1
Econ 100
Winter 2012
Problem set 2
Due January 27
1.
Consider that the U.S. supply of ethanol follows the function
S
(
p
) =
5p,
and that the US
demand for ethanol is
D
(
p
) = 13.5 – 2.5
p.
Without any government role, there are 9 Billion
gallons/year transacted at a price of $1.80/gallon.
a.
Calculate the supply and demand elasticities at this market equilibrium point.
Supply elasticity = dS(p)/dp * p/Q = 5*1.8/9
= 1
Demand elasticity = dD(p)/dp * p/Q = 2.5 * 1.8/9 = .5
Now
consider that the government is going to provide a
subsidy
of $0.60/gallon in order to
stimulate this market.
In other words, the government will provide funds that allow the price
paid by customers to be 60 cents/gallon
lower
than the price earned by suppliers.
b.
Using supply and demand curves, draw the equilibrium points before and after the
provision of the 60 cent/gallon subsidy
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c.
Calculate the new price earned by sellers, the price paid by customers, and the
equilibrium quantity sold in the market (again with the 60 cent/gallon subsidy).
Note that the subsidy can be thought of as a negative tax.
Applying the standard formula gives
Δ
p
customer
=
η
−
ε
Δ
tax
=
1
1.5
*
−
.60
=
−
$0.4
So new price for buyers is 40 cents lower, or $1.40/gallon.
Change in price for sellers is
the
remainder not absorbed by customers, or $0.20.
New seller price is $2.00/gallon.
Method 2:
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 Fall '11
 JAMESBUSHNELL
 Microeconomics, Supply And Demand, Marginal rate

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