Midterm 2- Econ. Uof Toronto, Practice PDF

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Midterm 2- Econ. Uof Toronto, and practical Practice for exercises and numerical and theoretical parts of the important parts in the chapter....

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Department of Economics University of Toronto

Prof. Gustavo Indart December 2, 2005

SOLUTIONS

ECO 100Y – L0101 INTRODUCTION TO ECONOMICS Midterm Test #2

LAST NAME

FIRST NAME

STUDENT NUMBER

INSTRUCTIONS: 1. 2. 3. 4.

The total time for this test is 55 minutes . Answer all questions in the space provided (if space is not sufficient, continue on the back of the previous page). Aids allowed: a simple, non-programmable calculator. Use pen instead of pencil.

DO NOT WRITE IN THIS SPACE

1.

/10

5.

/13

2.

/10

6.

/12

3.

/16

7.

/9

4.

/12

8.

/18

TOTAL

/100 Page 1 of 9

Question 1 (10 marks) The diagram below illustrates a typical taxi driver’s individual supply curve (assume that each taxi ride is of the same distance).

Price of taxi ride S $8 $6 $4

40

60

80 Quantity of taxi rides

a) Suppose that the city sets the price of taxi rides at $6 per ride. What is this typical taxi driver’s producer surplus? Explain. (5 marks)

If the price of taxi rides is $6, then the number of taxi rides supplied by this taxi driver will be 60. The producer surplus is the area below the price line and above the supply curve, that is, the difference between the price of a taxi ride and the minimum amount the taxi driver is willing to accept for each ride. The area representing the producer surplus is an inverted right-angle triangle where the base is 60 rides and the height is $6 for a total producer surplus equivalent to $180 (recall that the area of a triangle is equal to ½ * the base * the height). This area is shown in the diagram above.

b) Suppose now that the city keeps the price of a taxi ride set at $6, but decides to charge taxi drivers a “licensing fee.” What is the maximum licensing fee the city could charge to the typical taxi driver? Explain. (5 marks)

The city could charge this taxi driver a maximum licensing fee equal to her consumer surplus, that is, $180. If this were the case, then the taxi driver would be obtaining just the equivalent to the minimum price she’s willing to accept for each of the 60 rides.

Page 2 of 9

Question 2 (10 marks) For each of the following situations, draw a diagram containing two indifference curves that will represent the consumer’s preferences, and explain your answer. a) For Isabel, cars and tires are perfect complements, but in a ratio of 1:4; that is, for each car, Isabella wants exactly four tires. Be sure to label and number the axes of your diagram. Place tires on the horizontal axis. (5 marks)

If cars and tires are perfect complements for Isabel, then an additional car without four additional tires will not give her any additional utility or satisfaction. Similarly, four more tires without an additional car will not give her any additional utility or satisfaction either. Her indifference curves, therefore, are L-shaped and vertices of these indifference curves must be multiples of the ratio 1:4 of cars to tires. In the diagram we can see two indifference curves where the vertices are 1 car and 4 tires, and 2 cars and 8 tires respectively. The curve further from the origin represents the higher level of utility.

Cars

2

1

4

8

Tires

b) Penelope gets utility only from her caffeine intake. She can consume coffee or tea, and coffee contains twice as much caffeine as tea. Be sure to label and number the axes of your diagram. Place tea on the horizontal axis. (5 marks) If caffeine is the only thing that gives utility or satisfaction to Penelope, then she will be indifferent between having one more coffee or two more teas since coffee has twice as much caffeine as tea. Therefore, the marginal rate of substitution of tea in place of coffee is constant and equal to 0.5. Her family of indifference curves will consist of straight lines with a slope equal to 0.5. In the diagram we can see two such indifference curves where the one further from the origin represents the higher level of utility.

Cups of coffee 4

2

4

8 Cups of tea

Page 3 of 9

Question 3 (16 marks) a) Tomato salad is Jack’s favourite salad. He buys one pound of tomatoes a week when the price of tomatoes is $1 per pound. However, the week when the price of tomatoes increased to $1.05 per pound he decided not to buy any. What is Jack’s consumer surplus when he buys one pound of tomatoes a week? Explain. (4 marks)

Given the wording of the question, two possible answers will be accepted as correct: 1. The price of $1.00 per pound of tomatoes is the maximum price Jack is willing to pay. This means that the benefit he obtains from consuming a pound of tomatoes is equivalent to $1.00, the price he pays. Therefore, he doesn’t obtain any consumer surplus. 2. If we interpret the wording of the question as indicating that the vertical intercept of Jack’s demand curve is 1.05, then Jack’s consumer surplus will be equal to the area below the demand curve and above the price line at P = 1.00. That is, the consumer surplus would be $0.025. This can be observed in the diagram on the right.

P 1.05 1.00 D

1

Tomatoes (lbs.)

b) John likes his job so much that he would be willing to do it for free. However, his annual salary is $80,000. What is John’s producer surplus as a supplier of labour services? Explain. (4 marks)

Since the minimum price he’s willing to accept for his labour is $0, his producer surplus is equal to his full salary: $80,000.

c) Robin goes to the CD store hoping to find a used copy of Carlos Santana’s Greatest Hits for up to $10. The store has one copy selling for $10. What is Robin’s consumer surplus? Explain. (4 marks)

She’s willing to pay a maximum price of $10 for this CD, and this is the actual price that she pays for it. Therefore, her consumer surplus is zero.

d) After baseball practice, Jennifer is willing to pay $2 for a bottle of mineral water. The vending machine sells mineral water for $2.25 per bottle. What is Jennifer’s consumer surplus? Explain. (4 marks)

The maximum price she’s willing to pay for a bottle of mineral water is $2.00 and the price is $2.25. Therefore, she won’t buy any mineral water and there is no consumer surplus.

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Question 4 (12 marks) Rachel has an income of $50, which she can spend on two goods: CDs and cups of hot chocolate. Both are normal goods for her; each CD costs $10, and each cup of hot chocolate costs $2. For each of the following situations, decide whether this is Rachel’s optimal consumption bundle. If not, what should Rachel do to achieve her optimal consumption bundle? You might want to use diagrams to help you answering the question. a) Rachel is thinking about buying 4 CDs and 5 cups of hot chocolate. At that bundle, her marginal rate of substitution of CDs for hot chocolate is 1; that is, she would be just willing to exchange 1 cup of hot chocolate for 1 more CD while keeping her utility constant. (6 marks)

Rachel’s budget line is given by 50 = 10CD + 2HC or HC = 25 – 5CD, and thus the slope of the budget line is – 5. At the combination bundle 4 CDs and 5 HCs, her MRS is 1. This bundle, therefore, is not her optimal consumption bundle. The MRS should be 5 at the optimal consumption bundle. Therefore, since the MRS increases as we move up the indifference curve, she should choose a combination with more than 5 cups of HC and less than 4 CDs.

HC 25

HC*

5

CD*

4

5

CD

b) Rachel is thinking about buying 1 CD and 10 cups of hot chocolate. At that bundle, her marginal rate of substitution of CDs for hot chocolate is 5; that is, she would be just willing to exchange 5 cups of hot chocolate for 1 CD while keeping her utility constant. (6 marks)

At the combination bundle 1 CDs and 10 HCs, her MRS is 5, but this is not her optimal consumption bundle because it represents an expenditure of $40 and her income is $50. Therefore, since both CDs and HCs are normal goods for Rachel, the will choose a bundle with more than 10 cups of HC and more than 1 CDs as shown in the diagram.

HC 25

HC* 10 5

1

CD*

4

5

CD

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Question 5 (13 marks) Sabine can’t tell the difference between Coke and Pepsi – the two taste exactly the same to her. Sabine has $6 to spend on cola this week. Coke costs $1.50 per bottle and Pepsi costs $1.00 per bottle. a) What is Sabine’s marginal rate of substitution of Coke for Pepsi, that is, how many bottles of Pepsi is she willing to exchange for one more bottle of Coke while keeping her utility constant? (4 marks)

Coke and Pepsi are perfect substitutes for Sabine and the MRS is constant and equal to 1. Therefore, her indifference map consists of straight lines with slopes equal to – 1.

b) What is Sabine’s optimal consumption bundle? (4 marks) Show Sabine’s utility-maximizing equilibrium in a diagram; that is, draw the corresponding budget line and indifference curve and show the utilitymaximizing bundle. Place Coke on the horizontal axis. (5 marks)

Sabine’s budget line is 6 = 1.5C + P or P = 6 – 1.5C. Sabine’s indifference curves are straight lines with slopes equal to – 1. Therefore, her indifference curves are flatter than her budget line. Since Sabine is trying to maximize her utility or satisfaction, the optimal consumption bundle will lie on the highest possible indifference curve and, therefore, she will consume 6 bottles of Pepsi and none of Coke. Intuitively, this should be also the answer: Rachel is completely indifferent between Pepsi and Coke but she can buy more bottles of Pepsi than of Coke since the price of Pepsi is lower.

P 6

Ɣ

6

C

Page 6 of 9

Question 6 (12 marks) Mike spends his income on gas for his car and food. The government raises the tax on gas, thereby raising the price of gas. But the government also lowers the income tax, thereby increasing Mike’s income. And this rise in income is just enough to place Mike on the same indifference curve as the one he was on before the price of gas rose. Will Mike buy more, less, or the same amount of gas as before these changes? Explain. Marks will be awarded only for your explanation. [Note: You don’t need to use diagrams to answer this question, but do so if you find it helpful]. The absolute increase in the price of gas also increases its relative price. Therefore, Mike will buy less gas and more food as a result of the substitution effect, that is, as a result of the increase in the relative price of gas Mike will buy less gas and more food if his real income were to remain constant (i.e., if he could remain on the same indifference curve).

Food

B

F2

The movement to a lower indifference curve as a result of the increase in the price of gas would represent the change in the quantity demanded of gas as a result of the income effect (while keeping relative prices constant at the new level). However, the reduction in income tax allows Mike to reach the same indifference curve as before and thus the income effect is offset. Therefore, Mike ends up buying less gas than before only as a result of the substitution effect. This result is also shown in the diagram on the right.

A

F1 BL2

BL3 G2

BL1

G1

Gas

Question 7 (9 marks) Consider the following table of long-run total cost for three different firms: Quantity

1

2

3

4

5

Firm A

$60

$70

$80

$90

$100

$110

6

$120

7

Firm B Firm C

$11 $21

$24 $34

$39 $49

$56 $66

$75 $85

$96 $106

$119 $129

Does each of these firms experience economies of scale or diseconomies of scale? Explain. Marks will be awarded only for your explanation. A firm experiences economies of scale when its LRAC curve is decreasing and diseconomies of scale when its LRAC curve is increasing. The table below shows the LRAC curves for these three firms. Here we can see that Firm A is exhibiting economies of scale while Firm B is exhibiting diseconomies of scale. In turn, Firm C exhibits first economies of scale up to level of output somewhere between 3 and 4 units and diseconomies of scale beyond that point. Quantity

1

2

3

4

5

Firm A Firm B

$60 $11

$35 $12

$26.7 $13

$22.5 $14

$20 $15

$18.3 $16

6

$17.1 $17

7

Firm C

$21

$17

$16.3

$16.5

$17

$17.7

$18.4

Page 7 of 9

Question 8 (18 marks) True or false? Explain your reasoning. Marks will be awarded only for your explanation. a) If the marginal product of labour is increasing, then short-run marginal cost must be decreasing. TRUE. By definition, the marginal product of labour is equal to the change in total product given a change in the quantity of labour: MPL = ¨Q / ¨L. Also by definition, marginal cost is equal to the change in total variable cost given a change in output: MC = ¨TVC / ¨Q. Since TVC = w*L, then MC = ¨TVC / ¨Q = w ¨L / ¨Q = w / (¨Q / ¨L) = w / MPL Therefore, if MPL increases, then MC must decrease.

b) When average product of labour reaches a maximum, short-run average variable cost reaches a minimum. TRUE. By definition, the average product of labour is equal to total product divided by the quantity of labour: APL = Q / L. Also by definition, average variable cost is equal to total variable cost divided by output: AVC = TVC / Q. Since TVC = w*L, then AVC = TVC / Q =wL/Q = w / (Q / L) = w / APL Therefore, when APL reaches a maximum, then AVC reaches a minimum.

c) A short-run average total cost can never be less than the long-run average total cost. TRUE. The short-run cost curves and the long-run cost curves are all derived from the same production function. The SRATC curve shows the lowest average cost of producing any output when K is fixed, and the LRAC curve shows the lowest average cost of producing any output when all inputs are variable. Therefore, no SRTAC curve can fall below the LRAC curve because as the level of output increases, input substitution in the long-run assures that the minimum possible cost per unit of output is achieved.

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d) In the long-run, choosing a higher level of fixed cost shifts the long-run average total cost curve upward.

FALSE. The long-run total cost function indicates the minimum cost of producing each level of output when all factors of production are variable. We can express this minimum cost for each level of output as a cost per unit of output, that is, we can express this minimum cost through the LRAC. Each point on the LRAC indicates the minimum cost of producing any level of output when all factors of production are variable. As output increases, the LRAC indicates the minimum cost of producing that level of output by increasing the size of the plant (i.e., by increasing the quantity of the fixed factor of production, capital). Therefore, changing the level of the fixed factor of production (and thus total fixed cost) represents a movement along the LRAC and not a shift of this curve.

e) A profit-maximizing firm should select the output level at which the difference between the market price and marginal cost is greatest.

FALSE. A profit-maximizing firm should choose the level of output at which MR = MC, that is, the level of output at which the last unit will increase total revenue by the same amount as it will increase total cost. Consider the case of perfect competition where MR = P, that is, where MR is constant. Also consider the general case where MC is an increasing function of output. Suppose that P > MC. In this situation, therefore, the firm will increase output since the additional unit will increase total revenue by more than it will increase total cost, and profits will increase. Suppose that P < MC. In this situation, therefore, the firm will decrease output since the additional unit will decrease total revenue by less than it will decrease total cost, and profits will increase. Therefore, the firm will maximize profits when P = MC. Here the firm cannot change the level of output in order to increase profits.

f)

An increase in fixed cost lowers the profit-maximizing quantity of output produced in the short-run.

FALSE. A profit-maximizing firm chooses the level of output at which MR = MC, that is, the level of output at which the last unit of output increases total revenue by the same amount as it increases total cost. Changes in TFC will affect TC, AC and AFC, but not MC, since TFC is not a function of output. Therefore, the increase in TFC will reduce the level of profits of the firm but it will not affect its decision as to how much to produce in the short-run.

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