QUESTION 1

Assume a production function:
                                          0.5  0.25
                                    Q= 10L    K

with a selling price for the product of 10, and factor prices of 5 for
L and 10 for K , determine the firm?s profit maximizing levels of
inputs. Ensure you have found a maximum by checking the second-order
sufficient conditions. Determine the level of output that this will
produce. Determine the corresponding values for total cost, total
revenue and profit.
L0000

QUESTION 2

Assume a production of the form:

                                 Q= F(k)
 
where K is capital input and L is fixed. Confirm that average product
(AP ) is equal to marginal product (MP ) when AP is at a maximum

QUESTION 3
                                                 
                                                -0.6p.
The demand function of a firm is given by Q= 20e         If fixed
costs are 100 and the variable costs are 2 per unit, find the price
needed to maximize profit

QUESTION 4

A monopolistic producer charges different prices at home and abroad.
The demand functions of the domestic and foreign markets are given by,
 P + Q  = 100
  1   1

and P + 2Q  = 80 , respectively. 
     2    2

                                          1   2  2.
The firm?s total cost function is, TC= ( Q + Q  )  

(a)Determine the profit maximizing level of demand for both markets.
Calculate the second-order sufficient conditions to ensure you have
found a maximum.

(b)The foreign country believes that the firm is guilty of dumping
because the good sells at a higher price in the home market, so
decides to restrict the sales to a maximum of 2. Use calculus to find
the value of Q1 and compare the corresponding profit with that of the
free market in part (a).