Answer all questions.
100 points possible.
1. [20 points]
Policymakers are concerned that Americans save too little.
more saving, some policymakers have suggested imposing a “consumption tax” on the
portion of income that is spent rather than saved.
To explore the effects of this type of
tax, we might begin with the model discussed in lecture.
Suppose a consumer will live
two periods, with consumption level x
in period 1 and consumption level x
in period 2.
The consumer’s utility function is given by U(x
); assume that both goods are normal
The consumer has income I in period 1, and no income in period 2.
consumer can save some of her income in period 1 in order to have positive consumption
in period 2.
Any income saved in period 1 is placed in the bank, earning interest at rate r.
Given no consumption tax, period 2 consumption is thus given by x
= (1+r)(I – x
Now suppose that consumption in period 1 (but not period 2) is subject to a consumption
More specifically, suppose that consumption in period 1 is taxed at rate t.
the consumer chooses x
, she must also pay tx
Consequently, period 1 saving
becomes I – (1+t)x
, and period 2 consumption is given by x
= (1+r)(I – (1+t)x
(a) Using a graph, show how the consumption tax affects the consumer’s budget
Then, reasoning about substitution and income effects, discuss how the
consumption tax will affect consumption and savings in period 1.
[HINT: Savings in
period 1 are proportional to consumption in period 2.]
If the consumption tax was instead imposed on consumption in
does this change your answers to part (a)? [HINT: The consumer’s bank balance in
period 2 must now cover her consumption plus her tax payment in period 2.]
2. [30 points]
Consider a firm with variable cost function VC(Q) = 10Q + 2Q
, where Q
is the quantity produced by the firm.
The firm has fixed costs FC = 98.
Assume that all
fixed costs are sunk costs.
a) Derive the firm’s marginal cost (MC), average cost (AC), and average variable cost
Then plot the MC, AC, and AVC curves for Q between 0 and 12.
[HINT: You can solve this problem by constructing a table or by solving analytically for
these functions using calculus.
Your graph doesn’t need to be perfectly to scale, but
should be properly labeled and indicate relevant x and y coordinates on the axes.]
b) Suppose that the firm has already entered the market, and can sell each unit of output
at price P = 50.
Compute the firm’s optimal quantity and profit level.
If the price falls to
P = 30, compute the firm’s new optimal quantity and new profit level.