Problem
1. Suppose the firm's production function is . The price for the factors of production are Pk=10 and PL=20
i.. Suppose that initially the firm employed 20 units of K and 30 units of L. What was the output of the firm and what was its cost of production in the immediate runs?
ii. Suppose the firm increases its number of units of K from 20 to 23, leaving L unchanged. How would this change the marginal cost (MC) of the firm?
iii. What would have happened to the MC, if the firm changes its number of units of L from 30 to 34 leaving K unchanged?
iv. What would the effect on the MC if the firm increases its inputs to K= 22 and L=33?
2. i. What kind of economics to scale does this firm exhibit?
ii. Suppose the firm double its production what can you say on its new production? Should the firm decentralize or centralize its operations?
iii. If the values of the parameters are changed, would you change your answer to b? Be specific and explain properly to gain credit.
• If the marginal revenue (MR) of x is $20 per unit of X, How many units of K should be employed, if L=30 is unchanged.
• Suppose that the demand function for is given as x=BPx-1/2 and the optimal units of the inputs are K=20, and L=30. What is the optimal price Px of the firm's output?
3. In railroading, about two-thirds of costs are said to be fixed and only one-third variable. If so,AVCis approximately one-third ofAC. It would therefore always be financially advantageous for railroads, it has been argued, to take onadditionaltraffic even at a price lower than Average Cost. Is this argument valid? Explain.
4. "In the long run, a firm could always produce twice as much simply by doubling the amount of every input employed. So in the long run there must be constant returns to scale." Evaluate.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.