Question 1

Compute the MRS for the following utility functions:
a.U(X,Y)= aln(X)+ bln(Y),
b.U(X,Y)=XᵃYᵇ,and
c.U(X,Y)=aX + bY,
where a and b are strictly positive constants.

Accepted Answer

The answer of Compute the MRS for the following utility...

Question 2

Joe consumes crawfish and shrimp.His utility function exhibits diminishing marginal utility of crawfish but the marginal utility of shrimp is constant.Will Joe's indifference curves be convex?

Accepted Answer

The answer of Joe consumes crawfish and shrimp.His utility function...

Question 3

What is the difference between ordinal and cardinal measurement?

Accepted Answer

The answer of What is the difference between ordinal and...

Question 4

Suppose sugar and artificial sweeteners are perfect substitutes for Sam.Her indifference curves for those two goods would be
A) downward-sloping and convex to the origin.
B) downward-sloping and straight lines.
C) L-shaped.
D) downward-sloping and concave to the origin.

Accepted Answer

If sugar and artificial sweeteners are perfect substitutes, the consumer is indifferent between consuming one unit of sugar and one unit of artificial sweetener. This means that the indifference curves are straight lines with a slope of -1, which represent all the combinations of sugar and artificial sweetener that give the same level of utility to the consumer.

Question 5

Joe's income is $500,the price of food (F)is $2 per unit,and the price of shelter (S)is $100.Which of the following represents his budget constraint?
A) 500 = 2F + 100S
B) F = 250 - 50S
C) S = 5 - .02F
D) All of the above

Accepted Answer

All the options represent the same budget constraint but in different forms. Option A directly states the budget constraint. Options B and C rearrange the equation in A to solve for F and S, respectively.

Question 6

Paul has the utility function U(q₁,q₂)= q₁q₂.If Paul consumes q₁ = 4 and q₂ = 2 his Marginal Rate of Substitution is
A) -2.
B) 1.
C) -1.
D) ₋₁/₂.

Accepted Answer

The answer of Paul has the utility function U(q₁,q₂)= q₁q₂.If...

Question 7

A friend whom you are studying with for this class has drawn three sets of indifference curves.Explain what he has done wrong on each graph and what assumption of preferences is violated by each particular graph.
(a) (b) (c)

Accepted Answer

The answer of A friend whom you are studying with...

Question 8

Joe's income is $500,the price of food (F)is $2 per unit,and the price of shelter (S)is $100.Which of the following represents his marginal rate of transformation of food for shelter?
A) -5
B) -50
C) -.02
D) None of the above

Accepted Answer

The formula for the marginal rate of transformation of food for shelter is the change in food divided by the change in shelter (-ΔF/ΔS). Since the price of food is constant at $2 per unit, we can use Joe's income and the price of shelter to calculate the maximum amount of shelter he can afford: $500 - $2F = $100S. Solving for F, we get F = 200 - 0.2S. Taking the derivative of this equation with respect to S gives us -0.2, which represents the change in food for a one-unit increase in shelter. Therefore, the marginal rate of transformation of food for shelter is -0.2/-1 = 0.2, or -50 when expressed as a ratio.

Question 9

Clifford lives by the motto "Eat drink and be merry today,for tomorrow doesn't matter." If today's consumption is represented by "x" and tomorrow's consumption is represented by "y",then which of the following best represents Clifford's utility function?
A) U = x - y
B) U = x/y
C) U = x
D) U = y

Accepted Answer

Clifford's motto suggests that he only values consumption in the present, and does not consider future consumption. Therefore, his utility function would only depend on today's consumption, represented by "x". Option C, U = x, represents this most accurately. Option A, U = x - y, suggests that Clifford considers tomorrow's consumption as well, which is contradictory to his motto. Option B, U = x/y, suggests that the ratio of today's consumption to tomorrow's consumption is important to Clifford, which is also not in line with his motto. Option D, U = y, suggests that today's consumption is not important to Clifford at all, which again contradicts his motto.

Question 10

All of the following utility functions rank bundles (q₁,q₂)in the same order except for which one? A) q₁^1/2 + q₂^1/2 B) q₁^1/2q₂^1/2 C) ln(q₁) + ln(q₂) D) All of the above rank bundles (q1,q2) in the same order

Accepted Answer

The answer of All of the following utility functions rank...

Question 11

For the following, please answer "True" or "False" and explain why
-The fact that most consumers are unable to describe their preferences in terms of a utility function implies that not all consumer preferences can be represented with utility functions.

Accepted Answer

Utility functions are used to represent the order of rankings an individual has,but this does not imply that consumers are aware of such a function when making their choices.

Question 12

Which of the following utility functions has the same MRS as U(q₁,q₂)= q₁ q₂? A) q₁^1/2 q₂^1/2 B) q₁ + q₂ C) q₁^1/2 + q₂^1/2 D) (q₁^1/2+ q₁^1/2)²

Accepted Answer

The answer of Which of the following utility functions has...

Question 13

Sarah has the utility function U(X,Y)=X.⁵Y.²⁵.When Sarah consumes X = 2 and Y = 6 she has a marginal rate of substitution of
A) -12.
B) -1/6.
C) -6.
D) ₋₁/₁₂.

Accepted Answer

The answer of Sarah has the utility function U(X,Y)=X.⁵Y.²⁵.When Sarah...

Question 14

Ed has the utility function U(F,M)=  ,where C = number of comic books per month and M=number of movies per month.Gloria has the utility function V(F,M)= 15 +  .Do Ed and Gloria have the same preference ordering of comics and movies? How can you tell?

Accepted Answer

The answer of Ed has the utility function U(F,M)= ...

Question 15

Suppose Joe's utility for lobster (L)and soda (S)can be represented as U = L⁰.⁵ S⁰.⁵.Draw the indifference curve that yields a utility level of 9.Calculate the MUL,MUS,and MRS of L for S on that indifference curve when S = 3.

Accepted Answer

The answer of Suppose Joe's utility for lobster (L)and soda...

Question 16

For the following, please answer "True" or "False" and explain why
-The absolute value of the slope of an indifference curve equals the ratio of the marginal utilities of the two goods involved.

Accepted Answer

The MRS can be represented as the ratio of both those quantities.

Question 17

Blutarsky is throwing a party at his Fraternity and is trying to choose what booze to buy.A bottle of vodka has four times the alcohol as a six-pack of beer.If Blutarsky only cares about the total amount of alcohol in his basket,what is his marginal rate of substitution of bottles of vodka for six-packs of beer? Devise a utility function to represent these preferences.

Accepted Answer

The answer of Blutarsky is throwing a party at his...

Question 18

Teddy has preferences given by the utility function U(K,L)= 2L + K where K = pounds of Kale per month and L = pounds of lettuce per month.What is Teddy's Marginal Utility of Kale? What is Teddy's Marginal Utility from Lettuce? If Kale is on the horizontal axis,what is Teddy's marginal Rate of Substitution?

Accepted Answer

The answer of Teddy has preferences given by the utility...

Question 19

Amanda consumes only two goods,X and Y.Her indifference curves satisfy the four standard assumptions.True or False: If she is indifferent between bundles (1,3)and (3,1),then bundle (2,2)must be strictly preferred.

Accepted Answer

Convexity implies that for any two bundles a consumer is indifferent to,any bundle that is a convex combination of the two is strictly preferred.(2,2)= 11ea57b3_0ced_e0cb_ace2_c1d23ecf2c92_TB5321_11 (3,1)+ 11ea57b3_0ced_e0cc_ace2_65e570124e94_TB5321_11 (1,3)
 11ea57b3_0cee_07dd_ace2_bf9751769e5e_TB5321_00

Question 20

Show that the utility functions V(X,Y)= XᵃY¹⁻ᵃ and U(X,Y)= a ln(X)+ (1-a)ln(Y)represent the same ordering of bundles.

Accepted Answer

The answer of Show that the utility functions V(X,Y)= XᵃY¹⁻ᵃ...

Quiz 3: A Consumers Constrained Choice

Compute the MRS for the following utility functions: a.U(X,Y)= aln(X)+ bln(Y), b.U(X,Y)=XᵃYᵇ,and c.U(X,Y)=aX + bY, where a and b are strictly positive constants.

Joe consumes crawfish and shrimp.His utility function exhibits diminishing marginal utility of crawfish but the marginal utility of shrimp is constant.Will Joe's indifference curves be convex?

What is the difference between ordinal and cardinal measurement?

Suppose sugar and artificial sweeteners are perfect substitutes for Sam.Her indifference curves for those two goods would be

Joe's income is $500,the price of food (F) is $2 per unit,and the price of shelter (S) is $100.Which of the following represents his budget constraint?

Paul has the utility function U(q₁,q₂) = q₁q₂.If Paul consumes q₁ = 4 and q₂ = 2 his Marginal Rate of Substitution is

A friend whom you are studying with for this class has drawn three sets of indifference curves.Explain what he has done wrong on each graph and what assumption of preferences is violated by each particular graph. (a) (b) (c)

Joe's income is $500,the price of food (F) is $2 per unit,and the price of shelter (S) is $100.Which of the following represents his marginal rate of transformation of food for shelter?

Clifford lives by the motto "Eat drink and be merry today,for tomorrow doesn't matter." If today's consumption is represented by "x" and tomorrow's consumption is represented by "y",then which of the following best represents Clifford's utility function?

All of the following utility functions rank bundles (q₁,q₂) in the same order except for which one?

For the following, please answer "True" or "False" and explain why -The fact that most consumers are unable to describe their preferences in terms of a utility function implies that not all consumer preferences can be represented with utility functions.

Which of the following utility functions has the same MRS as U(q₁,q₂) = q₁ q₂?

Sarah has the utility function U(X,Y) =X.⁵Y.²⁵.When Sarah consumes X = 2 and Y = 6 she has a marginal rate of substitution of

Ed has the utility function U(F,M)= ,where C = number of comic books per month and M=number of movies per month.Gloria has the utility function V(F,M)= 15 + .Do Ed and Gloria have the same preference ordering of comics and movies? How can you tell?

Suppose Joe's utility for lobster (L)and soda (S)can be represented as U = L⁰.⁵ S⁰.⁵.Draw the indifference curve that yields a utility level of 9.Calculate the MUL,MUS,and MRS of L for S on that indifference curve when S = 3.

For the following, please answer "True" or "False" and explain why -The absolute value of the slope of an indifference curve equals the ratio of the marginal utilities of the two goods involved.

Amanda consumes only two goods,X and Y.Her indifference curves satisfy the four standard assumptions.True or False: If she is indifferent between bundles (1,3)and (3,1),then bundle (2,2)must be strictly preferred.

Show that the utility functions V(X,Y)= XᵃY¹⁻ᵃ and U(X,Y)= a ln(X)+ (1-a)ln(Y)represent the same ordering of bundles.