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# 3. Analytic Question on Consumption and Labor decisions during the Pandemic

In this question we will study how workers change their labor supply. Imagine there is a

consumer/worker with preference over consumption C and leisure & given by the equation below:

U(C,) = log(C) + log(l)

1. Assume the consumer faces a wage rate of w and consumption price P. She

also has one unit of available time to spend working or resting. Solve for the consumer's

optimal choice of consumption and hours worked.

2. Now assume a pandemic hits the economy and the consumer receives more

utility from leisure. We model this by changing the preferences to:

U(C,) -log(C) + 0 log(l)

0

with > 1. Solve for the hours worked and consumption under these new preferences.

Compute the elasticity of labor supply and consumption with respect to real wages. Compare

your answer with the previous part (when 0-1). Does the consumer wants to work more or

less?

3. The government wants to increase hours worked, and so it enacts a law

that includes a subsidy on wages. This subsidy is proportional to labor income. Explain why

the new budget constraint can be expressed as: PC = (1+7)w(1-0), where is the subsidy

(with 7 > 0). Solve for the optimal hours worked and consumption and compare your answer

with that of the previous question. What is the effect of this subsidy on hours worked?

4. Now the government wants to try a different fiscal policy. Instead, it creates

a new lump-sum tax that the consumer has to pay regardless of income or consumption.

Explain why the new budget constraint can be written as: PC w(1)-T, where T

is the new lump-sum tax. Assume 0

consumption. Solve for hours worked and consumption. Compare with part 2.

-

5. Imagine the government wants to choose the tax amount T such that the

worker supplies exactly the same number of hours worked as in part 1. Find this tax amount.

Assume < 1+0. Is the consumer better off? Relate your answer to the First Welfare

Theorem, assuming the given prices clear markets in a competitive equilibrium.