Download Economics 101 Syllabus

Economics 207
Intermediate Microeconomics
Spring 2007
Dr. Léonie L. Stone
Homework 1
1.
a. If demand for concert tickets is described by the equation QD  100 – p, and supply is QS
 20  p, find the equilibrium price and quantity. Carefully graph your results, labeling
everything relevant including intercepts and slopes.
Set QD  QS and solve.
For QS  20  p
100 – p  20  p
p*  40
Q*  60
Answer should include a graph with intercepts and slopes for both curves labeled.
b. Now suppose that the government levies a specific tax of $10 per ticket on sellers of
concert tickets. Find the new equilibrium price and quantity, the incidence of the tax, and
the price elasticity of demand and of supply.
QS  20  p,so p=-20+q
Price with tax = p + 10 = 10 + -20 + q = -10 + q
For Q  10  p
100 – p  10  p
p*  45
Q*  55
Note that the price rises by $5, so clearly consumers and producers split the tax; each pays 50%.
From this we can infer that their elasticities were the same at the original equilibrium point, but the
question asks for the exact elasticity.
At the original point, price elasticity of demand equals -1(40/60) = -2/3; price elasticity of supply
equals +1(40/60) = 2/3; you can plug this into the incidence formula to get 50% if desired.
IMPORTANT: You need to find elasticities at the ORIGINAL equilibrium point, not at the new
point.
2. Suppose the demand for antibiotics is Q  100,000. What is the elasticity of demand? If a
specific tax of $1 per dose were levied, who would bear the burden of the tax? Support
your answer with a carefully-labeled graph.
Price elasticity of demand is obviously 0; demand is perfectly inelastic and thus vertical.
Assume any upward-sloping supply curve (you could choose an equation for this, or just draw
it). The supply curve shifts leftward by the $1 tax; at the new equilibrium, quantity is unchanged,
but price is exactly $1 higher. Consumers are the more inelastic group and thus bear the burden
of the tax; they will pay 100% of the tax (unless supply is also perfectly inelastic, which would be
highly unlikely).