The Cobb-Douglas production function for a particular product is N(x,y) = 40x0.6.0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $120. Answer the questions (A) and (B) below. (A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000 is budgeted for the production of the product.
The Cobb-Douglas production function for a particular product is N(x,y) = 40x0.6.0.4, where x is the number of units of labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40 and each unit of capital costs $120. Answer the questions (A) and (B) below. (A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to maximize production, and find the maximum production. (B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000 is budgeted for the production of the product.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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Transcribed Image Text:The Cobb-Douglas production function for a particular product is N(x,y) = 40x0.6.0.4, where x is the number of units of
labor and y is the number of units of capital required to produce N(x, y) units of the product. Each unit of labor costs $40
and each unit of capital costs $120. Answer the questions (A) and (B) below.
(A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to
maximize production, and find the maximum production.
(B) Find the marginal productivity of money in this case, and estimate the increase in production if an additional $50,000
is budgeted for the production of the product.
(A) If $300,000 is budgeted for production of the product, determine how that amount should be allocated to
maximize production, and find the maximum production.
Production will be maximized when using
units of labor and
units of capital.
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