macro econ theory

ECO 303 Problem Set 1 Deadline: Wednesday, February 15, AT THE BEGINNING OF

CLASS

[I will collect all works and then discuss the solutions in class, so you may wish to make a copy of your work before submitting]

1. A stock or a �ow? (a) labor-force participation rate (b) tax revenue

2. Which component(s) (if any) of U.S. GDP would be a¤ected and how (increase or decrease) if: (a) a French citizen buys a new house in Miami beach and rents it to a

Brazilian citizen (b) GM sells some cars that entered its inventory last year (c) you pay your tuition (d) Miami-Dade County builds a new public school (e) you buy Apple stock from a broker who charges you a small fee (f) you buy an old computer for your business (g) you pay some teen to mow your lawn (h) you clean your apartment (i) United Airlines buy a new Airbus airplane produced in Europe (j) the government decreases the monetary transfers to the poor

3. An economy is producing just oranges and apples. The table below contains information about the quantity and prices of both goods from 2014 to 2016.

Year Quantity of oranges Orange price Quantity of apples Apple price 2015 20,000 $1.50 20,000 $2.00 2016 15,000 $2.00 25,000 $2.10

(a) Calculate the nominal GDP for each year. (b) Assume 2015 is the base year and �nd the real GDP and the GDP

de�ator for each year. (c) Assume the typical consumer buys 1,000 oranges, 1,000 apples, and noth-

ing else. (i) Let 2015 be the base year and estimate the CPI for each year. (ii) What is the percentage change in the CPI from 2015 to 2016? (iii) What is the respective percentage change in the GDP de�ator? (iv) Why may using the GDP de�ator (in this case) understate the

increase in the cost of living, while using the CPI (in this case) may overstate the increase in the cost of living?

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4. A country�s population (age 16 or older) is 250 million. Moreover, we know that 150 million people are employed and 8 million are unemployed. (a) Find the unemployment rate and the labor force participation rate. (b) Imagine a recession hits the economy and 1 million workers are �red.

Half of them could not �nd jobs for some time, got desperate and decided to wait for better economic conditions. The other half are still looking for a job, but are not successful yet. Find the unemployment rate and the labor force participation rate.

5. The production function of an isolated island economy is F(K;L) = 4K1=4L3=4. (a) Assume the supply of labor is 1,296

(i) How much is the supply of capital if the market clears at a real rental rate of 8?

(ii) A hurricane hits the island in question. There are no casualties, but some capital stock has been destroyed. Would the equilibrium rental increase or decrease? Explain. (b) Assume the supply of labor is 1,000. How much is the supply of capital

if the market for LABOR clears at a real wage of 6?

6. Consider a closed-economy market-clearing model with the following pro- duction function:

F(K;L) = AK1=5L4=5;

where K denotes capital, L denotes labor, and A > 0 is referred to as total factor productivity. Assume the supply of labor increases by 20%. Calculate the resulting percentage change in the output, in the real wage, and in the real rental rate.

7. Consider a closed-economy market-clearing model where:

Y = F(K;L) = 2K1=2L1=2

K = 100;L = 2;500;G = 200;T = 100 C = 50+0:8(Y �T) I = 200�10;000r

(a) Find private saving, public saving, and national saving. Compute the equilibrium real interest rate. (b) Imagine the government achieves a balanced budget by raising taxes.

Find the resulting private saving, public saving, and national saving. Compute the new equilibrium interest rate.

8. Consider a closed-economy market-clearing model where the marginal propensity to consume (MPC) equals 0.8, MPL = 20, and MPK = 10. Find the change in private saving, public saving, and national saving if capital decreases by 10 units (i.e., �K = �10). Use graphical analysis to demonstrate whether the equilibrium real interest rate will increase or decrease.

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9. [Based on slide set 5] You sell some government bonds to the Fed and deposit the proceeds of $1,000,000 in Bank 1. Bank 1 keeps 3 percent of this amount as reserves and lends the rest to borrower 1. Borrower 1 keeps 20 percent of the loan as currency and deposits the rest in Bank 2. Bank 2 keeps 10 percent of the deposited amount as reserves and lends the rest to borrower 2. Borrower 2 spends the loan to buy a $450,000 Lamborghini from a car dealer and $240,000 worth of government bonds from the Fed, keeping the remaining amount as currency. The car dealer deposits the $450,000 in Bank 3. Bank 3 keeps 5 percent of this amount as reserves and uses the rest to buy some securities from a pension fund. The pension fund uses the proceeds to buy government bonds on the open market. The seller of the government bonds happens to be the Fed. Calculate the change in the money supply.

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