Suppose that Wanda’s income is $480 (I0 = $480), the price of good X is $3 (PX0 = $3), and
the price of good Y is $4 (PY0 = $4). In order to raise tax revenue and reduce the consumption of good
X, suppose that policymakers are considering two "equal-cost" (equal revenue) tax schemes or
policies: a $3 excise tax on good X (ET); and, a lump sum income tax (LSIT). Recall that "equal cost"
means that each tax scheme must generate the same revenue for the government (i.e., the amount of
tax paid by Wanda is the same under each tax scheme). Wanda’s preferences are represented by the
indifference curves in the graph below. Insert additional indifference curves if needed.
a) Given PX0, PY0, and I0, Wanda’s initial consumption bundle is (x0,y0) = (80X, 60Y) and her marginal
utility of good X is 15 utils and marginal utility of good Y is 20 utils; i.e., at (x0,y0), MUX = 15 and
MUY = 20. In the graph below, illustrate Wanda’s budget line and initial consumption bundle
(x0,y0) = (80X, 60Y). Is Wanda maximizing her utility? Clearly state the conditions that (x0,y0)
satisfies.
b) Under the excise tax on good X, ET, the government taxes Wanda $3 for every unit of good X that
she buys (i.e., t = $3). In the graph below, illustrate (and label) Wanda’s budget line and her utility
maximizing bundle, (xET,yET), under the $3 excise tax. Round each quantity to the nearest 10.
Clearly state the conditions that (xET,yET) satisfies. Determine the amount of tax paid by Wanda
and illustrate it graphically (as measured in terms of good Y).
c) Under the LSIT, the government taxes Wanda a lump sum, IT, of her income I0. In the graph below,
illustrate (and label) Wanda’s budget line given the LSIT. Under the LSIT, does the bundle (xET,yET)
maximize Wanda’s utility? Explain. If not, illustrate the bundle, (xLSIT,yLSIT), that maximizes her
utility under the LSIT. Round each quantity to the nearest 10. Clearly state the conditions that
(xLSIT,yLSIT) satisfies.
d) To address equity concerns, suppose policymakers combine the excise tax above, ET, with a lump
sum income subsidy, LSIS, where the LSIS is a cash transfer to Wanda of the amount of the excise
tax paid by Wanda. Given the "Excise Tax + (Lump Sum) Income Subsidy policy, ETIS, illustrate
(and label) Wanda’s budget line. Illustrate the bundle, (xETIS,yETIS), that maximizes Wanda’s utility
under this third policy, ETIS. Clearly state the conditions that (xETIS,yETIS) satisfies.
e) Evaluate the desirability of each of the three policies (ET, LSIT, and ETIS) in terms of Wanda’s
consumption of good X and her happiness (utility). Which policy is best? Does any of the policies
impose an excess burden (deadweight loss or "loss in efficiency") upon Wanda or society? Explain.
How can this excess burden or deadweight loss be measured? Explain.