This exam is due no later than 4:30 on Tuesday December 17. You may put the exam in my mailbox or bring it to my office. If possible, I strongly prefer receiving a hard copy of the exam. If that is not possible, you may email it to me.
You may not collaborate with anyone on this test. You may use your textbook and your course notes. Each student in this course is expected to abide by the Cornell University Code of Academic Integrity.
Please answer all of the following questions. Show all of your work and label clearly your answers. Good luck.
1. A competitive industry faces a market demand for their product of P=40-1.2Q. The marginal cost function is P=.4Q.
A. How many units of the product will the firm produce? What will be the market price? Sketch your solution.
The government has determined that this industry is polluting the air and a careful study estimates that the marginal external cost of the pollution is P=.1Q.
B. What is the marginal social cost of production taking into account the externality? What is the socially optimal level of production? What is the dead weight loss from unregulated production?
C. What should be the amount of a government imposed Pigouvian tax be in order to bring about the optimal level of production? Add your solutions to parts b. and c. to your sketch.
D. What are the revenues from the tax? What is the price elasticity of demand and the price elasticity of supply at the efficient level of production? What is the economic incidence of the optimal Piguovian tax?
2. Given concerns about externalities associated with automobile usage, many have proposed increasing the tax on gasoline. Suppose a consumer has annual income of $50,000 and suppose the price of gas is currently $2.50 per gallon.
A. Illustrate the consumer’s budget constraint with gallons of gasoline per year on the horizontal axis and dollars spent on all other goods on the vertical axis (i.e., you can assume the price of a unit of all other goods is $1).
B. Illustrate how the budget constraint changes if the government imposes a tax on gasoline that raises the price per gallon to $5.00.
C. Map a plausible indifference curve onto your original budget constraint and label the consumer’s optimal bundle A. Use a second indifference curve to show how the consumer’s optimal consumption bundle changes after the gas tax and label that point B.
One of the concerns about using gas taxes to discourage automobile use and carbon emissions is that they are potentially regressive taxes and, thus, impose hardships on lower income consumers. Some have therefore suggested that the government should simply rebate all revenues from a gasoline tax back to the taxpayers.
D. Suppose our consumer subsequently receives a rebate equal to the amount that person had spent in gas taxes. Illustrate how this rebate alters the budget constraint of our consumer and also their optimal consumption bundle (add a new indifference curve and label the optimal consumption bundle point C).
E. Can you tell whether the tax-with-a-rebate policy is successful at getting our consumer to consume less gasoline than they were consuming before there was either the tax or the rebate? Use your understanding of income and substitution effects to explain your reasoning.
F. True or False and briefly explain and illustrate your reasoning: Since the government is giving back in the form of a rebate exactly the same amount as it collected in gasoline taxes from our consumer, the consumer is made no worse off from the tax/rebate policy than they were originally before any tax or rebate.