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Suppose Jim has preferences that can be described as complete, transitive, and monotonic. There are 26 goods in Jim's world, each represented by a letter in the alphabet. We know that Jim has the following ranking: A > E > I > O > U and E > D > C > B. If I offer Jim good C and good A, which will he choose and why?

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Related questions

1. Suppose the price of x1 is $20 and the price of x2 is $4. If good x1 is on the horizontal axis, what is the slope of the consumer's budget constraint?

a. -0.20

b. -0.25

c. -5.0

d. -0.2

e. -4.0

f. -20.0

2. Suppose the price of x1 is $5 and the price of x2 is $1 and Toni's income is $20. Suppose Toni gets a $5 gift card that can only be used for the purchase of x1 and there is no resale value of the gift card. With the gift card, the commodity bundle (1,20) is on Toni's budget constraint.

True

False

3. Tiffany's utility function is given by the formula U(x1, x2) = min{20x1, 10x2}. If x1 = x2, which commodity will have a greater marginal utility?

A. Both x1 and x2 have the same marginal utility

B. It is not possible to determine which commodity has higher marginal utility

C. x2

D. x1

4. For U(x1,x2) = 6x11/3 + x2, preferences are

a. consistent with diminishing marginal rate of substitution.

b. consistent with constant marginal rate of substitution.

c. consistent with increasing marginal rate of substitution.

d. not consistent with a utility function.

5. For a utility function of the form U(x1,x2)=min{5x1,10x2}, the individual will have excess x2 for commodity bundles where

a. x2>2x1 b. x2>5x1

c. x2>0.5x1 d. x2>10x1

6. Matt enjoys Fuji and Gala apples and finds 1 Fuji apple to be just as good as 4 Gala apples.

a. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=0.25F+G

b. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=F+4G

c. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+.25G

d. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+G

e. Both A and B

f. Both C and D

1.Dr. Claw is hatching a plan to steal all of the cherry blossoms in Japan, cornering the market on haiku inspiration. He likes his henchmen to be big, fast, and obedient. Lou the Lunk weighs 340 pounds, runs slowly, and is somewhat obedient. Turncoat Tom weighs 240 pounds, runs very fast, and is very disobedient. Brainwashed Bobby weighs 150 pounds, has average speed, and is extremely obedient.

(a) Suppose Dr. Claw prefers henchman A to henchman B if A is superior to B in at least two of these dimensions, otherwise he is indifferent. Are Dr. Claw’s preferences complete? Are they transitive? Explain your answer.

(b) Now suppose Dr. Claw only prefers henchman A to henchman B if A is superior to B in all three dimensions. If A and B are identical in all three traits, then he is indifferent. Otherwise, Dr. Claw cannot compare the two henchmen. Are Dr. Claw’s preferences complete in this case? Are they transitive? Explain.

2. In this exercise, I will show you how to plot some indifference curves for the utility function u(x, y) = xy. Carefully read and follow these steps.

(a) For each of the values x = 1, 2, 3, 4, 5, find the corresponding value of y such that u(x, y) = 5. Plot these points on a graph of the x, y coordinate plane.

(b) Find the formula for the slope of the indifference curve passing through any point (x, y). Calculate these slopes for each point from part (a).

(c) Plot the slopes from part (b) on the same graph by drawing a short line segment at each point with its corresponding slope. For example, at (1, y1), draw a small line segment with the slope of the indifference curve through (1, y1).

(d) On the same graph, approximate the indifference curve corresponding to u(x, y) = 5 by sketching a curve that passes through each of the plotted points from (a), matching the slope of the line segments from (c) at each point.

(e) Repeat parts (a)-(d), but now for u(x, y) = 10, using the same graph.

Let us have an economy that lives only for 2 periods. The representative household has a utility function that values consumption goods for any period as follows

u(c) = ln(c).

The valuation throughout both periods can be represented as a total utility function that discounts future utility with a β discount parameter as follows,

U(c1, c2) = u(c1) + βu(c2) = ln(c1) + β ln(c2),

where ct represent consumption good in period t for every period t = 1, 2. The budget constraint for this person in every period is expressed as

(1+τtc)ct + xt =(1−τtI)(wtnt +rtkt), t=1,2.

where xt represent investment in period t, wt the wages earned by hours worked, rt the return of capital in period t, nt the hours worked supplied by the household in every period t, kt the stock of capital that the household has in period t, τtc the tax rate imposed by the government in consumption goods in every period t, and τtI the tax rate imposed by the government to total household income in every period t. In every period, the total amount of hours that the representative household is of H ̄ = 1. Investment in every period can be defined by the following law of motion of capital

kt+1 = xt +(1−δ)kt, t=1,2.

Acknowledge that k3 = 0 because there is no period 3 in this economy. The household starts with a given amount of capital k ̄1 > 0. The representative firm produces good by the following production function in every period t,

Yt =ztKtαNt1−α, t=1,2.

There is a government that covers government expenditures in period 1 and period 2 by taxing capital rent and labor. Hence, their budget can be expressed as

τtcct +τtI(wtnt +rtkt)=gt, t=1,2.

a) Before writing any competitive equilibrium definition or the Social Planner Problem, can we modify the budget constraint in 
order to get rid a variable in every period? Explain.

b) Define the Social Planner Problem.

c) Solve the Social Planner Problem. This is, find the Euler equation in terms of exogenous variables and the only endogenous variable k2.

d) Define the tax distorted competitive equilibrium of this economy.

e) Solve the representative household problem.

f) Solve the representative firm problem in period 1 and 2.

g) Find the optimal Euler equation in terms of exogenous variables and the only endogenous variable k2.

h) Imagine that the government can only implement income taxes. This is τtc = 0 for every period t = 1, 2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem?

i) Imagine that the government can only implement consumption taxes. This is τtI = 0 for every period t = 1,2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem? 


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