Economic
ECO 303 Problem Set 1
Deadline: Wednesday, Feb 13, 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) private saving
2. Which COMPONENT(S) (if any) of U.S. GDP (consumption C, invest- ment I, government spending G, and/or net exports NX) THIS YEAR would be a¤ected and how (INCREASE or DECREASE) if: (a) Miami-Dade County builds a new public school. (b) You buy an old computer for your business. (c) A French tourist buys some ice cream while visiting Key West. (d) General Motors produces some cars, but does not manage to sell them
this year. (e) Spirit Airlines buys a new Airbus airplane produced in Europe. (f) Boeing sells an airplane, which was produced last year, to Japan Airlines. (g) A Brazilian citizen buys a new house in Miami Beach and rents it to a
Colombian citizen. (h) You cook yourself a dinner. (i) The government increases the monetary transfers to the poor. (j) You buy some shares of Tesla stock from a broker who charges you a
small fee.
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 2016 $1.50 25,000 $2.00 25,000 2017 $1.65 30,000 $2.10 50,000 2018 $2.00 35,000 $2.20 80,000
Assume that the listed quantities are also the ones bought by the �typical� consumer in the economy. (a) Find the nominal GDP in 2018. (b) Find the real GDP in 2018 if the base year is 2016. (c) Find the GDP de�ator in 2018 if the base year is 2016. (d) Find the CPI in 2018 if the base year is 2016, assuming that the �xed
basket used in estimating the CPI re�ects the quantities bought in 2016. (e) Find the 2018 GDP in chained 2016 dollars. (f) If the implicit price de�ator is set to 100 in 2016, �nd the implicit price
de�ator in 2018. (g) If the PCE price index is set to 100 in 2016, how much is it (approxi-
mately) in 2018?
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4. A country�s population (civilians, age 16 or older) is 200 million. We know that 100 million people are employed and 8 million are unemployed. (a) Find the unemployment rate and the labor force participation rate. (b) Imagine that a recession hit the economy and 3 million workers were
�red. 2 million of them were not able to �nd jobs for some time, got desperate, and decided to wait for better economic conditions. The remaining 1 million 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) = 5K1=5L4=5. Assume the supply of labor is 7,776. (a) How much is the supply of capital if the market clears at a real rental
rate of 16? (b) A hurricane hits the island in question. There are no casualties, but
some capital stock has been destroyed. Would the equilibrium real rental rate increase or decrease? Explain.
6. Consider a closed-economy market-clearing model with the following pro- duction function:
F(K;L) = AK1=4L3=4;
where K denotes capital, L denotes labor, and A > 0 is referred to as total factor productivity. Assume the supply of capital increases by 20%. Calculate the resulting percentage change in the output, in the real wage, and in the real rental rate.[In answering this question, you are allowed to use the approxima- tions regarding percentage changes; see slide 4 of the math review (slide set 2)].
7. Consider the following closed-economy market-clearing model (notation as in class):
Y = F(K;L) = 3K1=3L2=3
K = 125; L = 8;000; G = 1;200; T = 1;000 C = 60+0:8� (Y �T)
I = 5;940�1;000�r, where the real interest rate r is measured in percent. (a) Find private saving, public saving, and national saving. Compute the
equilibrium real interest rate. (b) Imagine that the government achieves a balanced budget by raising tax
revenue. Find the resulting national saving and compute the new equilibrium real interest rate.
8. Consider a closed-economy market-clearing model where the marginal propensity to consume MPC = 0.9, the marginal product of labor MPL = 30, and the marginal product of capital MPK = 20. (a) Find the change in private saving, public saving, and national saving if
labor increases by 1 unit (i.e., �L = 1). [You may have a look at pages 43 to 45 of slide set 5] (b) Use graphical analysis to demonstrate whether the equilibrium real in-
terest rate will increase or decrease.
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