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Question 1: The production function of a textile factory is given by Y=10LK, and therefore MPL=10K...

Question 1: The production function of a textile factory is given by Y=10LK, and therefore MPL=10K and MPK=10L. The plant manager is required to produce a given output level and will choose the amount of labor and capital. The prices of inputs are ?? and ??.

a. Find the conditional input demand functions

b. Find the cost function

c. Assume ?? increases. Explain how this affects the conditional input demands and the cost function.

d. Assume ?? increases. Use a graph to show how this affects the choice of inputs needed to produce the targe

Solutions

Expert Solution

1. (a) The cost minimization would be where or or . Putting it to the production function, we have or or or or , and since or . These are the conditional input demands.

(b) The cost function would be or or or .

(c) We have

or ,

or ,

and or or .

Hence, as wL increase, the demand for labor decrease, the demand for capital increase, and the cost function also increases.

(d) The graph is as below (supposing Y=50 and wK=1, we would have ).

As the Y increases, this labor demand shifts right/upward.

Rahul Sunny answered 1 year ago
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