Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure

U(c,l) = lnC + 4lnl

1) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl.

Which worker places a higher value on labour market work?

Given the utility function:

U=lnc + l + lnc' + l'

and the budget constraint:

w(h-l) + w'(h-l')/(1+r) = c + c'/(1+r) where c = current consumption, c'= future consumption, l=current leisure, l'=future leisure, and r is the market interest rate. Suppose that the current wage, w=20 and the future wage w'=22.

What is the optimal value of current consumption, c? Show all steps.

Willy the Worker has unavoidable personal commitments taking 8 hours per day. He can choose to work or to play (i.e., take leisure, a normal good) in the remaining hours. Being a graduate in Economics, he can charge $100 per hour for his consulting services when he chooses to work. The government's income tax system has a 0% tax rate for daily incomes from $0 to $ $600 per day; above $600 per day, the tax rate is 20%. Willy has a certain Utility Function U(L, I) where L = leisure play time and I = Income. His Marginal Rate of Substitution is known to be derived from this equation: MRSLI = 21/L . [Note that the "price" of Income is $1.] 1.1 (4) Willy thinks he pays enough taxes via the excise taxes on things he buys. So he decides to work the maximum number of hours he can without paying any income taxes. According to our Indifference Theory model, is Willy maximizing his satisfaction with his "no tax" choice, or should he work fewer hours? Explain your answer. [No diagram; use "the logic" of the model only.] At equilibrium, MRSLA = price ratio =PL/P1 = 100/1 = slope of BL = wage rate = 100 At "no tax” point, L = 10 and I = $600, hence MRS = 1200/10 = 120 Since MRS > P ratio, he must reduce MRS by taking more Leisure and working less He should (be at the "no tax" point / work fewer hours than the "no tax" point*)

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) = 6x₁^1/3 + 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{5x₁,10x_2}, 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