Consider two bonds (i) 3 year bond with zero coupons, and (ii) 3 year bond with 5% annual coupon. Assume the yield curve is flat at 5.5%. (a) Calculate the price and modified duration of each bond. (b) Suppose the yield curve shift up by 0.1%. What are the new prices of each bond? Check that the % change is close to MD times the yield change. (c) Suppose the yield curve shifts up by 2%. Show that the approximation is not very close. (d) You have $10 million and invested 40% of them in the zero coupon bond and 60% in the 5-year coupon bond. What is the modified duration of your portfolio?

Consider a pure exchange economy with two consumers, A and B, and two goods, x and y. Consumer A has endowment (3, 1). Consumer B's endowment is (0, 2). Both agents regard goods x and y as perfect (one-for-one) complements.(a) Depict this situation in an Edgeworth Box. (b) What is the contract curve for this economy? (c) What prices are consistent with general equilibrium in this economy? Can you determine the final allocation of goods that will result from market exchange at equilibrium prices? (d) How would your answers to (a)-(c) change if B regarded x and y as perfect (one-for-one) substitutes? (e) Your answers above may suggest that it is better not to have linear indifference curves in an Edgeworth Box economy. What is the intuition for this? Does this intuition apply in exchange economies with many more than two consumers?

A pension fund has the following liability: A 20-yr annuity, that will pay coupons of 7% at the end of each year.(t=1...t=20). The pension fund's liability has a face value of 100. The yield curve is flat at 5%. (a) Calculate the PV and duration of this liability. (b) The same pension fund has the following assets: a 1-yr discount bond with face value 100, and a 20-yr discount bond which also has a face value of 100. Calculate the PV and duration of the portfolio of assets. (c) How would you change the portfolio composition of assets (keeping the PV of assets the same), so that the NPV of the firm, defined as P VA P VL, that is Present Value of assets minus the Present Value of liabilities, is unaffected by interest rate changes? (d) After making the change above in (c), what is the change in the NPV of the firm if interest rates increase by 10 basis points.

Consider a pure exchange economy with two goods, wine (x) and cheese (y) and two con sumers, A and B. Let cheese be the numeraire good with price of $1. Consumer A's utility function is UA(x, y) = x/2y/2 while B's utility function is UB (x, y) = x/4/4. A's initial allocation is 30 units of x and 30 units of y. B's initial allocation is 70 units of x and 20 units of y. (a) Put wine r on the horizontal axis and cheese y on the vertical axis. Measure goods for consumer A from the lower left and goods for consumer B from the upper right. Mark the initial allocation with the letter W. Draw the indifference curves for each person through this point. Calculate utility at this allocation for both consumers. Is the initial resource allocation consistent with Pareto efficiency? Explain. (b) Identify the contract curve of Pareto efficient allocations in this economy and show this on your graph. (c) Find the competitive equilibrium prices and consumption for each type of consumer. Derive A's and B's demand functions (gross/Marshallian). Calculate the equilibrium price of wine assuming price of cheese is $1, using Walras' Law. (d) Verify that the First Fundamental Theorem of Welfare Economics holds.

3.Anthony's Bees is an Internet e-tailer that sells equipment to aspiring beekeepers. A complete starter kit in this competitive market sells for $900. Anthony's total costs are given by =3^3, where Q is the number of starter kits he sells each year. The corresponding marginal cost of producing beehives is =92.

a. What is Anthony's marginal revenue from selling another starter kit?

=$MR=$

b. How many starter kits should Anthony sell each year in order to maximize his profits?

c. How much profit will Anthony earn at this output level?

d. Suppose Anthony is producing the quantity indicated in part b. If he decides to produce one more starter kit, what will his new profit be?

Yankee Inc. has sold the Super Coupon Absolute Marvel (SCAM) security to raise new funds. Unlike ordinary bonds, it pays no par value/face value at the end of its life. It only pays coupons every year as follows: $100(1 + 0.05) at the end of year one, $100(1 + 0.05)2 at the end of year two, and so on. This security lasts for 4 years (i.e., makes 4 payments). The current interest rate is 5% for all maturities. (a) What is the price today of SCAM? (b) What is the duration today of SCAM? (c) Yankee Inc. sold $10 million worth of SCAM. It plans to invest the proceeds in two assets, A1 and A2, for the short run. A1 is a 12-month T-Bill, whereas A2 is a 4-year STRIPS. How much should Yankee Inc. invest in A1 and A2 to avoid interest rate risks? 30. You manage a pension fund, and your liabilities consist of two payments as follows: Time Payment 10 years $20 million 30 years $30 million Your assets are $18 million. The term structure is currently flat at 5%. (a) Compute the present value of your liabilities. (b) Compute modified duration of your liabilities. (c) Compute an approximate change in the present value of your liabilities, using duration, when interest rates fall by 0.25%. (d) Suppose that you invest the $18 million in 1-year Treasury bills (i.e., 1-year zerocoupon bond) and in a Treasury bond with modified duration of 20. How would you allocate your assets to avoid interest rate risk of your portfolio, which includes both assets and liabilities?

4.In western Kansas, corn can be grown in two wayswith or without irrigation. Dryland farmers, who do not irrigate their corn, have relatively higher costs. Their long-run average cost is =220+105 and their long-run marginal cost is =3240+105 where Q is measured in thousands of bushels.

Farmers lucky enough to have water rights or river access have lower costs. Their long-run average cost is =216+6 and their long-run marginal cost is =3232+67.

Assume corn is a perfectly competitive market.

a. If the corn market is in long-run equilibrium, with both dryland and irrigated corn being grown, what must the price of corn be?

P =

Use the market price identified in part a to answer each of the following questions.

Round answers to two places after the decimal when necessary.

b. What quantity of corn will each farm with access to irrigation produce?

c. What is total revenue for each farm with access to irrigation? TR =

d. What is total cost for each farm with access to irrigation?

TC =

e. Farmers with access to irrigation earn ( economic profit or economic rent)

5. Five hundred small almond growers operate in areas with plentiful rainfall. The marginal cost of producing almonds in these locations is given by MC = .02Q, where Q is the number of crates produced in a growing season. Three hundred almond growers operate in drier areas where costly irrigation is required. The marginal cost of growing almonds in these locations is given by MC = .04Q.

When entering an equation, be sure to use captial Q for quantity and capital P for price.

a. Find the individual supply curve for each type of almond grower.

Rainy-area growers supply curve: Q =

Dry-area growers supply curve: Q =

b. "Add up" the individual supply curves to derive the market supply curve.

Market supply curve: Qs =

c. If the market demand for almonds is Qd = 105,000 - 2,500P, what will be the equilibrium price and equilibrium quantity?

P* = $

Q* =

d. How many almonds will each type of almond grower produce at that price?

Rainy-area growers:

Dry-area growers:

6.For the past nine months, Iliana has been producing artisanal ice creams from her small shop in Chicago. She's been just breaking even (earning zero economic profit) that entire time. This morning, the state Board of Health informed her that it is doubling the annual fee for the dairy license under which she and other ice cream makers operates. The increase will be retroactive to the beginning of her operations.

a. In the short run, the increase in the fee will(decrease, not affect, increase) Iliana's profit and (decrease, not affect, increase) her output level. In the long run, Iliana will (exit the market , continue to operate)

b. Suppose that instead of doubling the annual fee for a license, the state Board of Health required each ice cream maker to treat every pint of ice cream to prevent the growth of bacteria. In the short run, the bacterial treatment will (decrease, not affect, increase) Iliana's profit and (decrease, not affect, increase) her output level. In the long run, Iliana will (exit the market , continue to operate).

Now consider a bank that invests in these projects. There are N=1,000 agents. All agents are identical ex ante in the above sense. Suppose they all deposit $1 each with the bank. The bank offers the following demand deposit contract (d, d) where di is the amount and agent can withdraw at T=1 and d is the amount he can withdraw at T=2. b) Suppose d=1.2. What is the amount d that the bank can offer an agent who withdraws at T=2? What is the expected utility of an agent? [4 Points] c) Suppose d=3.6. What is the amount d that the bank can offer an agent who withdraws at T=1? What is the expected utility of an agent? [4 Points] Suppose the bank offers (d,d) = (1.4, 3.6). An agent expects that M=640 other agents will withdraw at T=1. d) What is the best response of the type-2 consumer, i.e. does he has an incentive to run to the bank and withdraw at T=1? [3 Points] e) What is the maximum number of withdrawals at T=1 such that a type-2 consumer has no incentive to withdraw at T=1.

Consider a 10 year bond with a face value of $100 that pays an annual coupon of 8%. Assume spot rates are flat at 5%. (a) Find the bond's price and duration. (b) Suppose that 10yr yields increase by 10bps. Calculate the change in the bond's price using your bond pricing formula and then using the duration approximation. How big is the difference? (c) Suppose now that 10yr yields increase by 200bps. Repeat your calculations for part (b). (d) Given that the bond has a convexity of 33.8, use the convexity adjustment and repeat parts (b) and (c). Has anything changed? 40. The yield to maturity of a 10-year zero-coupon bond is 4%. (a) Suppose that you buy the bond today and hold it for 10 years. What is your return? (Express this return as an annual rate.) (b) Given only the information provided, can you compute the return on the bond if you hold the bond only for 5 years? If you answered yes, compute the return. If you answered no, explain why.