A monopolistic company has to spend exactly $3000 as total cost for the production of a number of Basic Science and Mathematics textbooks for three schools. The Basic Science textbook sells at P1 = 455 – Q1 – Q2 and the Mathematics textbook at P2 = 910 – Q1 – 4Q2 where P1 and P2 denote the prices; Q1 and Q2 denote the number of Basic science and mathematics textbooks produced respectively. The joint cost of producing these textbooks is given as TC = 5Q1 + 10Q2 (i) Find the maximum profit the producer can make (ii) Estimate the new profit if the company decides to reduce the total cost by $50 (Assume that 2nd order conditions are satisfied) Question 2 A monopolistic producer of two goods, G1 and G2, has a joint total cost function as ?? = 10?1 + 4?1?2 + 5?2 Where Q1 and Q2 denote the quantities of G1 and G2 respective. If P1 and P2 denote corresponding prices then the demand equations are P1 =50–1.5Q1 +Q2 P2 =52.5+Q1 –1.5Q2 (a) Find the total revenue function for the monopolist (b) Find the profit function for the firm (c) Determine the firm’s pricing policy that maximizes profit using the first and second order conditions (d) Calculate the value of the maximum profit (e) Now, suppose that firm is contracted to produce a total of 12 goods of either type, find the level of Q1 and Q2 that maximizes profit. (f) Estimate the new optimal profit if the production quota increases to 14 units.
A monopolistic company has to spend exactly $3000 as total cost for the production of a number of Basic Science and Mathematics textbooks for three schools. The Basic Science textbook sells at P1 = 455 – Q1 – Q2 and the Mathematics textbook at P2 = 910 – Q1 – 4Q2 where P1 and P2 denote the prices; Q1 and Q2 denote the number of Basic science and mathematics textbooks produced respectively. The joint cost of producing these textbooks is given as TC = 5Q1 + 10Q2
(i) Find the maximum profit the producer can make
(ii) Estimate the new profit if the company decides to reduce the total cost
by $50 (Assume that 2nd order conditions are satisfied)
Question 2
A monopolistic producer of two goods, G1 and G2, has a joint total cost function as ?? = 10?1 + 4?1?2 + 5?2
Where Q1 and Q2 denote the quantities of G1 and G2 respective. If P1 and P2
denote corresponding prices then the demand equations are P1 =50–1.5Q1 +Q2
P2 =52.5+Q1 –1.5Q2
(a) Find the total revenue function for the monopolist
(b) Find the profit function for the firm
(c) Determine the firm’s pricing policy that maximizes profit using the first and second order conditions
(d) Calculate the value of the maximum profit
(e) Now, suppose that firm is contracted to produce a total of 12 goods of either type, find the level of Q1 and Q2 that maximizes profit.
(f) Estimate the new optimal profit if the production quota increases to 14 units.
Question 3
A manager hires and rents capital equipment in a very competitive market. Currently the wage rate is GH¢2 per hour and the capital is rented at GH¢5 per hour. The unit price is GH¢0.25 and the total cost is GH¢1000. Suppose the firm’s production function is as follows:
0.5 0.5 ?=14? ? +10
(a) What is the amount of labour and capital the firm should employ in order to maximize output?
(b) What is the maximum profit?
Step by step
Solved in 2 steps
