function.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2. A farm has the following production function for producing lentils: q = f(K, L) = A (ak/3 + BL'/3) where q is output per acre, K is capital, L is labour, and (A, a, B) are pa- rameters. Denote the wage rate by w, the price of capital by r, and the output price by p. a) Assume that the farmer is operating during a labour shortage, so that labour is fixed at L. Derive the short-run cost function. b) Describe the role of A in the production function. Calculate the ef- fect of a marginal increase in A on the short-run cost function, and explain how that result is related to the impact of A on production. c) Using the short-run cost function derived in part a), setup the profit maximization problem with output as the choice variable. 3
Transcribed Image Text:2. A farm has the following production function for producing lentils: q = f(K, L) = A (ak/3 + BL'/3) where q is output per acre, K is capital, L is labour, and (A, a, B) are pa- rameters. Denote the wage rate by w, the price of capital by r, and the output price by p. a) Assume that the farmer is operating during a labour shortage, so that labour is fixed at L. Derive the short-run cost function. b) Describe the role of A in the production function. Calculate the ef- fect of a marginal increase in A on the short-run cost function, and explain how that result is related to the impact of A on production. c) Using the short-run cost function derived in part a), setup the profit maximization problem with output as the choice variable. 3
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