Deck 8: A: Slutsky Equation

Question 1

John purchases two goods,x and y.Good x is an inferior good for some range of income.There must be another range of income for which good x is a normal good.

Answer 1

True

Question 2

Jimmy's utility function is U(a,b)= ab,where a is his consumption of apples and b is his consumption of bananas.If prices and income change in such a way that Jimmy's old consumption lies on his new budget line,then Jimmy will not change his consumption bundle.

Answer 2

False

Question 3

Walt considers x and y to be perfect substitutes.They originally cost $10 and $9 respectively.His income is $720.One day the price of x drops to $8.

A) The income effect increases the quantity of y by 90.
B) The substitution effect increases the quantity of y by 80.
C) The substitution effect increases the quantity of x by 90.
D) The income effect increases the quantity of x by 80.
E) None of the above.

Answer 3

The substitution effect increases the quantity of x by 90.

Question 4

Cindy consumes goods x and y.Her demand for x is given by x(p_x,m)= 0.04m -4.24p_x.Now her income is $322,the price of x is $2,and the price of y is $1.If the price of x rises to $3 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS,then

A) DI = 0 and DS = -2.00.
B) DI = -0.18 and DS = -0.52.
C) DI = -0.52 and DS =-0.52.
D) DI =-0.18 and DS =-4.06.
E) None of the above.

Question 5

When the price of a good rises and income remains constant,there is a substitution effect on demand but there cannot be an income effect.

Question 6

The Hicks version of the substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indifference curve as before the price change.

Question 7

If the Engel curve slopes up,then the demand curve slopes down.

Question 8

Jessica's preferences for peanut butter and jelly are represented by the utility function U(p,j)= min{2p,5j}.If prices and income change,but her old consumption bundle lies somewhere on her new budget line,she will not change her consumption.

Question 9

An increase in the price of a Giffen good makes the people who consume that good better off.

Question 10

The compensated demand function refers to the demand function of someone who is adequately paid for what he or she sells.

Question 11

Cindy consumes goods x and y.Her demand for x is given by x(p_x,m)= 0.05m -5.15p_x.Now her income is $419,the price of x is $3,and the price of y is $1.If the price of x rises to $4 and if we denote the income effect on her demand for x by DI and the substitution effect on her demand for x by DS,then

A) DI = -0.28 and DS = -0.52.
B) DI=-0.28 and DS =-4.88.
C) DI= -0.52 and DS =-0.52.
D) DI = 0 and DS = -2.00.
E) None of the above.

Question 12

The Slutsky substitution effect measures the movement between two points on the same indifference curve.

Question 13

If a good is an inferior good,then an increase in its price will increase the demand for it.

Question 14

In the case of homothetic preferences,the entire change in demand from a price change is due to the substitution effect.

Question 15

A consumer has the utility function U(x,y)=x +2y^1/2.The price of good x is 2 and the price of good y is 1.The consumer's income is 20.If the price of good y rises to 2,then entire change in demand for y is due to the substitution effect.

Question 16

Suppose a consumer has strictly convex preferences and her Engel curve for a good is a vertical line for some range of income.In that same income range,her demand curve for the good slopes down.

Question 17

A Giffen good must be an inferior good.

Question 18

A rational consumer prefers more of good x to less.If the price of good x rises and the prices of all other goods remain constant,then the consumer must necessarily demand less of x.

Question 19

Ivan spends his entire income on two goods.One of them is a Giffen good.If the price of the Giffen good rises,demand for the other good must fall.

Question 20

If two goods x and y are perfect complements,then if the price of x falls,the entire change in the demand for x is due to the income effect.

Question 21

Suppose that Agatha has $465 to spend on tickets for her trip.She intends to spend the entire amount $465 on tickets and prefers traveling first class to traveling second class.She needs to travel a total of 1,500 miles.Suppose that the price of first-class tickets is $.40 per mile and the price of second-class tickets is $.10 per mile.How many miles will she travel by second class?

A) 450
B) 600
C) 225
D) 550
E) 150

Question 22

When the price of x rises,Marvin responds by changing his demand for x.The substitution effect is the part of this change that represents his change in demand

A) holding the prices of substitutes constant.
B) if he is allowed to substitute as much x for y as he wishes.
C) if his money income is held constant when the price of x changes.
D) if the prices of all other goods are held constant.
E) None of the above.

Question 23

Ernest's income elasticity of demand for natural gas is 0.4.His price elasticity of demand for natural gas is -0.3,and he spends 10% of his income on natural gas.What is his substitution price elasticity?

A) -.26
B) -.34
C) .20
D) -.12
E) None of the above.

Question 24

Waldo consumes only apples and bananas and bananas are an inferior good for him.The price of apples increases,but there is an increase in his income that keeps him on the same indifference curve as before.(Waldo has convex preferences,and he prefers more to less of either good. )

A) After the change,Waldo will buy more bananas and fewer apples.
B) After the change,Waldo will buy fewer bananas and more apples.
C) After the change,Waldo will buy more of both goods.
D) After the change,Waldo will buy fewer of both goods.
E) We would need to know his utility function to determine whether any of the above statements are true.

Question 25

Charlie consumes apples and bananas.His utility function is U(X_A,X_B)=x_Ax²_B.The price of apples is $1 the price of bananas is $2,and his income is $30 per week.If the price of bananas falls to $1

A) Charlie demands fewer apples and more bananas.
B) the substitution effect of the fall in banana prices reduces his apple consumption,but the income effect increases his apple consumption by the same amount.
C) the substitution effect of the fall in the price of bananas reduces his banana consumption but the income effect increases his banana consumption by enough so that his banana consumption rises.
D) the income used to calculate the substitution effect is higher than his original income,since the change made Charlie better off.
E) More than one of the above is true.

Question 26

The following can be said about the income and substitution effects of a price increase on the demand for a good whose price rose:

A) The former is always positive and the latter is always negative.
B) Both can be either positive or negative.
C) While the latter is always negative,the former can be either positive or negative.
D) While the former is always negative,the latter can be either positive or negative.
E) The former can at times be negative,but it will never overwhelm the latter.

Question 27

Suppose that bananas are a normal good and Woody is currently consuming 100 bananas at a price of 10 cents each.

A) His Slutsky compensated demand curve going through this point is steeper than his ordinary demand curve.
B) His ordinary demand curve going through this point is steeper than his Slutsky compensated demand curve.
C) His ordinary demand curve is steeper to the left and his Slutsky compensated demand curve is steeper to the right of this point.
D) Whether his ordinary demand curve or his Slutsky compensated demand curve is steeper depends on whether his price elasticity is greater than 1.
E) None of the above.

Question 28

Herbie consumes two goods and his utility function is U(x₁,x₂)=x³₁x⁴₂.The price of good 2 does not change and his income does not change,but the price of good 1 decreases.

A) The substitution effect of the price change reduces the demand for good 2 and increases the demand for good 1.
B) The substitution effect reduces the demand for good 2,and since the income effect is zero,the demand for good 2 falls.
C) The substitution effect on the demand for good 2 is zero,since the price of good 2 did not change.
D) The income effect is zero,since his income remained constant.
E) More than one of the above statements is true.

Question 29

Charlie's utility function is x_Ax_B.The price of apples used to be $1 per unit and the price of bananas was $2 per unit.His income was $40 per day.If the price of apples increased to $1.50 and the price of bananas fell to $1.75,then in order to be able to just afford his old bundle,Charlie would have to have a daily income of

A) $23.75.
B) $47.50.
C) $96.
D) $71.25.
E) $190.

Question 30

Charlie's utility function is x_Ax_B.The price of apples used to be $1 per unit and the price of bananas was $2 per unit.His income was $40 per day.If the price of apples increased to $2.25 and the price of bananas fell to $1.25,then in order to be able to just afford his old bundle,Charlie would have to have a daily income of

A) $57.50.
B) $116.
C) $28.75.
D) $86.25.
E) $230.

Question 31

Neville from your workbook has a friend named Peregrine.Peregrine has the same demand function for claret as Neville,namely q = .02m - 2p,where m is income and p is price.Peregrine's income is $6,500 and he initially had to pay a price of $50 per bottle of claret.The price of claret rose to $60.The substitution effect of the price change

A) reduced his demand by 20.
B) increased his demand by 20.
C) reduced his demand by 14.
D) reduced his demand by 26.
E) reduced his demand by 24.

Question 32

Polly consumes crackers and fruit.The price of fruit rose and the price of crackers stayed constant.The income effect on Polly's demand is

A) zero because Polly's income didn't change.
B) the change in Polly's demand if her income is decreased by the change in the price of fruit times her old consumption of fruit.
C) the change in Polly's demand if her income is decreased by the total amount she used to spend on fruit.
D) the change in Polly's demand if her income is increased by the amount she used to spend on fruit.
E) the change in Polly's demand if her income is increased by the change in the price of fruit times the amount she used to buy.

Question 33

In 2000,Bruce spent his income on two goods,x and y.Between 2000 and 2001,the price of good x rose by 8% and the price of good y rose by 8%.In 2001,Bruce bought the same amount of x as he bought in 2000,but he bought more of good y than he had bought in 2000.

A) y is a normal good.
B) y is an inferior good.
C) x is an inferior good.
D) Nothing can be said about inferiority or superiority,since we don't know what happened to income.
E) Bruce is acting irrationally,since the relative prices of x and y did not change.

Question 34

Charlie's utility function is x_Ax_B.The price of apples used to be $1,the price of bananas used to be $2,and his income used to be $40.If the price of apples increased to $5 and the price of bananas stayed constant,the substitution effect on Charlie's apple consumption would reduce his consumption by

A) 4 apples.
B) 13 apples.
C) 8 apples.
D) 16 apples.
E) None of the above.

Question 35

Goods 1 and 2 are perfect complements and a consumer always consumes them in the ratio of 2 units of good 2 to 1 unit of good 1.If a consumer has an income of $120 and if the price of good 2 changes from $3 to $4,while the price of good 1 stays at $1,then the income effect of the price change

A) is 4 times as strong as the substitution effect.
B) does not change the demand for good 1.
C) is exactly twice as strong as the substitution effect.
D) accounts for the entire change in demand.
E) is 3 times as strong as the substitution effect.

Question 36

Charlie's utility function is x_Ax_B.The price of apples used to be $1,the price of bananas used to be $2,and his income used to be $40.If the price of apples increased to $6 and the price of bananas stayed constant,the substitution effect on Charlie's apple consumption would reduce his consumption by

A) 16.67 apples.
B) 5 apples.
C) 8.33 apples.
D) 13.33 apples.
E) None of the above.

Question 37

Ben consumes two goods and his utility function is U(x₁,x₂)=x²₁x⁴₂.The price of good 2 does not change and his income does not change,but the price of good 1 decreases.

A) The income effect is zero,since his income remained constant.
B) The substitution effect on the demand for good 2 is zero,since the price of good 2 did not change.
C) The substitution effect reduces the demand for good 2,and since the income effect is zero,the demand for good 2 falls.
D) The substitution effect of the price change reduces the demand for good 2 and increases the demand for good 1.
E) More than one of the above statements is true.

Question 38

Neville from your workbook has a friend named Cedric.Cedric has the same demand function for claret as Neville,namely q = .02m -2p,where m is income and p is price.Cedric's income is $6,000 and he initially had to pay a price of $40 per bottle of claret.The price of claret rose to $60.The substitution effect of the price change

A) reduced his demand by 24.
B) reduced his demand by 40.
C) reduced his demand by 56.
D) increased his demand by 40.
E) reduced his demand by 34.

Question 39

Rob consumes two goods,x and y.He has an allowance of $50 per week and is not endowed with either of the goods.If the price of good x increases and his substitution and income effects change demand in opposite directions,

A) good x must be a Giffen good.
B) good x must be an inferior good.
C) WARP is violated.
D) good x must be a normal good.
E) There is not enough information to judge whether good x is a normal or inferior good.

Question 40

Goods 1 and 2 are perfect complements and a consumer always consumes them in the ratio of 2 units of good 2 to 1 unit of good 1.If a consumer has an income of $300 and if the price of good 2 changes from $5 to $6,while the price of good 1 stays at $1,then the income effect of the price change

A) is 6 times as strong as the substitution effect.
B) does not change the demand for good 1.
C) accounts for the entire change in demand.
D) is exactly twice as strong as the substitution effect.
E) is 5 times as strong as the substitution effect.

Question 41

Gladys loves music and spends her money only on tapes and compact discs.She is always willing to trade 2 tapes for 1 compact discs.Originally,music stores sold compact disc for $9 each and tapes for $5 each.Then the price of compact discs fell to $8 each.The change in her consumption of compact discs that resulted was

A) entirely due to the substitution effect.
B) entirely due to the income effect.
C) partly due to the income effect and partly due to the substitution effect.
D) due to the income effect for low incomes and the substitution effect for high incomes.
E) There was no change in her demand for compact discs.

Question 42

Carlos consumes only two goods,apples and bananas.His utility function is given by U(x,y)=a³b².He is endowed with w_a apples and w_b bananas.Unaware that prices are about to change,Carlos buys the quantities of apples and bananas that maximize his utility subject to his budget constraint.After he has made his purchases but before he has eaten them,the relative prices change.Carlos is then free to make further trades at the new relative prices if he wishes.

A) Carlos will definitely be better off after the price change.
B) Carlos will definitely be worse off after the price change.
C) Carlos will be better off after the price change if the price of the good for which he is a net seller rises relative to the price of the other good.
D) Carlos will be better off after the price change if the price of the good for which he is a net buyer rises relative to the price of the other good.
E) Carlos's utility will not be affected by the price change.

Question 43

Carlos consumes only two goods,apples and bananas.His utility function is given by U(x,y)=min{x,2y}.He is endowed with w_a apples and w_b bananas.Unaware that prices are about to change,Carlos buys the quantities of apples and bananas that maximize his utility subject to his budget constraint.After he has made his purchases but before he has eaten them,the relative prices change.Carlos is then free to make further trades at the new relative prices if he wishes.

A) Carlos will definitely be better off after the price change.
B) Carlos will definitely be worse off after the price change.
C) Carlos will be better off after the price change if the price of the good for which he is a net seller rises relative to the price of the other good.
D) Carlos will be better off after the price change if the price of the good for which he is a net buyer rises relative to the price of the other good.
E) Carlos's utility will not be affected by the price change.

Question 44

Draw two different diagrams,one illustrating the Slutsky version of income and substitution effects and the other illustrating the Hicks version of income and substitution effects.How do these two notions differ?

Question 45

A taxpayer says,"Sure I pay a lot of income tax,but I don't mind because I get back just as much money as I pay in." Assuming that his facts are correct,explain why the taxpayer's reasoning is faulty.Use a diagram to show that an income tax can make a person worse off even if he is rebated an amount of money equal to what he paid in.

Question 46

Suggest at least one reason why it might be worth the trouble it takes to learn how to decompose the effects of a price change into an income effect and a substitution effect.

Question 47

What conditions ensure that the quantity of a good demanded increases as its price falls? Explain your answer,using diagrams.

Question 48

Suppose that Agatha has $825 to spend on tickets for her trip.She intends to spend the entire amount $825 on tickets and prefers traveling first class to traveling second class.She needs to travel a total of 1,500 miles.Suppose that the price of first-class tickets is $.60 per mile and the price of second-class tickets is $.30 per mile.How many miles will she travel by second class?

A) 125
B) 400
C) 350
D) 250
E) 83.33

Question 49

Use a diagram to prove that in case there are two goods,the substitution effect of an increase in the price of good x reduces the demand for good x.

Question 50

Maude thinks delphiniums and hollyhocks are perfect substitutes,one for one.If delphiniums currently cost $2 per unit and hollyhocks cost $3 per unit and if the price of delphiniums rises to $7 per unit,

A) there will be no change in the demand for hollyhocks.
B) the income effect of the change in demand for delphiniums will be bigger than the substitution effect.
C) 1/5 of the change will be due to the income effect.
D) the entire change in demand for delphiniums will be due to the substitution effect.
E) 4/5 of the change will be due to the income effect.

Question 51

Maude thinks delphiniums and hollyhocks are perfect substitutes,one for one.If delphiniums currently cost $5 per unit and hollyhocks cost $6 per unit and if the price of delphiniums rises to $8 per unit,

A) the income effect of the change in demand for delphiniums will be bigger than the substitution effect.
B) there will be no change in the demand for hollyhocks.
C) the entire change in demand for delphiniums will be due to the substitution effect.
D) 1/3 of the change will be due to the income effect.
E) 2/3 of the change will be due to the income effect.