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). |