Download Economics Principles II New York University Marc

Economics Principles II
Marc Lieberman
New York University
Spring, 2012
Supplemental Problem Set #2
Instructions: Do this on your own before the recommended due date listed in the Aplia course outline. After the due date, the
answer sheets will be posted, and you can check your own answers.
[Note: Recitation this week (starting Thurs, Feb 2) will cover problems similar to some of these. Some of the problems are
difficult, so unless you can easily answer all of them, you should plan on attending recitation.]
I. Consider the following demand and supply schedule for cell phones in New York City:
QD = 22,000 – 70P
QS = -2,000 + 10P
where:
QD = number of cell phones demanded in NYC per month
QS = number of cell phones supplied in NYC per month
P = price per cell phone
1. According to the supply equation, cell phone producers need a minimum price or they won’t produce any.
What is that minimum price? (i.e., in the equation, at what price does the value of quantity supplied switch
from negative to positive, or—the same thing—at what price does quantity supplied equal zero?)
2. Solve for the equilibrium price and quantity.
3. Rewrite both the demand and the supply equation so that P is on the left hand side and everything is on the
right hand side. (If you use decimals, carry them out to 3 places.) Using these two new equations: solve
again for the equilibrium price and quantity, and verify that you get the same answer as in 2. above. (If the
answers are different from something other than rounding, you’ve made an error.)
4. Now suppose that, because cell phones are so annoying, the government imposes a tax of $50 on suppliers.
That is, the government collects $50 from cell phone suppliers each time they produce and sell a cell
phone. After the tax is imposed:
a. What is the new equilibrium quantity of cell phones bought and sold each month?
b. What is the new equilibrium price buyers will pay to sellers for each cell phone?
c. What is the new equilibrium price that sellers will get net of the tax they must pay to the
government?
d. How much of the $50 tax burden (per cell phone) ends up being borne (i.e., effectively paid by)
cell phone suppliers?
e. How much of the $50 tax burden (per cell phone) ends up being borne (i.e., effectively paid by)
cell phone buyers?
[Hint: To answer the above questions, use the versions of the supply and demand equations with just price on the
left hand side. After the tax is imposed on sellers, what happens to the price they must get in order for these
sellers to continue supplying any given number of cell phones (i.e., any specific Q S)? Change your supply
equation accordingly. Sketching a diagram may help.]
5. Now suppose that, instead of imposing the $50 tax on cell phone suppliers, the same tax is imposed on
(collected from) cell phone buyers. To make this concrete, imagine that each time someone buys a cell
phone, they must send a check to the government for $50. After the tax is imposed:
a. What is the new equilibrium quantity of cell phones bought and sold each month?
b. What is the new equilibrium price buyers will pay to sellers for each cell phone?
c. What is the new equilibrium price that buyers will pay for each cell phone, including the tax they
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must pay to the government?
d. How much of the $50 tax burden (per cell phone) is borne (i.e., effectively paid by) cell phone
suppliers?
e. How much of the $50 tax burden (per cell phone) is borne (i.e., effectively paid by) cell phone
buyers?
[Hint: To answer the above questions, once again, use the versions of the supply and demand equations with just
price on the left hand side. Now think carefully: after the tax is imposed on buyers, what happens to the price that
buyers would be willing to pay to continue buying any given number of cell phones? Change your demand
equation accordingly. It may help to draw a supply and demand diagram of what happens when the tax is
imposed, although no diagram is required.]
6. Consider the following statement: “If a $50 tax is going to be imposed on cell phones, people who buy cell
phones would be better off if the tax requires suppliers, rather than buyers, to pay the tax to the
government.” True or false? Explain.
II. Go back to the original supply and demand equations of this problem set. Now suppose that the government—
instead of viewing cell phones as annoying—decides that they are good, because they allow people to report
potentially dangerous situations to the proper authorities. The government accordingly decides to subsidize cell
phones by paying out $50 each time a cell phone is produced and sold.
1. Suppose the government pays the $50 subsidy to buyers each time they purchase a cell phone. After the
subsidy is applied:
a. What is the new equilibrium price buyers will pay to sellers for each cell phone?
b. What is the new equilibrium price buyers will pay for each cell phone, net of the subsidy (i.e., after
the subsidy is deducted from what buyers pay)?
c. What is the new equilibrium quantity of cell phones bought and sold each month?
d. What is the incidence of the $50 subsidy (per cell phone)? (That is, how are the benefits of the $50
subsidy split between buyers and sellers for each cell phone purchased?)
[Hint: Use the versions of the supply and demand equations with just price on the left hand side. After the
subsidy is applied, what happens to the price that buyers will pay to continue demanding any given number
of cell phones (i.e., any specific Q D)? Change your demand equation accordingly. Sketching a diagram may
help.]
2. Now suppose that—instead of giving the $50 subsidy to cell phone buyers, the same subsidy is given to cell
phone suppliers. That is, each time a cell phone is produced and sold, the supplier receives a $50 subsidy
from the government. After the subsidy is applied:
a.
b.
c.
d.
What is the new equilibrium price buyers will pay to sellers for each cell phone?
What is the new equilibrium price sellers will get, including the subsidy?
What is the new equilibrium quantity of cell phones bought and sold each month?
What is the incidence of the $50 subsidy (per cell phone)? (That is, how are the benefits of the $50
subsidy split between buyers and sellers for each cell phone purchased?)
[Hint: Once again, use the versions of the supply and demand equations with just price on the left hand side.
After the subsidy is applied, what happens to the price that sellers will charge to continue supplying any
given number of cell phones (i.e., any specific Q S)? Change your supply equation accordingly. Sketching a
diagram may help.]
3. Consider the following statement: “If a $50 subsidy is going to be given for each cell phone bought and
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sold, people who buy cell phones would be better off if the subsidy is given directly to them, rather than
given to suppliers.” True or false? Explain.
III. Go back to the original equations of this problem. Suppose that instead of a subsidy, the government imposes a
price ceiling on cell phones of $250, to make them more affordable to buyers. Assume that the price ceiling is
effectively enforced on cell-phone producers—they cannot charge any price greater than $250.
1. After the price ceiling is imposed, will there be an excess demand (shortage) or an excess supply (surplus)
of cell phones each month? State which, and give its numerical value.
2. How many cell phones will actually be bought and sold?
3. Suppose that the government, while enforcing the price ceiling on producers, cannot monitor the price
charged by “cell phone scalpers.” Suppose, too, that these scalpers buy up all the available cell phones.
What price will be charged to those who buy in this illegal market for cell phones?
[Hint: how high a price can scalpers charge and still sell all of the cell phones they’ve bought from the
producers? Sketching a diagram may help.]
4. Suppose that over the long run, as a result of the price ceiling, some cell phone producers who suffer losses
go out of business. With fewer firms in the industry, quantity supplied at each price shrinks by 200 per
month (i.e., the supply curve shifts leftward by 200). If the price ceiling is maintained, what price will be
established in the illegal market after the supply curve shifts?
5. Consider the following statement: “In the short run, a price ceiling may paradoxically cause consumers to
pay a higher price for a product. However, over the longer-run, as the industry adjusts, the price ceiling
will reduce the price consumers pay.” True or false? Explain.
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