# UCSD Factor Prices Questions

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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
=
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.
Select file(s)
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.
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
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.
Select file(s)
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
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.
Select file(s)
Q2.1
1 Point
Identify all of the endogenous variables in the model.
A
?
K
Y
L
N
R/P
W/P
*Unsaved Changes
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
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.
Select file(s)
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

attachment

2 Questions

Tags:
equation

Income Tax

Labor Supply

household utility

real rental rate

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