**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.

*Decision:*

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} ,

MR=15-2Q.

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.

*Decision:*

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.

*Decision:*

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?

*Decision:*

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:

units

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?

*Decision:*

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 |

– | – | – | – | -100 | |||||

-28 | |||||||||

+34 | |||||||||

+86 | |||||||||

+128 | |||||||||

+140 | |||||||||

+122 | |||||||||

+74 | |||||||||

-fourteen | |||||||||

-142 | |||||||||

-eighteen | -310 |

*Decision*

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).

Gross approach |

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