# If the PCE price index is set to 100 in 2015, how much is it (approximately) in 2017?

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 áow?
(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
(e) Miami-Dade County builds a new public school
(f) you buy Apple stock from a broker who charges you a small fee
(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 ìtypicalî
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 deáator 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 deáator is set to 100 in 2015, Önd the implicit price
deáator in 2017.
(g) If the PCE price index is set to 100 in 2015, how much is it (approximately)
in 2017?
1
4. A countryís 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 Öred.
Half of them could not Önd 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=4L
3=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 production
function:
F(K; L) = AK1=5L
4=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=2L
1=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.