For exercises 1-3, use the benchmark model in class where the government taxes household
labor income and lump sum transfers it back to them.
Exercise 1: What if we were Italian? Calibrate α so as to match the average work week for Italia
for the 1970-74 period as reported in Table 2 in Prescott (2004).
Exercise 2: (Laffer Curve) Use Excel to show how the equilibrium varies with the tax rate given
the value for from Exercise 1 above. Vary in steps of 0.01 from 0.00 to 1.00. Plot
c, h, and tax revenue variables, hw versus .
Exercise 3: Determine the welfare gain associated with lowering the tax rate in Europe from 0.60
to the U.S. tax rate of 0.40.
(Recall, the welfare gain in lifetime consumption equivalents of changing the tax rate from the
current U.S. rate of 0.40 to the European rate of 0.60 is the value of such that
Therefore, (1+) is the factor that consumption must be scaled if there is a change in the tax rate
from 40% to 60% to leave people indifferent to the change. The welfare loss in consumption
equivalents is c . In effect, find the values of . and ),60.0( ),60.0( ),40.0( hcc
Consider the model economy with an alternative government policy. The commodities are labor
h and consumption c. The price of c is normalized to 1. The price of labor is the wage rate w.
A household’s problem is to maximize utility
)100ln(ln sd hc
subject to its budget constraint sd whc , where is a lump sum transfer from the
government. Here the superscripts s and d indicate supply and demand
A firm’s problem is to maximize profits dd whhA )1( . Notice that the government
imposes a tax on the firm’s output or sales.
The government’s budget constraint is dAh .
The consumption and labor markets clear which means that ccc ds and hhh ds .
Find the equilibrium for this economy; that is equilibrium ( , , , )c h w as a function of utility
function parameter and tax policy parameter . Note set the TFP parameter A=1
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