Microeconomics Problem Set 3: Present Value, Financial Markets, and Expected Utility | Assignments Microeconomics

Problem set 3: present value, financial markets, and expected utility

J. Wahl – Microeconomic Principles-Winter 2009

1. Suppose a new tractor plus 2 years' supply of fuel costs $10,000. You plan to use

the tractor for 2 years and then sell it. You expect the annual increase in your harvest

from using the new tractor to be 20 bushels of wheat. Wheat currently costs $20 per

bushel and 2-year-old tractors are selling for $8500. (Just in case you don’t have a

farming background, assume that a harvest takes place one year after planting. This isn’t

strictly accurate, but assume that it is for the sake of answering this problem). You

expect that both the price of wheat and the price of used tractors will increase at the rate

of inflation, which is currently running at 10 percent annually. What is the maximum

interest rate at which you will borrow to purchase a new tractor? Show your work.

2. Suppose you could put your money in a Wells Fargo account, on which you

would have to pay taxes at a 15-percent marginal tax rate. This account pays 8.5% per

year simple interest. Alternatively, you could invest in a tax-exempt municipal bond

issued by the city of Northfield with a one-year maturity. What is the minimum return

you would have to receive on the Northfield bond to make you willing to hold it? Explain

your answer.

3. Suppose oil currently costs $30 a barrel. You own an oilfield. You can either sell

oil today or keep it in the ground. Suppose today’s interest rate is 8% (simple annual

rate). What must the expected price of oil be a year from now for you to be just

indifferent between selling the oil and keeping it in the ground? Explain your answer.

4. Ever since the oil embargo in the late '70s, people have come up with various

proposals to cut U.S. oil usage. Assume that all schemes cut gasoline

consumption by the same amount. Using the average consumer’s budget

constraint-indifference curve map, show (and explain in words) the effects on utility

of:

a. an excise tax on gasoline (a per-gallon charge) coupled with a lump-sum

rebate of the tax revenue that is just the right amount to enable the average

consumer to obtain the same amount of utility as before the tax and rebate.

b. quantity rationing of gasoline (with ration coupons). Please use the same

graph to show a and b, labeling carefully.

c. Suppose, instead of the rebates in part a., the government wastes excise tax

revenues on some unproductive project. Under these circumstances, show

graphically that consumers are better off with the quantity rationing of part

b than with gasoline excise taxes.

5. One of the new financial instruments that appeared in the late 1970's was the zero-

coupon bond. Such bonds are issued at a price lower than the face value of the

bond, pay no coupon (hence the name), and are redeemable at maturity for the face

value.

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Problem set 3: present value, financial markets, and expected utility J. Wahl – Microeconomic Principles-Winter 2009

Suppose a new tractor plus 2 years' supply of fuel costs $10,000. You plan to use the tractor for 2 years and then sell it. You expect the annual increase in your harvest from using the new tractor to be 20 bushels of wheat. Wheat currently costs $20 per bushel and 2-year-old tractors are selling for $8500. (Just in case you don’t have a farming background, assume that a harvest takes place one year after planting. This isn’t strictly accurate, but assume that it is for the sake of answering this problem). You expect that both the price of wheat and the price of used tractors will increase at the rate of inflation, which is currently running at 10 percent annually. What is the maximum interest rate at which you will borrow to purchase a new tractor? Show your work.
Suppose you could put your money in a Wells Fargo account, on which you would have to pay taxes at a 15-percent marginal tax rate. This account pays 8.5% per year simple interest. Alternatively, you could invest in a tax-exempt municipal bond issued by the city of Northfield with a one-year maturity. What is the minimum return you would have to receive on the Northfield bond to make you willing to hold it? Explain your answer.
Suppose oil currently costs $30 a barrel. You own an oilfield. You can either sell oil today or keep it in the ground. Suppose today’s interest rate is 8% (simple annual rate). What must the expected price of oil be a year from now for you to be just indifferent between selling the oil and keeping it in the ground? Explain your answer.
Ever since the oil embargo in the late '70s, people have come up with various proposals to cut U.S. oil usage. Assume that all schemes cut gasoline consumption by the same amount. Using the average consumer’s budget constraint-indifference curve map, show (and explain in words) the effects on utility of: a. an excise tax on gasoline (a per-gallon charge) coupled with a lump-sum rebate of the tax revenue that is just the right amount to enable the average consumer to obtain the same amount of utility as before the tax and rebate. b. quantity rationing of gasoline (with ration coupons). Please use the same graph to show a and b, labeling carefully. c. Suppose, instead of the rebates in part a., the government wastes excise tax revenues on some unproductive project. Under these circumstances, show graphically that consumers are better off with the quantity rationing of part b than with gasoline excise taxes.
One of the new financial instruments that appeared in the late 1970's was the zero- coupon bond. Such bonds are issued at a price lower than the face value of the bond, pay no coupon (hence the name), and are redeemable at maturity for the face value.

a. Suppose a zero-coupon bond with a maturity of three years is issued at a price of $800 and a face value of $1000. What is the implicit interest rate on this bond? b. Suppose you could either buy the zero-coupon bond or a bond of equal maturity and equal risk that sells for $800 and pays a coupon such that the interest rate on the latter bond is equivalent to the rate you found in part a. Which bond would you buy? Why?

Suppose Brian’s wage is $8 per hour. Brian has no nonwage income and receives no governmental services. a. Suppose Brian pays 10% tax on all income. Draw Brian’s daily budget constraint in income/leisure space, putting leisure on the horizontal axis. b. Now suppose the tax regime changes. Income from Brian’s first 4 work-hours each day is not taxed, but income from the remaining daily work-hours is taxed at 20%. Draw the new daily budget constraint on the same graph as you used for part a, indicating which constraint is old and which is new. c. What will happen to the number of hours that Brian works under the new tax scheme? Explain carefully.

Microeconomics Problem Set 3: Present Value, Financial Markets, and Expected Utility, Assignments of Microeconomics

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