Consider the Cobb-Douglas production function f(x, y) = 40x^(1/4)y^(3/4) where x is the number of units of labor, y is the number of units of capital, and f(x, y) is the number of units produced. Use differentials to estimate the change in production if the number of units of labor is increased from 64 to 65 and the number of units of capital is increased from 81 to 80. If at the current levels the number of units of capital decreases by 4 units, approximately how many units of labor should be added to keep the production level unchanged?
Consider the Cobb-Douglas production function f(x, y) = 40x^(1/4)y^(3/4) where x is the number of units of labor, y is the number of units of capital, and f(x, y) is the number of units produced. Use differentials to estimate the change in production if the number of units of labor is increased from 64 to 65 and the number of units of capital is increased from 81 to 80. If at the current levels the number of units of capital decreases by 4 units, approximately how many units of labor should be added to keep the production level unchanged?
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.14P
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Consider the Cobb-Douglas production function
f(x, y) = 40x^(1/4)y^(3/4)
where x is the number of units of labor, y is the number of units of capital, and f(x, y) is the number of units produced. Use differentials to estimate the change in production if the number of units of labor is increased from 64 to 65 and the number of units of capital is increased from 81 to 80. If at the current levels the number of units of capital decreases by 4 units, approximately how many units of labor should be added to keep the production level unchanged?
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