Test 1 Answers

EconS 301, Spring 2015, Dr. Rosenman
Test 1
Do any three of questions 1, 2, 3 and 4, and do question 5. The three questions you do out of 1-4 are worth 10 points
each, and question 5 is worth 20 points. I am figuring 10 minutes each for the first 3, and 30 minutes for question 5.
That leaves 15 minutes for panic and other activities.
1. Consider the following demand and supply for golf balls: Qd=90-2P-2T and Qs=-9+5P-2.5R where P is
the price of golf balls, R is the price of rubber and T is the price of titanium.
a. If R=2 and T=10, find the equilibrium price of gold balls.
b. At the equilibrium values, calculate the price elasticity of demand and the price elasticity of supply.
c. At the equilibrium values, calculate the cross price elasticity of demand for golf balls with respect to the
price of titanium, and indicate if golf balls and titanium are substitutes or complements.
d. It is possible to find the elasticity of golf balls with respect to the price of rubber at the equilibrium
values, but this would not be a cross-price elasticity of demand. Explain why.
a. Qd=90-2P-2T=90-2P-20=70-2P and Qs=-9+5P-2.5R=-9+5P-5=-14+5P
Set Qs=Qd to get 70-2P=-14+5P sp 84=7P so Pe=12 Put this into the demand curve Qe=7—24=46
b.
dQd P
12 24
 2

dP Q
46 46
dQ P
12 60
es  s  5

dP Q
46 46
c.
ex 
ep 
dQd T
10 20
 2

 0  complements
dT Q
46 46
d. Rubber effects the supply curve not the demand curve. It affects only the equilibrium value, not the
demand for golf balls. Hence, it is not a cross price elasticity.
2. Ann has a utility function for food (F) and clothing (C) of the form U(F,C)=FC+F.
a. Find Ann’s demand curve for Food as a function of PF, PC and income (M).
b. Find her income elasticity of demand for food and her cross-price elasticity of demand for food with respect to the
price of clothing.
c. If food costs $1 per unit and clothes cost $2 per unit and income is $22 find Ann’s utility maximizing choice of food
and clothing.
d. What is the marginal rate of substitution of food for clothing when utility is maximized?
e. If the price of clothes decreases to $1 per unit, will Ann’s marginal rate of substitution of food for clothing increase
or decrease? Explain how her consumption will change.
a. Set up the Lagrangian and solve for F
L  FC  F   ( PF F  PC C  M )
L
L
L
 C  1   PF  0 and
 F   PC  0 and
 PF F  PC C  M  0
F
C

From the first two derivatives:
C  1 PF

 PF F  PC  PC C. Use this in the budget constraint (the third derivative):
F
PC
PF F  PC C  M  0  PF F  PF F  PC  M  0
F
M  PC
2 PF
b.
eI 
dF M
1 M

0
dM F 2 PF F
dF PC
1 PC
ex 

0
dPC F 2 PF F
F
c. From a.
Since both are positive, food is a normal good, and food and clothes are substitutes
M  PC 22  2

 12
2 PF
2
PF F  PC  PC C  C 
d. MRS=
PF F
1 12
1 
1  5
PC
2
PF 1

PC 2
e. The MRS now equals 1. Since the MRS= the ratio MUF/MUC she needs to decrease MUF and/or increase MUC.
To accomplish that she will increase F and decrease C.
3. It was recently announced that China would now allow all varieties of US apples to be imported for sale to
Chinese consumers. Previously China limited the types of apples US growers could sell there. Defend your answer to
parts a, b and c with a graph. No graph is needed for parts d, e and f.
a. How will the relaxed Chinese import rules for apples will change the consumer’s surplus for Chinese consumers of
apples?
b. How will the relaxed Chinese import rules for apples will change the producer’s surplus for Chinese producers of
apples?
c. How will the relaxed Chinese import rules for apples will change the produce’s surplus for Washington producers
of apples?
d. If the goal of Chinese leaders is to increase the welfare of the country’s population, what can you say about the
relative change in surplus values?
e. Did US apple producers necessarily gain from the quota being removed? Explain.
f. What happens to the consumer surplus of US consumers of apples? Explain.
This is an application of quotas covered in chapter 3 of the Rosenman readings. Below is the relevant graph:
k
a. Consumer surplus for Chinese consumers increased to triangle abPe from triangle ajPr in the third panel.
b. Chinese producer’s surplus decreased from triangle ckPr to triangle cfPe.
c. The change for Washington producers is uncertain. They pick up triangle mhn but lose rectangle PrLnPe.
Whether they gain or lose depends on which is bigger.
d. Probably that the gain to consumers is bigger than the loss to producers.
e. No. See the answer to part c.
f. The Chinese quota kept more apples in the US,, shifting out the supply of apples in the US, and thus probably
lowering price in the US. Since more apples will now be shipped to China, likely the US price will go up,
cutting the consumer surplus of US consumers.
4. Social Security is covered by cost-of-living adjustments (COLA) which is intended to keep seniors at the same level
of consumption as before. Seniors claim the COLA is too small, and does not allow them to keep the same
consumption. Budget writers claim the COLA is overly generous and compensates seniors too much. Assume seniors
spend their income on only 2 goods, X and Y, and they have utility functions U(X,Y)=X*Y so we know PxX=PyY always
so if M is their social security benefit, one-half is always spent on X and the other half is always spent on Y.
a. Let Px=Py=1. Draw an indifference curve/budget constraint map of the optimum for seniors.
b. Now suppose Px doubles so Px=2. If there is no COLA, show the new consumption for a senior.
c. Decompose the change in consumption into the income and substitution effects. Be very clear which change is
which.
d. The COLA is based on the previous consumption so if Px doubles, the social security benefit will go up by 50%, and
the new benefit=1.5M. Is this more than, less than, or the same as the income effect? Explain how you know.
e. At least in theory, who is correct, seniors or budget writers? Explain why.
a. Given the utility function we know the individual always
consumes at the midpoint of the budget constraint (because
PxX=PyY always). The original indifference curve/budget
constraint is given by the solid lines, and consumption is at point
1, consuming Q1 of X
b. If Px doubles, the budget constraint pivots inward. With no
COLA, consumption is at point 3, and they would consume Q2.
c. The substitution effect is given by the change in consumption
from point 1 to point 2 on the graph. The income effect is from
point 2 to point 3.
Q1
d. The COLA allows the person to consume the same about as before, so point 1. It is larger than the income effect.
That means that seniors are not hurt – if they can consume as much as before, they can achieve the same utility. But,
the budget writers are correct. The budget constraint going through point 1 at the new price ratio – the red line –
shows that seniors would take advantage of the change in prices and substitute Y for the now more expensive X. As a
result, on the red budget line, they can achieve a higher utility than before.
5. For any FIVE (5) of the statements below, indicate if it is True, False or Uncertain, and explain why. Each is worth 4
points. You may also choose TWO (2) additional questions as extra credit on the test. Each extra credit question is
worth 2.5 points. Clearly indicate which questions are for extra credit. If you don’t, the first 5 you do will be the
regular test questions.
a. In a one-sector market, a quota on supply creates a shortage. In a two-sector market with foreign and
domestic supply sectors, a binding quota on the foreign supply will raise price but will not affect equilibrium
quantity.
False. If equilibrium quantity goes down, consumer surplus goes down. Domestic producer surplus goes up, foreign
producer surplus change is uncertain.
b. If a 10% increase in the price of automobiles reduces the quantity demanded by 8%, a seller interested in
profits will likely increase the price.
True. These indicate demand is inelastic. Sellers should produce where the price elasticity of demand is elastic
because an increase in P lowers Qd, costs go down (since less has to be supplied) but because ep is inelastic, total
revenue goes up, so profit goes up. The seller should keep increasing price until demand becomes elastic.
c. A shift in the demand curve identifies the demand curve but not the supply curve.
False. We observe only Qe and Pe. If the demand curve shifts, it shows us the equilibrium points on the supply
curve, not the demand curve.
d. It was recently observed that even though the price of chicken increased, the quantity of chicken sold also
went up. This is an indication that the supply of chicken shifted in.
False. Chicken might be an inferior good, so a decrease in income increases demand. How does this relate to price?
When the price of income went up, the substitution effect was away from chicken. But the income effect of an
inferior good is towards chicken when the price rises. In this case, the income effect towards chicken overwhelmed
the substitution effect away from it, and the demand went up. (This is called a Giffen god).
e. Aluminum takes a lot of electricity to produce, while plastic is mostly produced with oil-based products.
Many of the power plants that produce electricity can run on either oil or natural gas. Fracking in North
Dakota and elsewhere in the US has increased the supply of both natural gas and oil, but the increase in
natural gas has been larger. As a result of these changes, we should see a fall in the equilibrium price of
aluminum and an increase in the equilibrium price of plastic.
False. The supply increase in oil and natural gas will decrease the price of both. This makes producing both
aluminum and plastic cheaper, shifting out both supply curves, and lowering the equilibrium price of both.
f.
An Engel curve with a slope that is increasing at a decreasing rate means the income effect that will occur
from a price change will get smaller as the price gets lower and lower.
True. An Engel curve shaped like that mean the income effect is getting smaller and smaller as income goes up. Price
drops are like an income increase, and the bigger the drop, the larger the “income like” effect.
g. Consumer surplus exists because most buyers of a good would willingly pay more if they had to.
True. The demand curve shows the reservation price of each unit produced. Consumers who value the good a lot
have a high reservation price, but only have to pay the market price.
h. The equivalent variation of a sales tax is an income tax that raises the same amount of money.
False. The equivalent variation is an income tax that results in the same loss of utlity
i.
If good A is on the horizontal axis and good B is on the vertical axis, and good B is an inferior good, the
income consumption line will be upward sloping.
False. IF B is an inferior good, an increase in income reduces the quantity demanded. Hence, the incomeconsumption line will have a negative slope.
j.
The quantity of gasoline consumed changes very little as the price of gasoline changes. If gasoline is on the
horizontal axis and “all other goods” are on the vertical axis, the Price-Consumption line for changes in the
price of gasoline will be almost vertical, and spending on other goods will be very responsive to changes in
the price of gasoline.
True. Since gasoline consumed changes little, the residual of income is spent on other goods. The price-consumption
line is almost vertical, and since the amount spent on gasoline changes only because of price, the amount available
for other goods responds to changes in gasoline prices. If M=PgG+PaA, we see that A=(M-PgG)/Pa. Holding G, M and
Pa constant, clearly A depends on Pg.
k. The supply of health insurance is relatively steep, while the demand for health insurance is relatively flat.
The subsidy provided by the ACA increases seller’s surplus more than it increases consumer surplus.
True. The steeper the supply curve and the flatter the demand curve, the greater the share of any subsidy going to
sellers. See the graph. The subsidy increases sellers surplus much more than consumers surplus.