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Economics 101
Fall 2014
Answers to Homework #3
Due 10/30/14
Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and
section number on top of the homework. Write legibly throughout the whole homework. Make sure you write your
name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the
section for which you are registered, because you will need that number when you submit exams and homework.
Late homework will not be accepted so make plans ahead of time to insure that your homework is submitted. Good
luck!
Your homework reflects you: please make sure that you submit a neat, organized, and legible set of answers!
Remember to show all your work. Also remember that calculators are not permitted on the exam, so you should try
these manually.
Part I: Excise Tax
1. Consider the ice cream market in Madison. In July, the ice cream market demand and supply curves are given by
the following equations where Q is the quantity to ice cream units and P is the price in dollars per unit of ice cream:
Demand: Q = 14000 – 10P
Supply: Q = 2000 + 20P
a) Find the equilibrium price and quantity of ice cream in July.
In equilibrium, we know that the quantity demanded = quantity supplied. Thus, by solving the two equations, we
have the equilibrium price = $400 per unit of ice cream and the equilibrium quantity = 10,000 units of ice cream.
b) Calculate the price elasticity of demand and supply at the equilibrium price in July. Use the point elasticity
formula to compute these two values of these elasticities.
Answer:
The point elasticity of demand formula is
Elasticity of Demand = (-1/slope)(P/Qd)
and the point elasticity of supply formula is
Elasticity of Supply = (1/slope)(P/Qs)
At the equilibrium quantity and price we know (Q, P) = (10000, 400). We also have the demand and supply
equations, but they are not in slope-intercept form. So, rewriting the two equations in slope-intercept form we have:
Demand Equation: P = 1400 – (1/10)Qd
Supply Equation: P = (1/20)Qd – 100
Now, we are ready to use the point elasticity formulas:
Point Elasticity of Demand = [-1/(-1/10)][400/10000] = .4 (hence, demand is inelastic at the point of equilibrium in
this market)
Point Elasticity of Supply = [1/(1/20)][400/10000] = .8
In October, ice cream demand in Madison decreases. So, the new demand curve is given by
Demand: Q = 7000 – 30P
Assume the supply curve doesn’t change.
c) Find the equilibrium price and equilibrium quantity in October, and calculate the price elasticity of demand and
supply at this new equilibrium price. Use the point elasticity formula in calculating these values.
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Answer:
By solving the two equations, we obtain the equilibrium price of $100 per unit of ice cream and quantity of 4,000
units.
To find the price elasticity of demand using the point elasticity formula:
Price elasticity of demand = [(-1)/(-1/30)][100/4000] = (30)(1/40) = .75
To find the price elasticity of supply using the point elasticity formula:
Price elasticity of supply = [(1)/(1/20)][100/4000] = (20)(1/40) = .5
Let’s return to the July. Suppose that the city of Madison imposes on producers an excise tax of $15 per unit of ice
cream.
d) For part (d), answer this set of questions based upon this new tax and the demand and supply curves you have
been given in this problem.
1. How does this excise tax affect the supply curve for ice cream producers in Madison? Explain your answers
in words as well as in an equation.
2. Then, calculate the new equilibrium price and quantity in July for this ice cream market.
3. Then, calculate the new equilibrium price and quantity in October for this ice cream market.
Answers:
1. The imposition of the excise tax on producers effectively increases the costs of production for the ice cream
producers since they now must also include paying the government an excise tax of $15 per unit of ice
cream they produce. We can model this in two different ways: as done in class, this excise tax will shift the
supply curve up so that the new y-intercept of the supply curve with the tax will now be the old y-intercept
plus 15 (this “plus 15” reflects the idea that the producers now have a new cost that they must cover). Thus,
if the supply curve was Q = 2000 + 20P, then we could rewrite the supply curve in slope intercept form as
P = (1/20)Q – 100. Therefore the new supply curve that includes the tax would be P = (1/20)Q – 85.
Alternatively, you could take the existent supply curve in July written in x intercept form and view the tax
as effectively decreasing the amount per unit that the producer receives by 15. Thus, instead of P in this
original supply curve, the tax results in the new price with the tax being “P – 15”. If, we plug that into the
original supply curve equation this is what we get:
Q = 2000 + 20(P – 15)
Q = 2000 + 20P – 300
Q = 1700 + 20P, the new supply curve in JULY written in x intercept form.
Let’s check that this new supply equation is the same as we found in the first method: that is, is P = (1/20)Q
– 85 the same as Q = 1700 + 20P?
20P = Q – 1700
P = (1/20)Q – 1700/20
P = (1/20)Q – 85
Yes, these two approaches give us the same new supply equation with the excise tax.
2. In July the relevant demand equation is Q = 14000 – 10P and the relevant supply equation is Q = 1700 +
20P (see explanation in the answer to #1 of part (d)). Solving for equilibrium with these two equations we
get:
14000 – 10P = 1700 + 20P
30P = 12300
P in July = $410 per unit of ice cream
Q = 1700 + 20(410)
Q in July = 9900 units
3. In October the relevant demand equation is Q = 7000 – 30P and the relevant supply equation is Q = 1700 +
20P (see explanation in the answer to #1 of part (d)). Solving for equilibrium with these two equations we
get:
7000 – 30P = 1700 + 20P
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50P = 5300
P in October = $106 per unit of ice cream
Q = 7000 – 30(106)
Q in October = 3820 units
e) Calculate the consumers’ tax burden ratio in July and in October given your answers in (d) and then analyze the
answers you get for these two calculations by filling out the table provided and then writing a verbal explanation of
the difference you find with regard to the two consumers’ tax burden ratios. Your explanation should include the
impact of demand and supply elasticities on these calculations. The tax burden ratio can be found by using the
following equation:
Consumers’ tax burden ratio = (consumers’ tax incidence)/(total tax revenue)
Here is a table that will help you organize your data:
July
October
No Tax
Tax
No Tax
Tax
Price
Quantity
Price Elasticity
of Demand
—
—
Price Elasticity
of Supply
—
—
Answers:
Total tax revenue in July is (tax per unit)(number of units sold with the tax) = ($15 per unit)(9900 units) , and
consumers’ tax incidence is (equilibrium price with the excise tax – the old equilibrium price)(number of units sold
with the tax) = ($410 per unit – $400 per unit)(9900) = ($10 per unit)(9900 units). Thus, consumers’ tax burden
ratio in July is 2/3 (that is, consumers end up paying 67% of the excise tax on ice cream in July.
Tax revenue in October is ($15 per unit)(3820 units), and consumers’ tax incidence is (equilibrium price with the
excise tax – the old equilibrium price)(number of units sold with the tax) = ($106 per unit – $100 per unit)(3820
units) = ($6 per unit)(3820 units). Thus, consumers’ tax burden ratio in October is 2/5 (that is, consumers end up
paying 40% of the excise tax on ice cream in October).
July
October
No Tax
Tax
No Tax
Tax
Price
$400 per unit
$410 per unit
$100 per unit
$106 per unit
Quantity
10,000 units
9900 units
4000 units
3820 units
Price Elasticity
of Demand
.4
—
.75
—
Price Elasticity
of Supply
.8
—
.5
—
In July, the price elasticity of demand is smaller than the price elasticity of supply. As a result, consumers pay more
than half of the excise tax in July. Equivalently, producers pay less than half of the tax in July. On the other hand, in
October, the price elasticity of demand is greater than the price elasticity of supply, and thus consumers pay less
than half of the excise tax in October. In general, the less elastic side of the market pays more of any given excise
tax.
Part II: International Trade
2. Suppose the domestic demand in the United States for glow–in-the-dark golf balls can be represented by the
following domestic demand curve and domestic supply curve equations where P is the price per glow–in-the-dark
