Solve the problem sets given below.

1. A firm’s production function is Q=5L^0.5*K^0.5, where L- amount of labour hours, К- amount of hours of machinery works. Let us suppose that the firm uses 9 hours of labor and 9 hours of machinery every day. What is the maximum amount product the firm can produce. What is the the maximum amount product the firm can produce if both labor and capital doubled. Calculate the return to scale for this firm.

2. A firm’s production function is given below. Calculate the marginal product of each factor of production:

А) Q=10L⁶K⁵_.

Б) Q=5L^0.5*K^0.5

В) Q(x₁,x₂) = 6x₁ + 17x₂

3. In the figure below the initial isocost (AB) and the new isocost (AC). The firm maximizes the profit and plan to spend 500 000 hrn. to purchase factors of production.

What was initial price of labor, the initial price of capital? Write down the equation for isocosts AB and AC. Calculate the slopes of isocosts. Find out the equilibrium points. What is the value of MRTS in these points?

4. A firm’s production function is Q=(LK)/2 Price of labor is 20 money units Price of kapital is 10 money units. How much labor and capital should use the firm to to produce 400 units of output?

5. A firm’s monthly payment for the equipment is 400 thousand hrn, monthly payment for hiring labor force is 300 thousand hrn. MP_L and MP_K are equal 0,5 and 1. Is it optimal quantity of resources used?

6. МР_L = 100К-L, МР_к=100L – К. What is the maximum potential output of the firm if labor capital expenditure is $1000, Р_к=$5., Р_л=$2.

Topic 8. Production costs (6 hours)

1. The treatment of costs in Accounting and Economic theory

2. Costs in the short-run. Fixed and variable costs

3. Average costs. Marginal Cost

4. Long run average cost. Returns to Scale

Give the definition for the following terms:

Cost

Accounting cost

Economic cost

Short-run period

Long-run period

Total cost

Fixed cost

Variable cost

Average cost

Marginal cost

Returns to scale

Answer the following question:

1. What is the difference between Accounting and Economic approach to the cost?

2. Name the kinds of costs in the short-run and provide their graphs.

3. What is the difference between short-run and long-run?

4. What are the relationships between average, marginal and total costs? (Provide the formulas and the graph)

5. What kinds of returns to scale do you know?

Solve the tasks below:

1. Analyze the graphs below. What segment corresponds to minimum averages and total costs, the area of which figure corresponds to fixed, average and total costs of the firm.

2. The function of total costs is presented by definite equation in accordance to the individual variant. Its general view is TC=a+bQ+cQ² (Q is quantity of produced units). Follow the instructions below to do the tasks 1.1 – 1.6 using basic cost function:

1.1. Write the functions of fixed costs and variable costs:

FC =__________________ VC =__________________

1.2. Fill the gaps in the following schedule after calculating all the costs for every definite volume of output. Then calculate total revenue under the price equals $P:

Q	FC, $	VC, $	TC, $	TR, $	Profit, $	Efficiencyecon	Profitability

Make a conclusion about production unit activity, using such terms as economic efficiency and profitability: ____________________________________

1.3. Plot the graph of FC, VC, TC, TR after choosing proper scale.

1.4. Write the functions of average total, average fixed and average variable costs:

ATC =___________________; AFC =____________; AVC = _______________.

1.5. Fill the gaps in the following schedule after calculating all the costs for every definite volume of output:

Q	AFC, $	AVC, $	ATC, $	MC, $	P, $

1.6. Plot the graph of AFC, AVC, ATC, MC, P after choosing proper scale.

VARIANT	Total Cost function	P, $
	TC=25+2Q+3Q^2
	TC=20+2Q+2Q^2
	TC=15+3Q+2Q^2
	TC=35+2Q+Q^2
	TC=30+3Q+2Q^2
	TC=24+4Q+Q^2
	TC=12+6Q+4Q^2
	TC=60+2Q+Q^2
	TC=45+Q+Q^2
	TC=10+5Q^2
	TC=25+5Q+3Q^2
	TC=40+2Q+2Q^2
	TC=15+3Q^2
	TC=44+2Q+Q^2
	TC=5+3Q+2Q^2
	TC=26+3Q+Q^2
	TC=12+5Q+2Q^2
	TC=50+2Q+Q^2
	TC=18+2Q+Q^2
	TC=60+5Q^2
	TC=24+2Q+Q^2
	TC=15+2Q+Q^2
	TC=16+2Q+Q^2
	TC=22+4Q+2Q^2
	TC=40+2Q+Q^2

Topic 9. Market of perfect competition (6 hours)

1. Different market forms. Market model of perfect competition and its characteristics

2. The market behavior of enterprises in the short term. Determination of optimum output: TRTC-model and in MRMC-model.

3. Equilibrium of the firm and industry. Firm and industry demand in P-competitive market

4. Market of perfect competition in the long run. Market efficiency of perfect competition.

Give the definition for the following terms:

Market structure

Perfect competition

Homogeneous product

Efficiency

Answer the following questions:

1. What are the main characteristics of perfectly competitive market?

2. What is the specific of demand for the perfectly competitive firm product?

3. Provide the specific of TR-TC model of profit maximization for perfect competition.

4. Provide the specific of MR-MC model of profit maximization for perfect competition.

5. Where do the perfect competitors get to know the market price?

Solve the tasks below:

1. Fill the gaps in the table below using the formulas of costs, revenues and profit. NB! Pay attention at the way of MC and MR writing (!).

Q

FC

VC

TC

MC

AVC

ATC

If P1=55

If P2=45

If P3=32

TR

MR

Pf

TR

MR

Pf

TR

MR

Pf

-

-

-

-

2. Plot the graphs of TRTC-model for this case, comparing the results of the production at each price level (optimal output, TR and Profit under this output).

3. Plot the graph of MRMC-model for this firm. Show the profit/losses area for each price level. Make your conclusions.

2. Suppose that costs function for a perfect competitor is TC=3Q² +6Q+9. Find the value of economic profit for this firm under the price equals 186. Explain your solution.

3. The functions of market supply and market demand on the perfectly competitive market are following: D=40-P/3 and S=P-20

The function of TC for the average firm on the market is TC=50+35Q+Q² .

Using the data above define the values of:

1) Individual firm’s supply;

2) Number of firms on the market;

3) Economic profit of a firm.

4. There are 1000 firms on the perfectly competitive market. On the graph A presented economic costs of an average firm. Market demand curve is on the graph B.

1) Plot the market supply curve on the graph B and determine equilibrium price.

2) Show the area of economic profit. Define the following values:

а) price (Р), taken per unit of product sold on the market;

b) optimal output (Q) of a firm (thousands units per week);

c) АТС for the optimal output;

d) average profit;

e) total profit.

Topic 10. Monopoly market (5 hours)

1. Definition of Monopoly Market. The "pure monopoly" and its characteristics Causes of monopoly.

2. Monopolies and monopoly power. Varieties of monopolies.

3. Monopoly Profit Maximization in the short and long run

4. Monopoly Inefficiency. Differentiation and price discrimination

5. Necessity of state regulation of monopolies, competition policy. "Natural" Monopoly

Give the definitions for the following terms:

Pure monopoly

Natural monopoly

Monopoly power

X-inefficiency

Price discrimination

Answer the following questions:

1. What are the main reasons of Monopoly appearance?

2. What is the difference between pure and natural monopoly?

3. Provide the principles of profit maximization for pure monopoly.

4. Why is monopoly ineffective in resource allocation and using?

5. What are the possible ways to regulate the monopoly and control it’s power?

Analyze the graph below and answer the questions corresponded to it:

1) Show the total and average revenue of the Monopoly on the graph;

2) Show the total and average cost of the Monopoly on the graph;

3) Show the total and average profit of the Monopoly on the graph;

4) Suggest the values you’ve found on the graph in the situation of perfect competition;

5) Show the price level under government regulation of a monopoly market.

Topic 11. Oligopoly and monopolistic competition (8 hours)

1. Theoretical models of oligopoly. Model duopoly of Cournot and Bertrand Generalization models duopoly by Stackelberg. Kinked Demand Model.

2. Profit Maximization in Monopolistic Competition. Non-price competition. The efficiency of monopolistic competition. Social costs of monopolistic competition

3. Comparison of market structures.

Give the definitions for the following terms:

Oligopoly

Duopoly

Monopolistic competition

Product differentiation

Non-price competition

Price war

Answer the following questions:

1. What are the differences between imperfect and monopolistic competition?

2. What is duopoly?

3. What are the differences between Cournot, Bertrand and Stackelberg models?

4. What is the price war and what is its connection with kinked demand model?

5. What is collusion and what are it’s consequences for the market?

6. What are the main types of oligopoly exist according to different classifications?

Solve the tasks below:

1. Two firms with identical cost structures produce a homogeneous good. Both firms choose the quantity to produce at the same time, but before then, one firm has the privilege of announcing its production quantity decision. Explain how the credibility of this announcement can change the outcome. Do we reach the Cournot equilibrium or the Stackelberg equilibrium?

2. Two firms have marginal costs of 10. They face a market demand curve of P = 100 - 4Q. The government imposes a tax of 10 dollars per unit sold. Determine the Cournot equilibrium quantity.

3. Assume three firms face identical marginal costs of 20 with fixed costs of 10. They face a market demand curve of P = 200 - 2Q. Find the Cournot equilibrium price and quantity.

4. Assume two firms have marginal costs of 20. They face a market demand of P = 90 - 3Q. Determine the Bertrand equilibrium quantity and price. Now assume one firm moves ahead of the other. Find the Stackelberg equilibrium and price.

5. A group of n identical firms face a market demand curve of P = 2000 - 3Q. MC = 100. Show that as n approaches ∞, the quantity approaches the perfectly competitive outcome.

Topic 12. Market of the factors of production (6 hours)

1. The maximum gain manufacturer of hiring labor

2. The market supply of labor services. Equilibrium in the labor market

3. The labor market with imperfect competition

4. Capital as a factor of production. Demand and supply of capital. The concept of discounted value. Types of interest rates

5. The land market. Features of supply and demand of land. Rent. Land price as capitalized rent.

Give the definitions for the following terms:

Labor force

Wages

Monopsony

Capital

Discounted value

Interest rate

Land market

Differentiated rent

Land price

Answer the following questions:

1) What is the main principle of optimal quantity of resourses?

2) What is the meaning of J.B. Klark’s concept?

3) What is marginal product value and how to calculate it?

4) What is specific of monopsony labor market?

5) What are the main approaches to the interest rate calculating?

6) What is the sense of discounted value?

7) What is land market and how to define the price of land?

Solve the following tasks:

1.Calculate the marginal productivity of labor (MP_L) and average product of labor (AP_L) Gragh the curves of TP MP and AP. Point the interception of MP and AP. Prove that law of diminishing marginal productivity works in this example.

Labor	Total product	МРL	АРL

2. Gabrielle runs a software development firm in Shreveport, Louisiana. She employs a number of C++ programmers. The MRP is defined as

a) The cost of an individual programmer.

b) The amount of labor times the wage

c) The price of the output times the average productivity of labor, in physical terms The

d) price of the output times the marginal productivity of labor, in physical terms such as lines of code.

e) both b and d

3. Gabrielle runs a software development firm in Shreveport, Louisiana. She employs a number of C++ programmers and Figure RR shows her programmer labor input, on the horizontal axis, and the wage and the value of the marginal product (VMP) of programmer labor on the vertical axis. Suppose Gabi employs L₃ programmers. Then

a) She is directing her firm efficiently.

b) Increasing labor input would increase profit.

c) She should "downsize," since decreasing labor input would increase profit.

d) She is directing her firm inefficiently.

e) both c and d above.

Fill the gaps in the table below. Graph curves TP, MP (figure 1) and MRP, w (figure 2). Find out the optimal number of worker the firm should employ. The price of a good produced is $100.

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