Suppose that an economy has a production function that uses 3 inputs: capital, K, labor, L, and intermediate inputs (materials), M. The production function is Y = K L MY Suppose that output Y has two uses: it can be consumed by people so it serves as consumption C, or it can be used as an intermediate input in production, M. The total resource constraint is: Y = C + M (a) What value must y have for the production function to exhibit constant returns to scale? Assume that y is equal to this value for the remainder of the problem. (b) Suppose that the price of output (and therefore consumption and materials) is equal to 1. The firm's problem is to maximize its revenue, Y, net of the input costs, RK + WL + M.

Suppose that an economy has a production function that uses 3 inputs: capital, K, labor, L, and intermediate inputs (materials), M. The production function is Y = K L MY Suppose that output Y has two uses: it can be consumed by people so it serves as consumption C, or it can be used as an intermediate input in production, M. The total resource constraint is: Y = C + M (a) What value must y have for the production function to exhibit constant returns to scale? Assume that y is equal to this value for the remainder of the problem. (b) Suppose that the price of output (and therefore consumption and materials) is equal to 1. The firm's problem is to maximize its revenue, Y, net of the input costs, RK + WL + M.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

See attached image. Answer questions A-C. Show all work please.

Suppose that an economy has a production function that uses 3 inputs: capital, K, labor, L, and
intermediate inputs (materials), M. The production function is
Y = KaLB MY
Suppose that output Y has two uses: it can be consumed by people so it serves as consumption
C, or it can be used as an intermediate input in production, M. The total resource constraint is:
Y = C + M
(a) What value must have for the production function to exhibit constant returns to scale?
Assume that Y is equal to this value for the remainder of the problem.
(b) Suppose that the price of output (and therefore consumption and materials) is equal to 1.
The firm's problem is to maximize its revenue, Y, net of the input costs, RK + WL+ M.
Find the first-order condition that determines the optimal choice of intermediate inputs of
the firm. Then use this first-order condition to express M as a function of K, L and the
parameters of the production function.
(c) Use the optimal choice of M derived above to derive the value added production function
in this economy, that is, a function that relates the amount of value added, V = Y - M
produced in the economy, as a function of K and L.

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