Econ 701 Homework 3
Spring 2015
Question 1
The following are the equations of the IS-LM model, here including a feature that taxes are not
simply given but depend on income through a tax function, T(Y).
IS Curve: Y = C(Y −T(Y)) + I(r) + G
LM Curve: M / P = L(r,Y)
a. Differentiate the model totally and solve for the government spending multiplier, dY/dG, in
terms of the various slopes of the functions: C' = marginal propensity to consume out of
disposable income, T' = marginal tax rate, I' = effect (derivative) of the interest rate on
investment, and Lr, LY = the effects (partial derivatives) of the interest rate and income on
liquidity preference.
b. From this, what would the multiplier be if taxes did not depend on income? Does the income
tax (T’>0) make the multiplier larger or smaller?
c. Can you tell whether this multiplier from part (a) is larger or smaller than one? What features
of behavior tend to make the multiplier smaller, and what makes it larger?
Question 2
We normally draw the IS curve as downward sloping and the LM curve as upward sloping, as
appropriate for our usual assumptions about behavior. How would either or both of these curves
look different if the following unusual assumptions were made? Either describe or draw your
answers, being sure in either case to make clear what you mean.
a.
b.
c.
d.
e.
f.
Investment does not depend on the interest rate.
The MPC is zero
The MPC is one
Demand for money does not depend on the interest rate
Demand for money does not depend on income
Supply of money rises endogenously as a result of increases in the interest rate
Question 3
Suppose that a moment in time neither the goods market nor the money market is in equilibrium,
so that the economy is neither on the IS curve nor on the LM curve. Based on what you know
about these two markets, which market would you expect to move more quickly towards
equilibrium?
Question 4
Suppose estimates of the Taylor rule during the 1970-1979 period in the US produce the
following values (ignoring constants):
𝑟𝑡 = 0.23(𝜋𝑡 − 𝜋 ∗ ) + 0.78(𝑦𝑡 − 𝑦 ∗ )
a) What are the implications of these estimates? In particular, do they help explain the US
economic experience during that time?
b) Suppose during that time there were misperceptions by the Fed about the actual output
gap y*. Based on the Taylor rule, how do you think these misestimates can lead to
persistently high inflation during that time?
Question 5
Consider a two sector model: a union and nonunion sector. In the union sector, wages are above
the equilibrium level due to effective bargaining. The nonunion sector functions competitively.
For simplicity, the demand for labor in the two sectors is assumed to be similar, i.e., the marginal
product of labor is the same in the union and nonunion sectors.
Suppose that we begin from an initial equilibrium in which wages are identical in the two
sectors. When the union increases the wage through bargaining, firms will reduce employment of
union labor. Thus, there may be some initial unemployment in the union sector and a differential
between union and nonunion wages. Can this situation be sustained in equilibrium, or will
demand and supply adjust further?
Question 6
Problem 10.1 in Romer’s “Advanced Macroeconomics” (link to text is on the class website)
Question 7
Suppose that the price-setting equation also takes into account the price of energy (another input
in production). In particular, 𝑃 = (1 + 𝜇)𝑊𝑞1−𝑎 where q is the price of one unit of energy. The
𝑧
wage-setting equation is given by W = 𝑃𝑒 𝑢. Derive the real wage and unemployment consistent
with equilibrium in the labor market in the medium run. How does the equilibrium
unemployment rate change when the price of energy increases? What is the intuition for this
result?