Question:

Suppose the firm's production function is X=10K^.2L^.6 

The price for the factors of production are P_k=10 and P_L =20

• A. 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 ?
• 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.  What would have happened to the MC  if the firm changes its number of units of L from 30 to 34 leaving K unchanged?  What would the effect on the MC if the firm increases its inputs to K= 22 and ?
• A. What kind of economics to scale does this firm exhibit? 
• B.  Suppose the firm double its production what can you say on its new production Should the firm decentralize or centralize its operations? 
• C.  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=BP_x^-1/2and the optimal units of the inputs  are K= 20 and L=30 . What is the optimal price P_xof the firm's output?