Micro economics excer, Exercises of Economics

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KRISTER AHLERSTEN

ESSENTIALS OF MICROECONOMICS:

EXERCISES

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Krister Ahlersten

Microeconomics

Exercises

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Microeconomics – Exercises Contents

Contents

1. Consumer Theory 1.1 Preferences 1.2 The Budget Line 1.3 Utility Maximization 2. Demand 2.1 Price Changes 2.2 Income Changes 2.3 Elasticities 3. Production 3.1 Definitions 3.2 The Production Function 4. Costs 4.1 Costs in the Short Run 4.2 Costs in the Long Run 5. Perfect Competition 5.1 Definitions and Assumptions 5.2 The Firm’s Short-Run Profit Maximization 5.3 The Firm’s Long-Run Profit Maximization 6. Monopoly 6.2 Monopoly Profit Maximization and Efficiency Problems 6.3 Price Discrimination

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Microeconomics – Exercises

7. Game Theory 7.1 Basic Concepts 7.2 Games on Normal Form 7.3 Games on Extensive Form 8. Oligopoly 8.2 The Cournot Model 8.3 The Bertrand Model **9. Monopolistic Competition

10. Labor** 10.1 The Supply of Labor 10.2 The Demand for Labor 11. General Equilibrium 11.1 Definitions 11.2 Efficient Production **12. Choice under Uncertainty
11. Other Market Failures** 13.1 Basic Concepts 13.2 Externalities 13.3 Public Goods

Contents

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Microeconomics – Exercises

7. Game Theory 7.1 Basic Concepts 7.2 Games on Normal Form 7.3 Games on Extensive Form 8. Oligopoly 8.2 The Cournot Model 8.3 The Bertrand Model **9. Monopolistic Competition

10. Labor** 10.1 The Supply of Labor 10.2 The Demand for Labor 11. General Equilibrium 11.1 Definitions 11.2 Efficient Production **12. Choice under Uncertainty
11. Other Market Failures** 13.1 Basic Concepts 13.2 Externalities 13.3 Public Goods

Contents

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Microeconomics – Exercises

1. Consumer Theory

1.1 Preferences

Exercise 1.1.

A basic assumption about consumers in microeconomics is that they have preferences over different baskets of goods. Explain the concepts “preference”, “preference order”, and “basket of goods”.

Exercise 1.1.

a) If there are only two goods, it is possible to illustrate a consumer’s preferences over them with an indifference map. Draw an indifference map with three indifference curves. b) There are a few standard assumptions about what an indifference map can and cannot look like. Which are these assumptions, and what reasoning lies behind them?

Exercise 1.1.

a) What is the marginal rate of substitution, MRS? State the definition and explain, in words, what it means. b) MRS will have an influence on the shape of an indifference curve. What influence?

Exercise 1.1.

a) Often, we assume that consumers have diminishing MRS. Explain what that means and how it is reflected in indifference curves. b) Can you draw an indifference curve that does not have diminishing MRS, but that is still allowed?

Exercise 1.1.

a) In Figure E.1.1, we have drawn an indifference curve for a certain consumer. Calculate an estimate of her marginal rate of substitution, MRS, in point A. b) Can we say anything about whether point B is better or worse for the consumer, as compared to point A? c) What about point C?

Consumer Theory

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Microeconomics – Exercises

Exercise 1.2.

a) Suppose there are two goods in a market, and that you buy q1 of the first and q2 of the second. Give a mathematical expression for the total cost. b) Now, use the answer to a) to show that the marginal rate of transformation, MRT, is equal to the slope of the budget line.

1.3 Utility Maximization

Exercise 1.3.

a) Explain briefly, what utility maximization is. b) What is a utility function? c) What is the criterion that a consumer maximizes her utility? Give the answer in the form of a mathematical expression. Exercise 1.3.

a) Suppose a consumer has two goods from which to choose. Draw a graph, with quantities on the X- and Y-axes, that illustrates how she can choose, given prices and income. b) Also, illustrate a few indifference curves in the graph. c) Show how the consumer maximizes her utility and where in the graph this occurs. d) Can you give an example of a situation in which the consumer will find more than one point where she maximizes her utility? Think about what the indifference curves must look like to make this possible. Exercise 1.3.

Look at Figure E.1.1 again. Suppose the consumer maximizes her utility at A, and that the price of good 2 is 100. What is the price of good 1? How large is the consumer’s income?

Consumer Theory

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Microeconomics – Exercises

2. Demand

2.1 Price Changes

Exercise 2.1.

a) Suppose there are two goods a consumer can choose between, and that the prices are equal. First, construct a diagram, with quantities on the X- and Y-axes, where you show a utility maximizing choice for the consumer. b) Then, show what happens if you vary the price of good 1. Construct one budget line corresponding to the case when the price is cut by half, and another one when it is doubled. Will the consumer maximize her utility in the same point as before? Show how to derive the price-consumption curve using this technique. c) Use the price-consumption curve to derive the consumer’s demand curve for good 1. d) Suppose that you also have another consumer’s demand curve. Show in a new diagram how you can derive the market’s demand curve, assuming the market only consists of these two consumers. You may assume that the consumers’ demand curves are straight lines.

2.2 Income Changes

Exercise 2.2.

Start, similarly to the previous exercise, with a consumer who has two goods between which she can choose. However, instead of varying the price, you now vary the income. Derive the income- consumption curve. Use the cases when the income is either doubled or cut by half. Then, use the income-consumption curve to derive the Engel curve.

Exercise 2.2.

a) Suppose there are two goods, that the prices are given, and that there is a consumer with a certain income. Show in a diagram how it is possible to split the effect of a price fall on good 1 into the income- and substitution effects. Assume that the good is a normal good. b) If the good had been an inferior good, what would have been different in the graph? c) If the good had been a Giffen good, what would have been different?

Exercise 2.2.

Can a Giffen good be a normal good? Why or why not? Use a market with only two goods in your reasoning.

Demand

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Microeconomics – Exercises

3. Production

3.1 Definitions

Exercise 3.1.

a) Sometimes it is said that producer theory is similar to consumer theory. In what ways are they similar? b) Describe in words what a production function is. Which variables are typically inputs? c) What is the difference between the short and the long run? d) What does “returns to scale,” mean?

Exercise 3.1.

a) State the definition of marginal product, MP, both as a mathematical definition and with your own words. b) What is the “law of diminishing marginal returns”? How has it been derived?

Production

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Microeconomics – Exercises

Exercise 3.1.

a) State the definition of the marginal rate of technical substitution, MRTS. What does that mean, in your own words? b) Show how to derive a relation between the marginal products of labor and capital, MPL and MPK, and MRTS.

3.2 The Production Function

Exercise 3.2.

In the short run, the relation between number of hours worked and quantity produced looks like in the table.

L q

a) Draw a graph of what the production curve looks like. b) Explain the concepts of “average product of labor,” APL, and “marginal product of labor,” MPL, and what they correspond to in the graph. c) Draw another graph below the production curve, illustrating the shapes of APL and MPL. Explain how to find the most characteristic points for APL and MPL on the production curve and indicate the relations in the graphs.

Production

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Microeconomics – Exercises

4.2 Costs in the Long Run

Exercise 4.2.

a) In the long run, both labor, L, and capital, K, are variable costs. Show in a graph, where you have the quantity of L on the X-axis, and the quantity of K on the Y-axis, how one can indicate combinations of L and K that cost the same to produce. What is this type of lines called? b) Then show how one can indicate combinations of L and K that produce the same quantity of the good. What is this type of lines called? c) The firm always wants to minimize its cost of production. Choose a certain quantity in your graph, and show how the firm would minimize its cost of producing that quantity. d) What is the mathematical criterion for a cost-minimizing choice of L and K? What does that correspond to in the graph? e) Show, in your graph, how to derive the long-run expansion path. f) Show how to derive the short-run expansion path. g) Use the information in your graph to derive the long-run cost curve. First, choose levels for the cost and the production in the graph you have constructed. Then, draw a new graph, with the quantity produced, q, on the X-axis, and the cost, C, on the Y-axis.

Costs

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Microeconomics – Exercises

Exercise 4.2.

In Figure E.4.1, we see the long-run average cost for the production of a good, LRAC.

Figure E.4.

a) In the short run, capital is a fixed cost. Draw, for a few different values of K, what the short-run average cost, SRAC, looks like in relation to the long-run average cost.

b) Sometimes, one talks of (dis-) economies of scale. What in the graph indicates whether we have economies or diseconomies of scale?

q

A

LRAC

Costs

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Microeconomics – Exercises

c) Below the graph, construct another graph with the same scale on the X-axis. First, draw the curve for average variable cost, AVC. Be careful to get the minimum point in the right place. How can you know at which quantity AVC reaches its lowest point? Then, draw the marginal cost curve, MC. At least one point is easy to find. Which one? Where will the MC curve be above the AVC curve and where will it be below it? Lastly, draw the marginal revenue curve, MR. d) Show how to find the point where the firm maximizes its profit. Where is that in the graph? e) The profit can be found in two different ways. Show both of them. Approximately, how large is the profit. f) How can one find the firm’s short-run supply curve from the graph? Indicate it in the graph. g) Can you find the firm’s long-run supply curve in the graph?

5.3 The Firm’s Long-Run Profit Maximization

Exercise 5.3.

a) Describe in a few sentences how to derive the market’s short-run supply curve from the individual firms’ short-run MC curves. b) Describe how to find the markets’ long-run supply curve.

Exercise 5.3.

On the left-hand side of Figure E.7.2, you see the total market supply and demand. Together, they determine the market price, p, and total quantity, Q. On the right-hand side, you see a representative individual firm’s marginal cost, MC, and average variable and average total cost, AVC and ATC.

The firm faces the price determined by the market, and therefore MR = p*.

Perfect Competition

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Microeconomics – Exercises

Figure E.7.

a) Will this firm make a profit, a loss, or break even in the short run? Why? How much will it produce? b) Describe the forces that will affect this situation in the long run. How will a long-run equilibrium arise? What will happen to p*? What will happen to the number of firms in the market? How will it affect this firm’s and other firms’ profits or losses?

p

Q

p

q

MC

ATC

AV

S

D

p *

Q*

MR = p

Perfect Competition

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