# LABOR ECONOMY PROBLEMS

### LABOR ECONOMY PROBLEMS

ECO 303 Problem Set 1 Deadline: Wednesday, February 14, 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 (C, I, G, and/or NX) 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 produces some cars, but does not manage to sell them this year. (c) GM sells some cars that entered its inventory last year (d) you pay your tuition (e) Miami-Dade County builds a new public school (f) you buy Apple stock from a broker who charges you a small fee (g) you buy a new computer for your business (h) you pay some teen to mow your lawn (i) you cook yourself a dinner (j) you drink some local beer while in the Bahamas (k) Spirit Airlines buys a new Airbus airplane produced in Europe (l) the government decreases the monetary transfers to the poor

3. A closed economy is producing just oranges and apples. The respective prices and quantities are listed below.

Year Orange price Quantity of oranges Apple price Quantity of apples 2015 \$1.50 20,000 \$2.00 20,000 2016 \$2.00 25,000 \$2.10 50,000 2017 \$2.50 30,000 \$2.20 70,000

Assume that the listed quantities are also the ones bought by the “typical” consumer in the economy. (a) Find the nominal GDP in 2017. (b) Find the real GDP in 2017 if the base year is 2015. (c) Find the GDP de‡ator in 2017 if the base year is 2015. (d) Find the CPI in 2017 if the base year is 2015. (e) Find the 2017 GDP in chained 2015 dollars. (f) If the implicit price de‡ator is set to 100 in 2015, …nd the implicit price

de‡ator in 2017. (g) If the PCE price index is set to 100 in 2015, how much is it (approxi-

mately) in 2017?

1

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 MPC = 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.

2

ECO 303 Problem Set 1 Deadline: Wednesday, February 14, 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 (C, I, G, and/or NX) 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 produces some cars, but does not manage to sell them this year. (c) GM sells some cars that entered its inventory last year (d) you pay your tuition (e) Miami-Dade County builds a new public school (f) you buy Apple stock from a broker who charges you a small fee (g) you buy a new computer for your business (h) you pay some teen to mow your lawn (i) you cook yourself a dinner (j) you drink some local beer while in the Bahamas (k) Spirit Airlines buys a new Airbus airplane produced in Europe (l) the government decreases the monetary transfers to the poor

3. A closed economy is producing just oranges and apples. The respective prices and quantities are listed below.

Year Orange price Quantity of oranges Apple price Quantity of apples 2015 \$1.50 20,000 \$2.00 20,000 2016 \$2.00 25,000 \$2.10 50,000 2017 \$2.50 30,000 \$2.20 70,000

Assume that the listed quantities are also the ones bought by the “typical” consumer in the economy. (a) Find the nominal GDP in 2017. (b) Find the real GDP in 2017 if the base year is 2015. (c) Find the GDP de‡ator in 2017 if the base year is 2015. (d) Find the CPI in 2017 if the base year is 2015. (e) Find the 2017 GDP in chained 2015 dollars. (f) If the implicit price de‡ator is set to 100 in 2015, …nd the implicit price

de‡ator in 2017. (g) If the PCE price index is set to 100 in 2015, how much is it (approxi-

mately) in 2017?

1

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 MPC = 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.

2

0 replies