econ problem set

Homework 1

GDP Accounting / Neoclassical Growth Model

April 5, 2022

Due date: April 13th 2022 by 3:30pm

Your homework must be submitted electronically using the link provided by your TA.

1 Question I – GDP Accounting

For each of the following, describe how the transactions would affect the GDP accounts of the relevant countries
using the income method, the production method and the expenditure method.

(a) The US exports $100 in solar panels to Japan that are used in homes. Japan exports $100 to in cars to the US.
Of these, 50% are stored in warehouses while the other 50% are sold at price. Report the accounting in both
countries.

(b) The Russian army has invaded Ukraine. Russian soldiers earn wages of 10,000 Rubles each and use ammunition
that the government buys for 5,000 Rubles. The ammunition is produced using 2,000 Rubles of imported steel
and 100 hours of work by Russian workers; these Russian workers are paid 1,000 Rubles in total. Do the GDP
accounting. Now assume that had Russia not invaded Ukraine, soldiers would have still been paid but the
ammunition would have not been produced. Would the GDP in Russia have been higher or lower?

(c) The retail company Levi Strauss sells 1000 jeans for a total value of $100,000 to Macy’s. Macy’s sells the jeans
for $120 each. Say Levi’s sells 50% of its inventory. Compute the effect on GDP. Next, suppose each pair of
jeans in Levi’s inventory is downgraded, such that each pair is worth only half of what it was valued before.
Compute the contribution to GDP in this scenario.

(d) Assume a 16 year old named William Gates writes a computer program in his garage. The software is stored in
his hardware. What is his contribution to GDP? Now, instead assume William Gates incorporates a company
called Microsoft, with himself as the only employee. Any production cost is attributed to his salary. He still
works in his garage. He creates the same computer program. Suppose he values the computer program for
$20,000. What is the contribution to GDP? What is the money that Bill Gates gets in his bank account by
the end of the year and how much is registered as salaries?

(e) Jeremy buys a house for $50,000. When is the transaction part of GDP?

2 GDP calculations

Solve question 1.3 from the course textbook.

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3 Question III – Kaldor Facts

Part 1) Consider the Cobb-Douglas production function:

Y = AK1−αLα,

where K and L are the capital stock and labor uses respectively.
Consider that the economy is composed of a representative firm that maximizes profits by hiring L workers and

paying them some real wage w, for a total wage bill of

wL

The firm also rents capital K at a rate r, paying
rK.

Labor and capital are its only costs.

a) Define the labor share and the capital share of income. What do they represent?

b) Write the firm’s profit function.

c) Calculate the firm’s choice of labor and capital inputs, taking prices as given.

d) Express the labor and capital shares of this economy in terms of a parameter.

e) Given the data plotted in class, what should be a reasonable approximation to the value of α?

Part 2) Consider the capital accumulation equation:

Kt+1 = It + (1 − δ) Kt.

This equation should hold for any t. For this question, assume that It is a constant equal to its steady state value
Iss.

a) Argue that if capital is at steady state, then

Kss =
1

δ
Iss.

b) In the US, we saw that the capital stock is roughly 4 times GDP. Assume that Iss is a constant share s of steady
state output, Yss. If depreciation is roughly 10% annually, what does this imply the savings rate s should be,
approximately? Give a percentage.

Part 3) Consider the answers to part 1-2. Which of all six Kaldor’s facts are guaranteed in a steady state. Which
are not?

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