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Econ 305: Intermediate Macroeconomics

Midterm 1

Fall 2023

Instructions: The exam consists of 4 short answer questions. The use of the textbook, notebook, computer, cell phone, or tablet is not allowed and will result in a score of zero. You are allowed to use a simple calculator. All steps, calculations, and explanations justifying an answer must be explicit to receive full credit. All answers must be handwritten in the paper exam and inserted in the assigned space to be graded. The time allowed is 1:20 minutes.

Question 1 (25 pts)

Assume an open economy in which consumption (C) is given by the equation C = 1000 + 0.5(Y−T). Investment (I) is given by I = 500 - 10r, where r is the real rate of interest in percent. The government has a balanced budget where taxes (T) and government spending (G) account to 1000. Exports (E) account to 500 and imports (M) account to 1000.

a) Derive and graph the IS relation using the information above. Graph the LM relation when the Fed fixes the real interest rate at 5% (r=5). 5pts

b) Calculate the equilibrium output, consumption, and investment. 5pts

c) Graph the expanded IS-LM Model with the Phillips curve underneath. Assume inflation is still anchored at ᴨ and the equilibrium output is the one obtained in part b). Now consider that the conflict in Israel is expected to increase oil prices, contracting the economy (IS curve). How is this shock expected to affect output and inflation in the short run? 10pts

d) How would the Fed intervene in the mid run? Show in the same graph from question c). 5pts

The Fed will intervene to reduce deflation and keep expectations anchored. The Fed will use its tools to reduce the interest rate such that the mid run output returns to 2900, the change in inflation returns to zero, and the real interest rate will be lower than 5%.

Question 2 (25 pts)

Consider the production function F = K^0.5L^0.5, where K is total capital and L is population. Suppose that the savings rate is 0.5, the depreciation rate, δ, equals 0.05, and population growth, n, is 0.05.

a) Show that the production function exhibits constant returns to scale. 2pts

b) Derive the per-worker production function y = f(k) 3pts

c) Solve for the steady-state level of capital per worker. 5pts

d) Solve for the steady-state output, consumption and investment level per worker. 5pts

e) Solve for the golden rule of capital. 5pts

f) Find the savings rate that allows the golden rule of capital to be the steady state. 5pts

Question 3 (25 pts)

Given the current events in the Middle East, an investor is actively trying to diversify her portfolio. She is considering purchasing a 3-year US Treasury Bond or a 3-year bond from a country in Latin America. The current interest rate is 5% and is expected to be constant for future years. The face value of the Treasury Bond is $10,000 and the face value of the corporate bond is $12,000. The probability of the Latin American country defaulting on debt payments during the next years is 10% each year. The bonds pay no coupons.

a) How much is the Treasury bond worth today? Show calculations. 5pts

b) How much is the Latin American bond worth today? Show calculations. 5pts

c) Why are the values different? Explain. 5pts

d) If both bonds are offered to the investor today for $8,000, which should be purchased? 5pts

e) Now assume that one year has passed and the investor wants to sell the bond chosen in d). At what price can this bond be sold? 5pts

Question 4 (25 pts)

A retiring journalist signed his final 2-year contract with his employer, agreeing to a fixed annual salary of $100,000, paid at the end of each year. The federal and state income tax adds to 25% and the interest rate is expected to remain at 5%. The journalist owns a duplex, he lives in one and rents the other one. Yearly rent payments are of $12,000, collected at the beginning of the year. Maintenance costs for the rental (depreciation) account for $2,000 that are spent at the end of the year. At the end of the 2^nd year, the journalist plans to sell the duplex (well-maintained) for $1,000,000 and will move to a beach in Mexico.

a) What is the expected present discounted value of the human wealth? 5pts

b) What is the expected present discounted value of the non-human wealth? 10pts

c) What is the expected present discounted value of the total wealth? 5pts

d) If this person is expecting to live for 25 more years past retirement and smoothens consumption, how much would the yearly consumption be? 5pts