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Homework: Factor Prices II

Q1 Household utility maximization with income tax

5 Points

A representative household receives utility from consumption c and supplying labor l:

u(c,l) = log c+s log(1 1)

–

As usual, l is the share of time that the household spends working. The household owns an

exogenously determined amount of capital k, earns the nominal rental rate R on each unit of its

capital holdings, earns the nominal wage W on each unit of labor it supplies, and pays the

price P per unit of consumption. However, now suppose that the household pays an

exogenous tax rate T on labor income. The household’s budget constraint is therefore:

Pc= (1 – 1)W1 + Rk

=

Answer the following:

Q1.1

4 Points

Solve the household’s utility maximization problem and derive the household’s labor supply

equation that expresses l as a function of the real wage W/P, the real rental rate R/P,

1

capital k, the labor income tax rate t, and the utility function parameter 4.

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Q1.2

1 Point

Suppose that the government raises the labor income tax rate T. Everything else equal, will the

household supply more or less labor? Explain in words the intuition behind this result.

Q1.2

1 Point

Suppose that the government raises the labor income tax rate T. Everything else equal, will the

household supply more or less labor? Explain in words the intuition behind this result.

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Q2 Equilibrium in the consumption-labor choice model

16 Points

Recall that equilibrium in the static consumption-labor choice model is given by the following

five equations:

–

1

=

Y AKL1-a

R

= a Aña-lLl-a

= (1 – a)AK L-a

RP

L

N

1+4

Y = C

W

P

1

=

(N 4 (W/P)

K

Answer the following:

Q2.2

4 Points

Suppose that y increases because households have developed a greater preference for

leisure relative to consumption. Construct a pair of well-labeled diagrams of equilibrium in the

factor markets to show how the change in y affects the supply of capital, the supply of labor,

the real wage, and the real rental rate.

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Q2.3

1 Point

When y increases:

O Y increases and C increases

O Y increases and C decreases

O Y decreases and C increases

OY decreases and C decreases

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Q2.4

4 Points

Suppose that A decreases. Construct a pair of well-labeled diagrams of equilibrium in the factor

markets to show how the change in A affects the supply of capital, the supply of labor, the real

wage, and the real rental rate.

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Answer the following:

Q2.1

1 Point

Identify all of the endogenous variables in the model.

A

?

K

Y

L

N

R/P

W/P

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Q2.5

1 Point

When A increases:

O Y increases and C increases

O Y increases and C decreases

O Y decreases and C increases

O Y decreases and C decreases

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Q2.6

4 Points

Suppose that K doubles and A decreases by half. Construct a pair of well-labeled diagrams of

equilibrium in the factor markets to show how the changes in A and K affect the supply of

capital, the supply of labor, the real wage, and the real rental rate.

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Q2.7

1 Point

When K doubles and A decreases by half:

O Y increases and C increases

O Y increases and C decreases

O Y decreases and C increases

O Y decreases and C decreases

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Explanation & Answer:

2 Questions

Tags:

equation

Income Tax

Labor Supply

household utility

real rental rate

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