Question

1. Several years ago Congress required the installation of anti-pollution devices on new automobiles sold in this country. Since these devices are relatively expensive, it is natural to ask what effect these requirements will have on automobile sales and prices. To analyze this question suppose that the yearly demand curve for automobiles is: (1) Pd=7.2-0.4C, where Pd is the price at which C cars can be sold. Pd is measured in thousands of dollars and C is millions of cars per year. Also assume that, before Congress imposes the anti-pollution requirements, the yearly automobile supply curve is: (2) Ps=2C In this equation Ps is the price at which c cars will be supplied.

A) When these are the supply and the demand curves what is the equilibrium price of automobiles and how many are sold? (What is the equilibrium quantity?)

B) Suppose that the new regulations cause the price at which C cars will be offered for sale to rise by 60%. Then the supply curve (2) is replaced by the supply curve: (3) Ps=3.2C

How does this shift in the supply curve affect the auto price and sales? Does the price rise by 60%? Why? Do you think the price could rise by 60% if the demand curve were different? What would the demand curve have to be like to make this happen?

C) Now suppose the demand curve is: 4) Pd=∝-βC, Where ∝ and β are positive constants. Also suppose that the supply curve shift caused by the anti-pollution device requirement results in a supply curve: (4) Ps=2C+.1 rather than (3). This would happen if the devices added $100 to the cost of each car. When the demand curve is (4) and the supply curve shifts from (2) to (5), what effect does this shift have on the price of autos and on auto sales? Does the auto price rise by $100? Why? How is the value of β related to the change in price and sales? Does this relationship make sense? Why?

Answer 1