Download Supply and Demand - Solved Homework and more Exercises Economics in PDF only on Docsity!
ANSWERS
ECNS 251
Homework 3 Supply & Demand II
- Suppose that policymakers have been convinced that the market price of cheese is too low.
a. Suppose the government imposes a binding price floor in the cheese market. Draw a supply-and-demand diagram to show the effect of this policy on the price of cheese and the quantity of cheese sold. Is there a shortage or surplus of cheese?
The imposition of a binding price floor in the cheese market is shown in the figure below. In the absence of the price floor, the price would be P 1 and the quantity would be Q 1. With the floor set at P (^) f, which is greater than P 1 , the quantity demanded is Q 2 , while quantity supplied is Q 3 , so there is a surplus of cheese in the amount Q 3 – Q 2.
b. Suppose the government agrees to purchase all the surplus cheese at the price floor, who benefits from this new policy? Who loses?
If the government purchases all the surplus cheese at the price floor, producers benefit and taxpayers lose. Producers would produce quantity Q 3 of cheese, and their total revenue would increase substantially. However, consumers would buy only quantity Q 2 of cheese, so they are in the same position as before. Taxpayers lose because they would be financing the purchase of the surplus cheese through higher taxes.
With a price floor of $10, the new market price is $10 because the price floor is binding. At that price, only two million Frisbees are sold, because that is the quantity demanded.
CS = .52,000,000$(11-10) = $1 million per period PS = .52,000,000$(6.67-6)+(2,000,000*(10-6.67)) = $667000+ $6,660,000 = $7,327,000 per period The deadweight loss is the loss in CS+TS = 15,000,000 -8,327,000 = $6,673,
Consumers are worse off because of this policy by $8 million per period
Producers are better off by $1.327 million per period.
c. Irate college students march on Washington and demand a reduction in the price of Frisbees. An even more concerned Congress votes to repeal the price floor and impose a price ceiling $1 below the former price floor. What is the new market price? How many Frisbees are sold? What is the deadweight loss from this policy? Who wins and who loses from the policy?
If there’s a price ceiling of $9, it has no effect, because the market equilibrium price is $8, which is below the ceiling. So the market price is $8 and the quantity sold is six million Frisbees.
- A friend of yours is considering two cell phone service providers. Provider A charges $120 per month for the service regardless of the number of phone calls made. Provider B does not have a fixed service fee but instead charges $1 per minute for calls. Your friend’s monthly demand for minutes of calling per month is given by the equation QD=150-50P, where P is the price of a minute. a. With each provider, what is the cost to your friend of an extra minute on the phone?
With Provider A, the cost of an extra minute is $0. With Provider B, the cost of an extra minute is $
b. In light of your answer to (a), how many minutes would your friend talk on the phone with each provider?
With Provider A, my friend will purchase 150 minutes [= 150 – (50)(0)]. With Provider B, my friend would purchase 100 minutes [= 150 – (50)(1)].
c. How much would he end up paying each provider every month?
With Provider A, he would pay $120. The cost would be $100 with Provider B
d. How much consumer surplus would he obtain with each provider? (Hint: Graph the demand curve and recall the formula for the area of a triangle)
The figure above shows the friend’s demand. With Provider A, he buys 150 minutes and his consumer surplus is equal to (1/2)(3)(150) – 120 = 105. With Provider B, his consumer surplus is equal to (1/2)(2)(100) = 100.
e. Which provider would you recommend that your friend choose? Why?
I would recommend Provider A because he receives greater consumer surplus
- A subsidy is the opposite of a tax. With a $0.50 tax on the buyers of ice-cream cones, the government collects $0.50 for each cone purchased; with a $0.50 subsidy for the buyers of ice-cream cones, the government pays buyers $0.50 for each cone purchased. a. Show the effect of a $0.50 per cone subsidy on the demand curve for ice-cream cones, the effective price paid by consumers, the effective price received by sellers, and the quantity of cones sold.
- Suppose that the government subsidizes a good: For each unit of the good sold, the government pays $2 to the buyer. How does the subsidy affect consumer surplus, producer surplus, tax revenue, and total surplus? Does a subsidy lead to a deadweight loss? Explain.
The figure and table below illustrate the effects of the $2 subsidy on a good. Without the subsidy, the equilibrium price is P 0 and the equilibrium quantity is Q 0. With the subsidy, buyers pay price P (^) C producers receive price PP , and the quantity sold is Q 1. Prices PC - P (^) P =$2. The following table illustrates the effect of the subsidy on consumer surplus, producer surplus, government revenue, and total surplus. Because total surplus declines by area D + H, the subsidy leads to a deadweight loss in that amount.
OLD NEW CHANGE
Consumer Surplus A + B A + B+ C + F + G +(C+ F + G)
Producer Surplus C + D B + C + D + E +(B + E)
Government Revenue 0 –(B + C + E + F + G + H) –(B + C + E + F + G + H)
Total Surplus A + B + C + D A + B + C + D - H – H
- Consider how health insurance affects the quantity of healthcare services performed. Suppose that the typical medical procedure has a cost of $100, yet a person with health insurance pays only $20 out of pocket. Her insurance company pays the remaining $80. (The insurance company recoups the $80 through premiums, but the premium a person pays does not depend on how many procedures that person chooses to undertake.)
a. Draw the demand curve in the market for medical care. (In your diagram, the horizontal axis should represent the number of medical procedures.) Show the quantity of procedures demanded if each procedure has the price of $100.
The figure below illustrates the demand for medical care. If each procedure has a price of $100, quantity demanded will be Q 1 procedures.
- The equations below give the demand and supply of designer blue jeans per week.
Demand: P = 240 – 4Q
Supply: P = 40 + 6Q
a. Graph these equations. Indicate their intercepts.
b. What is the equilibrium price and quantity?
240 - 4Q = 40 + 6Q
10Q = 200 Q* = 20
P* = 40 + 6(20) = $
0
40
80
120
160
200
240
280
0 10 20 30 40 50 60
Price Per Pair
Pairs per period
D S
c. Suppose the government imposes a tax of $20 per pair of jeans on the buyers this market. What is the new equilibrium quantity? How much do demanders now pay for each pair of jeans? How much do suppliers receive for each pair sold? How much tax revenue does the government earn?
See the graph below. The demand curve associated with this tax is:
D': P = 240 – 4Q (- 20) = 220 - 4Q
Supply: P = 40 + 6Q The new equilibrium price along the supply curve is:
220 - 4Q = 40 + 6Q 10Q = 180 Q = 18 P s^ = 40 + 6(18) = 148
The equilibrium price along the demand curve is $20 higher than on the supply curve or
168
We can also compute this along the original demand curve, since when Q = 18, P on the original demand curve is: P = 240 - 4Q = 240 - 4(18) = 168
The government earns Q = 18 * Tax = $20 or $360 in tax revenue per period.
(^200) 4060
(^10080) 120140
160180
200220
240
0 10 20 30 40 50 60
Price Per Pair
Pairs per period
D S D'
- Suppose that a market is described by the following supply and demand equations: QS^ =2P QD= 300-P a. Solve for the equilibrium price and equilibrium quantity.
Setting quantity supplied equal to quantity demanded gives 2P = 300 – P. Adding P to both sides of the equation gives 3P = 300. Dividing both sides by 3 gives P = 100. Plugging P = 100 back into either equation for quantity demanded or supplied gives Q = 200.
b. Suppose that a tax of T is placed on buyers, so the new demand equation is: QD=300-(P+T). Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold?
Now P is the price received by sellers and P+T is the price paid by buyers. Equating quantity demanded to quantity supplied gives 2P = 300 − (P+T). Adding P to both sides of the equation gives 3P = 300 – T. Dividing both sides by 3 gives P = 100 –T/3. This is the price received by sellers. The buyers pay a price equal to the price received by sellers plus the tax (P +T = 100 + 2T/3). The quantity sold is now Q = 2P = 200 – 2T/3.
c. Tax revenue is T x Q. Use your answer to part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 300.
Because tax revenue is equal to T x Q and Q = 200 – 2T/3, tax revenue equals 200T − 2T 2 /3. The figure below shows a graph of this relationship. Tax revenue is zero at T = 0 and at T = 300
d. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Recalling that the area of a triangle is ½ BH, solve for deadweight loss as a function of T. Graph this relationship for T between 0 and
- (Hint: Looking sideways, the base of the deadweight loss triangle is T, and the height is the difference between the quantity sold with the tax and the quantity sold without the tax.)
As the figure above shows, the area of the triangle (laid on its side) that represents the deadweight loss is 1/2 × base × height, where the base is the change in the price, which is the size of the tax (T) and the height is the amount of the decline in quantity (2T/3). So the deadweight loss equals 1/2 × T × 2T/3 = T 2 /3. This rises exponentially from 0 (when T = 0) to 30,000 when T = 300, as shown in the figure below.
