S2012 - Solution to Test 2 - ECO100 - June 26, 2012...ECO 100Y INTRODUCTION TO ECONOMICS Midterm...

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Department of Economics Prof. Gustavo Indart University of Toronto June 26, 2012

ECO 100Y INTRODUCTION TO ECONOMICS

Midterm Test # 2

LAST NAME

FIRST NAME

STUDENT NUMBER

Check your section of the course: □ L0101 (M/W from 2:00 to 4:00 PM) □ L0201 (T/R from 2:00 to 4:00 PM) INSTRUCTIONS:

1. The total time for this test is 1 hour and 50 minutes. 2. Aids allowed: a simple calculator. 3. Write with pen instead of pencil.

DO NOT WRITE IN THIS SPACE

Part I /25

Part II 1. /5

2. /5

3. /5

4. /5

5. /5

Part III 6. /15

7. /10

TOTAL /75

SOLUTIONS

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PART I (25 marks) Instructions: Enter your answer to each question in the table below. Only the answers recorded in the table will be marked. Table cells left blank will receive a zero mark for that question. Each question is worth 2.5 marks. No deductions will be made for incorrect answers.

1 2 3 4 5 6 7 8 9 10

B D C A C B B D E B

1. The average product for six workers is 18. If the marginal product for the seventh worker is 15, which one of the following statements is correct?

A) Marginal product is rising and average product is falling. B) Both marginal product and average product are falling. C) Marginal product is falling and average product is rising. D) Both marginal product and average product are rising. E) Not enough information to determine which one is correct.

2. Suppose fixed cost is $500 and average variable cost is $20 at all levels of output. Given

this information, which one of the following statements is true? A) Marginal cost will be less than average variable cost. B) Average total cost will be constant. C) Marginal cost will equal average total cost. D) Average total cost will always decrease as output increases. E) None of the above is true.

Use this space as scrap paper.

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3. When the 5th unit of labour is hired, total product increases from 100 to 120 units of output per unit of time. Given this information, which one of the following statements is true?

A) Marginal product must be increasing. B) Marginal product must be greater than average product. C) Marginal product must be decreasing. D) Marginal product must be constant. E) Not enough information to determine which one is true.

4. For a certain firm, total cost is $100 at 5 units of output and $130 for 6 units. In that range of

output, which one of the following statements is true? A) Marginal cost is rising and greater than average total cost. B) Marginal cost is decreasing and less than average total cost. C) Marginal cost is rising and less than average total cost. D) Marginal cost is decreasing and greater than average total cost. E) Not enough information to determine which one is true.

5. A firm is using its plant to produce 500 units of output daily. Its marginal cost at this output is

$8.00; its average cost is $7.50; its average variable cost is $4.00. Therefore, the daily fixed cost associated with this plant must be

A) $7.50. B) $750. C) $1,750. D) $3,750. E) none of the above.


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Table 1 shows the marginal cost, average variable cost, and average (total) cost of producing various quantities of a commodity by a profit-maximizing firm in a perfectly competitive industry.

Table 1 Output (units) 3 5 8 10 20Marginal Cost $8 $10 $15 $30 $45Average Variable Cost … $10 … 22.5 …Average Cost $40 $25 $27.375 … $33.75

6. Given the information in Table 1 above, what is the firm’s total fixed cost? A) $36. B) $75. C) $84. D) $96. E) It cannot be determined with the information provided.

7. A perfectly competitive firm’s marginal cost is $35, its average cost is $40, its average

variable cost is $30, and its output is 800 units. What is its total cost of producing 801 units? A) Less than 32,000. B) More than 32,035 but less than 32,040. C) 32,035. D) More than 32,000 but less than 32,035. E) None of the above.

8. Jack has a monthly income of $85 which he spends on books (measured on the X-axis) and

CDs (measured on the Y-axis). The price of books is $20 a piece and the price of CDs is $5 a piece. Jack buys 3 books and 5 CDs each month. With this consumption bundle, his MRS of books for CDs is 4. Given this information, which one of the following statements is true?

A) Jack could increase his utility by buying more CDs and fewer books. B) Jack could increase his utility by buying more books and fewer CDs. C) Jack could increase his utility by buying more CDs and more books. D) Jack is maximizing his utility at the present consumption bundle. E) Not enough information to determine which one is true.


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Diagram 1: Rachel’s Budget Lines

9. Refer to Diagram 1 above. Suppose that Rachel’s budget line has changed from BL1 to BL2. Which one of the following would explain the change in Rachel’s budget line?

A) Both the price of food and Rachel’s income increased. B) Both the price of clothing and Rachel’s income decreased. C) The price of food increased and Rachel’s income decreased. D) The price of food decreased and Rachel’s income increased. E) Both the price of food and Rachel’s income decreased.

10. John consumes only two goods: Good X and Good Y. Good X is an income-independent

good for John. He is presently consuming a combination of X and Y that allows him to maximize his utility. If the price of Good X increases and John wishes to maximize his utility, which one of the following statements is correct?

A) John will definitely decrease his consumption of Good X but will increase his consumption of Good Y.

B) John will definitely decrease his consumption of Good X but his consumption of Good Y could either increase or decrease.

C) John will definitely decrease his consumption of both Good X and Good Y. D) John will definitely decrease his consumption of Good Y but will keep his

consumption of Good X unchanged. E) John will definitely decrease his consumption of Good Y but will increase his

consumption of Good X.


BL1 Q

uant

ity o

f clo

thin

g

Quantity of food

BL2

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PART II (25 marks) Instructions: Answer all questions in the space provided. Each question is worth 5 marks.

1. Jessica spends all her disposable income on video games [X-axis good] and books [Y-axis good]. The price of video games increases. Jessica has a negative income elasticity for video games and her substitution effect is always greater than her income effect.

Statement: Samantha believes that Jessica will purchase fewer video games after the price increase, her income-consumption line will be negatively sloped, and her demand curve for video games will have a positive slope.

Position: Do you agree with Samantha’s beliefs? Use a proper consumer indifference curve diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Samantha’s beliefs.

When the price of VGs is P1, Jessica maximizes her utility by consuming bundle A on indifference curve IC1. This combination of price and quantity is also one point on her demand curve — point A’. When the price of VGs increases to P2, Jessica’s budget line rotates inward to BL2. She cannot any longer enjoy the level of utility represented by indifference curve IC1 — her new utility-maximizing bundle will necessarily lay on a lower indifference curve. But will she end up consuming more or less VGs than before? The total change in the quantity demanded as a result of the price increase can be split into the substitution and the income effects. The substitution effect is the change in the quantity demanded as a result of the change in relative prices while keeping real income constant, i.e., while remaining on the same indifference curve IC1. The new relative prices is given by the slope of the new budget line BL2, and indifference curve IC1 has the same slope as the new budget line at point B. Therefore, the decrease in the quantity demanded of VGs from VGA to VGB represents the substitution effect. VGs are an inferior good for Jessica since her income elasticity for video games is negative. Therefore, as we allow now real income to fall — i.e., to move to a lower indifference curve — while keeping relative prices constant at the new level, Jessica’s quantity demanded increases. The substitution and the income effects move in opposite directions but, since we are told that the substitution effect is (in absolute value) always greater than the income effect, the total effect is a decrease in the quantity demanded. As shown in the diagram, Jessica consumes now bundle C. Therefore, the increase in the quantity demanded of VGs from VGB to VGC represents the income effect. This new combination of price and quantity is another point on her demand curve — point C’. So Samantha is correct that Jessica will buy fewer VGs after the increase in price. She is also correct that Jessica’s income consumption line has a negative slope since VGs are an inferior good for her. But Samantha is incorrect with respect to the slope of Jessica’s demand curve — the slope is negative since as price increases, Jessica’s quantity demanded decreases.

BA

BB

BC

C’

VGA VGB

VGC VG

BL1 BL2

ICL

IC2

s.e. i.e.

B

C

A

VGA

VGC

IC1

VG

P

P1

P2

A’

D

B

Demand Curve

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2. As more labour is used in the process of production, it is generally assumed that the marginal product of labour first increases, it reaches a maximum at some point, and then it decreases.

Statement: Kalifa, an ECO100 student who misses classes regularly, believes that diminishing marginal productivity starts at the quantity of labour at which a straight line through the origin is tangent to the total product curve.

Position: With the help of a proper diagram explain whether you agree or disagree with Kalifa’s belief.

L

L

TP TP

AP

MP

APL MPL

A

A’

B’

B

LB

LB

LA

LA

The marginal product of labour (MPL) represents the change in total product (TP) given a change in the quantity of labour, i.e., it is equal to the slope of the TP curve. In the general case, it is assumed that as labour (L) increases the MPL first increases, reaches a maximum, and then decreases—i.e., the TP curve first becomes steeper as L increases and then it becomes flatter as L continues to increase. This is shown in the diagram on the left. The point of inflection on the TP curve (point A) represents the level of L at which the MPL reaches a maximum (LA). Therefore, it is at LA that diminishing MPL starts — and thus I disagree with Kalifa’s belief.

The average product of labour (APL) is the TP per unit of L, i.e., it is equal to TP/L. At any point on the TP curve, the corresponding APL is represented by the slope of a straight line joining that point to the origin. The slope of the straight line joining point A to the origin (as shown in the diagram) is steeper than the slope of the TP curve at that point, which means that MPL > APL at LA. The diagram also shows that as L increases, APL first increases, reaches a maximum (at point B), and then decreases as L continues to increase. It is, therefore, diminishing average (and not marginal) productivity that starts at the quantity of L at which a straight line through the origin is tangent to the TP curve.

Also note that at LB, MPL = APL; for L < LB, MPL > APL and thus APL is increasing; and for L < LB, MPL < APL and thus APL is decreasing.

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3. Assita consumes only tuna [X-axis good] and lamb chops [Y-axis good]. The price of tuna falls. In order to maximize her level of consumer satisfaction, Assita chooses to purchase the same quantity of tuna after the decrease in price.

Statement: Christelle, another economics student who misses classes regularly, believes that Assita’s behaviour is not consistent with consumer theory.

Position: Do you agree with Christelle’s view? Use a proper consumer indifference curve diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Christelle’s beliefs.

When the price of tuna is P1, Assita maximizes her utility by consuming bundle A on indifference curve IC1. When the price of tuna decreases to P2, Assita’s budget line rotates outward to BL2. She can now enjoy a higher level of utility than the one represented by indifference curve IC1 — her new utility-maximizing bundle will necessarily lay on a higher indifference curve. But can she end up consuming the same quantity of tuna as before? The total change in the quantity demanded as a result of the price decrease can be split into the substitution and the income effects. The substitution effect is the change in the quantity demanded as a result of the change in relative prices while keeping real income constant, i.e., while remaining on the same indifference curve IC1. The new relative prices is given by the slope of the new budget line BL2, and indifference curve IC1 has the same slope as the new budget line at point B. Therefore, the increase in the quantity demanded of tuna from TA to TB represents the substitution effect.

The income effect is the change in the quantity demanded as a result of the increase in real income, while keeping relative prices constant at the new level (i.e., moving to a higher indifference curve tangent to the new budget line). Therefore, the change in the quantity demanded as a result of the income effect could be positive (normal good), negative (inferior good), or nil (income-independent good). Since Assita ends up consuming the same quantity of tuna as its price falls, the income effect offsets the substitution effect (i.e., they move in opposite directions but are of the same absolute value) and thus tuna is an inferior good for Assita. This is represented in the diagram below as the movement from point B on the higher indifference curve to point C on the lower indifference curve.

Therefore, I disagree with the statement: Assita’s behaviour is consistent with consumer theory.

LC

TA

A

B

C

s.e.

i.e. BL1 BL2

IC1

IC2

T TB

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4. Abdul spends all his disposable income on steak [X-axis good] and tuna fish [Y-axis good]. Abdul’s income and the substitution effects for steak work in the same direction but the substitution effect is greater than the income effect. The price of steak increases.

Statement: Jad, a good friend of Abdul, suggests that as a result of this price increase, Abdul would now maximize his level of consumer satisfaction by purchasing fewer units of steak; his income consumption curve would have a negative slope; and Abdul’s demand curve for steak would also have a negative slope.

Position: Do you agree with Jad’s suggestions? Use a proper consumer indifference curve diagram to analyze this situation and indicate, with reasons, whether you agree or disagree with Jad’s suggestions.

When the price of steaks is P1, Abdul maximizes his utility by consuming bundle A on indifference curve IC1. This combination of price and quantity is also one point on his demand curve — point A’. When the price of steaks increases to P2, Abdul’s budget line rotates inward to BL2. He cannot any longer enjoy the level of utility represented by indifference curve IC1 — his new utility-maximizing bundle will necessarily lay on a lower indifference curve. But will he end up consuming more or less stakes than before? The total change in the quantity demanded as a result of the price increase — i.e., the decrease in the quantity demanded of steaks from SA to SC — can be split into the substitution and the income effects. The substitution effect is the change in the quantity demanded as a result of the change in relative prices while keeping real income constant, i.e., while remaining on the same indifference curve IC1. The new relative prices is given by the slope of the new budget line BL2, and indifference curve IC1 has the same slope as the new budget line at point B. Therefore, the decrease in the quantity demanded of steaks from SA to SB represents the substitution effect. Steaks are a normal good for Abdul since his substitution and income effects move in the same direction. Therefore, as we allow real income to fall — i.e., move to a lower indifference curve — while keeping relative prices constant at the new level, Abdul’s quantity demanded decreases further. As shown in the diagram, Abdul consumes now bundle C and thus the decrease in the quantity demanded of steaks from SB to SC represents the income effect. This new combination of price and quantity is another point on her demand curve — point C’. So Jad is correct that Abdul will buy fewer steaks after the increase in price. He is also correct that Abdul’s demand curve for steaks has a negative slope since as price increases, his quantity demanded decreases. But Jad is incorrect with respect to the slope of Abdul’s income consumption line since it could be either positive or negative. Indeed, if food is a normal good (as it is implicitly assumed in the diagram), then the income consumption line will have a positive slope; but if food is an inferior good, then the income consumption line will have a negative slope.

FA

FB

FC

C’

SA SB

SC S BL1

BL2

ICL

IC2 s.e. i.e.

F

C

A

SA

SC

IC1

S

P

P1

P2

A’

D

B

Demand Curve

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5. Stephenny’s marginal rate of substitution (MRS) between coffee (X-axis good) and donuts (Y-axis good) is 3. Stephenny’s tastes change after reading that coffee is bad for one’s health.

Statement: Joudi, a good student of economics, is of the view that Stephenny’s MRS will now be less than 3 at the initial consumption bundle.

Position: Do you agree with Joudi’s view? Analyze this situation and indicate, with reasons, whether you agree or disagree with Joudi’s view.

Let’s assume that Stephenny is initially maximizing her utility and thus at the utility-maximizing bundle her MRS = PC/PD = 3, where PC is the price of coffee and PD is the price of donuts. After reading that coffee is bad for one’s health, Stephenny’s tastes change, i.e., the shapes of her indifference curves change.

The new information about the impact of coffee on one’s health decreases the utility or satisfaction that Stephenny gets from consuming coffee. In other words, the additional utility or satisfaction of consuming each cup of coffee is now lower than before, i.e., her MUC has decreased for each and every cup of coffee. Given that MRS = MUC/MUD and that her MRS was equal to 3 before, at the initial equilibrium bundle her MRS will now be less than 3 since MUC decreased.

Therefore, I agree with Joudi’s view.

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PART III (25 marks)

Instructions: Answer all questions in the space provided.

6. (15 marks) Alexander has a monthly income of $200 which he totally spends on gas for his car and food. Gas is an income-independent good for Alexander. The price of gas is $2.00 per litre and the price of food is $2.50 per unit.

a) Write the expression for Alexander’s budget line. Sketch Alexander’s budget line in the above diagram. (2 marks)

E = PF*F + PG*G

F = E/PF – (PG/PF) G

200 = 2.50 F + 2.00 G

F = 200/2.50 – (2.00/2.50) G

F = 80 – 0.8 G

Food

(uni

ts p

er m

onth

)

Gas (litres per month) 50 100 35

B

80

40

20

60

25

C

A

75

70

70 40

10 BL1

BL2

I3

I2

I1

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b) Suppose that at the utility maximizing combination of food and gas, Alexander consumes 50 litres of gas per month. How many units of food does Alexander consume when maximizing his utility? (Show how you obtained this figure.) Without drawing any indifference curve, show this utility-maximizing equilibrium in your diagram (label it point A). (2 marks)

Since F = 80 – 0.8 G, if G = 50 then:

F = 80 – 0.8 (50) = 80 – 40 = 40

c) Suppose now that the government raises the tax on gas, thereby raising the price of gas to $5.00 a litre. Draw Alexander’s new budget line in your diagram. If at the new utility maximizing combination of food and gas Alexander consumes now 10 units of food per month, how many litres of gas does Alexander consume per month? (Show how you obtained this figure.) Without drawing any indifference curve, show this utility-maximizing equilibrium in your diagram (label it point B). (2 marks)

Budget line: F = E/PF – (PG/PF) G

F = 200/2.50 – (5.00/2.50) G

F = 80 – 2 G

Since F = 80 – 2 G, if F = 10 then:

10 = 80 – 2 G

2G = 70

G = 35

d) After the increase in the tax on gas, the government lowers the income tax, thereby increasing Alexander’s disposable income just enough to allow him to afford bundle A of part b) above. What is Alexander’s new level of disposable income? (Show how you obtained this figure.) (2 marks)

Since Alexander’s budget line is now E = 5.00 G + 2.50 F and bundle A consists of F = 40 and G = 50, then:

E = 5.00 (50) + 2.50 (40) = 250 + 100 = 350

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e) Keeping in mind that gas is an income-independent good for Alexander, how many units of food does Alexander consume now per month? (Show how you obtained this figure.) Without drawing any indifference curve, show this utility-maximizing equilibrium in your diagram (label it point C). (2 marks)

Budget line: F = E/PF – (PG/PF) G

F = 350/2.50 – (5.00/2.50) G

F = 140 – 2 G

Since G is an income-independent good, G = 35 when income increases from $100 to $350. Therefore, F = 140 – 2 (35) = 140 – 70 = 70

f) Assuming smooth and convex indifference curves, draw in your diagram Alexander’s initial indifference curve (i.e., the one he was on before the increase in the price of gas) and the one he reached after the increase in the price of gas but before the decrease in the income tax. (2 marks)

g) Comparing bundles A and C, which one will Alexander prefer? Why? Briefly explain. (3 marks)

Alexander would not be maximizing his utility if he were to consume bundle A. Indeed, given his new budget line after the income-tax reduction, MRS < PG/PF at point A since his MRS is 0.8 and relative prices is 2. Therefore, keeping in mind that MRS = MUG/MUF, to maximize his utility Alexander should increase the quantity consumed of food and reduce the quantity consumed of gas until MRS = 2. Indeed, by moving up along his budget line he reaches higher and higher indifference curves until he achieves a new equilibrium when his MRS = 2.

As shown in the diagram, Alexander will be maximizing his utility when consuming bundle C — at this point, his MRS is equal to 2 and he is reaching the highest possible indifference curve.

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7. (10 marks) Martine owns a small fruit juice shop close to the St. George campus. She pays each of her workers $50 per day. The cost of her other variable inputs (e.g., fruits, cups, etc.) is $0.50 per cup of juice. Her fixed cost is $180 per day. Martine estimates that her daily production when she varies the number of workers she employs is as follows:

Quantity of labour (workers) 0 1 2 3 4 5 6 Quantity of fruit juice (cups) 0 100 210 330 440 540 630

a) What is the MP of the fourth worker? What is the AP of the first five workers? (2 marks) As the quantity of labour increases from 3 to 4 workers the total output increases from 330 to 440 cups of fruit juice per day, the marginal product of the fourth worker is 110 cups of fruit juice per day.

MP = TP / L = 110. Since AP = TP / L, the AP of the first five workers is:

AP = TP / L = 540 / 5 = 108. b) What is Martine’s average variable cost (AVC) when she produces 210 cups of fruit

juice? (2 marks) Martine’s total variable cost (TVC) includes the cost of labour plus the cost of her other variable inputs (fruits, cups, etc.). Therefore, her TVC of producing 210 cups of fruit juice per day is the cost of two units of labour plus the cost of her other variable inputs: TVC (210) = 50 (2) + 0.50 (210) = 100 + 105 = 205. Therefore, her AVC when Q = 210 is: AVC (210) = TVC (210) / 210 = 205 / 210 = 0.976.

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c) What is Martine’s total average cost (ATC) when she produces 330 cups of fruit juice? (2 marks)

Martine’s total cost (TC) of producing 330 cups of fruit juice includes her total fixed cost (TFC) and her TVC. Her TFC is $180 per day. Her TVC includes the cost of labour plus the cost of her other variable inputs (fruits, cups, etc.). Therefore, her TVC of producing 330 cups of fruit juice per day is the cost of three units of labour plus the cost of her other variable inputs:

TFC = 180

TVC (330) = 50 (3) + 0.50 (330) = 150 + 165 = 315

and thus,

TC (330) = 180 + 315 = 495.

Therefore, her ATC when Q = 330 is:

ATC (330) = TC (330) / 330 = 495 / 330 = 1.5.

d) What is the marginal cost (MC) per cup of juice for the first 100 cups of juice? (2 marks)

Martine’s MC per cup of juice is the increase in total cost divided by the increase in output:

MC = TC / Q.

The increase in TC is equal to the increase in TVC, which includes the cost of labour plus the cost of all the other variable inputs. Since on unit of labour is required to produce the first 100 cups of juice, the MC per cup of producing the first 100 cups is:

TC = 50 (1) + 0.50 (100) = 50 + 50 = 100.

Therefore,

MC = TC / Q = 100 / 100 = 1.

e) Suppose that her fixed cost increases to $210 per day. What is now the MC per cup of

juice for the first 100 cups of juice? (2 marks) An increase in the price of a fixed input (factor of production) does not affect MC. Indeed, MC is the additional cost of producing additional output and TFC does not change as more output is produced — only the quantities of the variable inputs change as more output is produced.

Indeed, the TC of producing zero output is now $210 (instead of $180) and the TC of producing 100 cups is:

TC(100) = TFC + TVC(100)

where TVC(100) = 50 (1) + 0.50 (100) = 100

and thus TC(100) = 210 + 100 = 310.

Therefore, MC(100) = TC / Q = 100 / 100 = 1 as before.

S2012 - Solution to Test 2 - ECO100 - June 26, 2012...ECO 100Y INTRODUCTION TO ECONOMICS Midterm...

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Transcript of S2012 - Solution to Test 2 - ECO100 - June 26, 2012...ECO 100Y INTRODUCTION TO ECONOMICS Midterm...