MATHEMATICS

Problem 02-03
Suppose the supply function for product X is given by QXS = – 30 + 2Px – 4Pz.

a. How much of product X is produced when Px = $600 and Pz = $60?
b. How much of product X is produced when Px = $80 and Pz = $60?
c. Suppose Pz = $60. Determine the supply function and inverse supply function for good X. Graph the inverse supply function.

Supply function:

Inverse supply function:

Problem 02-05 (Algo)
The demand curve for product X is given by QXd = 340 – 4PX.

a. Find the inverse demand curve.
b. How much consumer surplus do consumers receive when Px = $45?
c. How much consumer surplus do consumers receive when Px = $30?
d. In general, what happens to the level of consumer surplus as the price of a good falls?

Problem 02-06 (Algo)
Suppose demand and supply are given by Qd = 60 – P and Qs = 1.0P – 20.

a. What are the equilibrium quantity and price in this market?
Equilibrium quantity:
Equilibrium price:

b. Determine the quantity demanded, the quantity supplied, and the magnitude of the surplus if a price floor of $50 is imposed in this market.

Quantity demanded:

Quantity supplied:

Surplus:

c. Determine the quantity demanded, the quantity supplied, and the magnitude of the shortage if a price ceiling of $32 is imposed in the market. Also, determine the full economic price paid by consumers.
Quantity demanded:
Quantity supplied:
Shortage:

Full economic price: $

Problem 02-07
Suppose demand and supply are given by

QXd = 14 – (1/2)PX and QXs = (1/4)PX – 1

Instructions: Round your answers to the nearest whole number.

a. Determine the equilibrium price and quantity. Show the equilibrium graphically.
Equilibrium price:
Equilibrium quantity:
Instruction: Use the tools provided to graph the inverse supply function ‘S’ and the inverse demand function ‘D’ from X = 0 to X = 6 (two points total for each) and indicate the equilibrium point.

 

Problem 02-10 (Algo)
Consider a market where supply and demand are given by QXS = -16 + PX and QXd = 83 – 2PX. Suppose the government imposes a price floor of $40, and agrees to purchase any and all units consumers do not buy at the floor price of $40 per unit.
a. Determine the cost to the government of buying firms’ unsold units.
b. Compute the lost social welfare (deadweight loss) that stems from the $40 price floor.
Problem 02-14
You are the manager of an organization in America that distributes blood to hospitals in all 50 states and the District of Columbia. A recent report indicates that nearly 50 Americans contract HIV each year through blood transfusions. Although every pint of blood donated in the United States undergoes a battery of nine different tests, existing screening methods can detect only the antibodies produced by the body’s immune system – not foreign agents in the blood. Since it takes weeks or even months for these antibodies to build up in the blood, newly infected HIV donors can pass along the virus through blood that has passed existing screening tests. Happily, researchers have developed a series of new tests aimed at detecting and removing infections from donated blood before it is used in transfusions. The obvious benefit of these tests is the reduced incidence of infection through blood transfusions. The report indicates that the current price of decontaminated blood is $60 per pint. However, if the new screening methods are adopted, the demand and supply for decontaminated blood will change to

Qd = 210 – 1.5P and Qs = 2.5P – 150.

What price do you expect to prevail if the new screening methods are adopted? How many units of blood will be used in the United States? What is the level of consumer and producer surplus? Illustrate your findings in a graph.

Instruction: Round your answers to the nearest whole number.

Price:

Units of blood:

Consumer surplus:

Producer surplus:

Instructions: Use the tools provided to graph the supply and demand curves from 0 to 150 pints of blood (two points total for each curve). Indicate consumer and producer surplus
Problem 02-16 (Algo)
You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as 25 percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by Qd = 250 – 5P and the market supply (including taxes) is QS = 3P – 110 (both in millions), where P is the monthly price of the telecommunication services.

The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of QS = 3.5P – 110. How much money per unit would a typical consumer save each month as a result of the proposed legislation?

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