Task 1 . Let the cost function of a monopolist firm be equal to TC=Q 2 +60. The demand function for the firm’s product is equal to Qd=30-2P. Determine the volume of production, price, total revenue, economic profit of the monopolist and his monopoly power.
1. based on the condition of monopolist profit maximization: MR=MC.
2. Marginal revenue MR=TR ‘ , and TR=P·Q.
From the demand function P=15-0.5Q,
TR=15Q-0.5Q 2 ,
3. Marginal cost МС=ТС ‘ , MC=2Q;
4. Equilibrium condition 15-Q=2Q,
Q=5 – profit maximizing output.
P=15-0.5Q=15-2.5; P=12.5 is the price of a monopoly.
5. Total revenue TR=12.5 5=62.5.
6. Monopoly power is measured by the Lerner index :
, I L =0.2.
7. Monopoly profit π=TR-TC.
TC=5 2 +60=85, π=62.5-85=-22.5.
The profit of the monopoly is negative, because there are large fixed costs with a narrow market demand.
Task 2 . The company “Ukraine” is a monopolist in the market. Its production cost function is: TC=2Q+10, where Q is the volume of production per month.
Determine at what price level the company’s profit will be maximum if it is known that the price elasticity of demand is 6.
1. Lerner index: .
2. Marginal cost: MC=TC’ , MC=2.
3. Monopoly price: , Р=2.5 – monopoly price.
Task 3. There are five firms in the industry with output volumes of 2, 3, 5, 10 and 20% of the total output of the industry. The rest of the output is produced by small firms, each of which has 1% of sales.
Calculate the degree of monopolization of the industry.
The degree of monopolization is calculated based on the index
Herfirdahl – Hirschman:
Because =598<1800, then the industry is weakly concentrated.
Task 4. There are three identical firms in the industry with marginal costs MC=298 UAH. Demand in the industry is determined by the equation P=1800-Q. If firms form a cartel and share the market equally, what will be the equilibrium price and how much output will each firm produce?
1. For a cartel, the profit maximization condition MC=MR
2. Gross income TR=P Q=1800Q-Q 2 , MR=TR’=1800-2Q,
1800-2Q=298, because MS=298 by condition.
Q=751 units – industry output.
3. Since the firms share the market equally, the output of each firm:
4. Market price Р=1800-751=1049 UAH.
Problem 5. IBM has a monopoly in the US market in the production of fifth generation personal computers. Domestic demand is described by the equation: , where Q d is the volume of the domestic market, million pieces/year.
In addition, IBM sells computers on the world market, where the price does not depend on quantity and is P m =20 thousand dollars. The marginal cost of production is equal to , where Q is the total volume in the domestic and foreign markets. How should IBM distribute domestic and international sales to maximize profits?
1. Profit maximization condition: .
2. In the foreign market, the price is constant, so MC = P:
10+0.1Q=20, Q=100million PCS. is the total volume that is divided between the markets
3. Gross income in the domestic market TR=P·Q=100Q-0.5Q 2 .
4. Marginal income in the domestic market MR=100-Q.
5. Profit maximization condition in the domestic market:
MR=MC, 100-Q=20; Q=100-20=80 million pieces – volume of sales in the domestic market.
6. Sales in the world market 100-80=20 million pieces.
Task 6. Based on the data on the work of a monopolist firm, use the methods of comparing gross and marginal indicators to find the most favorable price and sales volume for the enterprise. Determine the firm’s maximum profit. Show a graphical solution to problems using gross and marginal revenue.
|Q, units||R, UAH||TR, UAH||MR, UAH||TS, UAH||MS, UAH||TVC||AVC, UAH||ATS, UAH||P, UAH|
1. Based on the given data Q, P, TC, we calculate the missing values using the following formulas:
1) Total income TR=P Q
2) Marginal revenue
3) Marginal cost
4) Total variable costs TVC=TC-TFC
5) General fixed costs TFC=100 UAH,
because at Q = 0: TC=TFC=100 UAH by condition.
6) Average variable costs .
7) Average gross costs .
8) Profit of the firm P=TR-TC.
The calculation results for each volume of output are summarized in the table.
Analysis of the obtained results allows us to draw the following conclusions:
1 – Profit is maximum (P=140 hryvnia) with the volume of output Q=5 units.
2 – Price P m =122 UAH. maximizes profit, because its value exceeds ATC=24 UAH. Economic profit is 122 – 94 = 28 UAH. per unit of production. On the graph, this profit is shown by the segment AP m , and the total economic profit is shown by the rectangle ABCP m .
Similarly, a profit-maximizing combination of output (Q) and price (P m ) can be determined graphically by comparing TR and TC (gross approach P=TR-TC→ max) and MR and MC (MR=MC).