If x1 and x2 are the factors of production of a typical firm, output price is...

If x1 and x2 are the factors of production of a typical firm, output price is p, price of x1 and x2 are w1 and w2, respectively and the firm’s production function is:

f (x1, x2) = x1^3 x2^3

i. Write up firm’s short run and long run profit maximization problem. Show firm’s short run profit maximization graphically please.

ii. Using the information above can you write the cost minimization problem for this firm if the firm decides to produce y1 level of output? Please show graphically how the firm minimizes its costs. What is the alternative method we can use to find the optimal quantity of x1 and x2 to solve the cost minimization problem for the firm? Explain.

iii. If the firm’s factor demand functions for x1 and x2 are as follows:

x1= p ^3/ (27 w1^2 w2)

x2= p ^3/ (27 w1 w2^2)

a. How the optimal quantity of each input changes when price of input changes?

b. How the optimal quantity of one input changes when price of other input changes?

c. How the optimal quantity of each input changes when price of that input changes?

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Expert Solution

Rahul Sunny answered 1 year ago

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