economic

Economics 100B Professor K. Kletzer UCSC Spring 2020

Problem Set 2 Due: Friday, April 24, 2020 at 11:59 pm

1. You are asked to analyze each of the following events using the Solow growth model (the events all happen at time 0):

a) The investment rate rises in Tanzania.

b) Immigration increases the population of France by 10%.

c) An earthquake destroys 10% of the capital stock of Chile. (Hint: does steady state GDP per

capita change in Chile?)

d) Malaysia realizes a 10% rise in TFP due to technology transfer.

For each of these:

Draw a Solow diagram to show what happens when the economy is initially in steady state.

Explain how steady-state GDP per capita changes. Use algebra to help in your explanation. Does

steady-state capital per capita change?

Explain how the growth rate of GDP per capita changes at time 0.

Explain how the economy adjusts from the short run to the long run after the change.

2. Predicting steady states and growth rates. Consider the data in the table below.

Country Per capita GDP, 2017 Investment Rate �̅�𝑠 in %

TFP �̅�𝐴

United States 1.000 23.5 1.000 Switzerland 1.151 28.8 1.052 Hong Kong 0.741 27.0 0.772 Canada 0.776 25.1 0.811 France 0.709 24.1 0.771 Japan 0.734 28.1 0.752 South Korea 0.666 36.9 0.713 Argentina 0.300 15.9 0.532 Mexico 0.311 19.6 0.502 Thailand 0.287 27.7 0.468 India 0.117 24.7 0.270 Kenya 0.056 11.9 0.194 Ethiopia 0.029 15.7 0.114

a) Assuming that there are no differences in TFP (ignore the last column for now) or the rate of depreciation across countries, use the data in the table to predict the ratio of per capita GDP in each country relative to that in the United States.

b) Do the same exercise (as in part a) assuming that relative TFP is given by the levels in the last column. Discuss briefly the differences you find between these two approaches. c) Based on the numbers you find with TFP differences (in part b), compute the percentage gap between the steady-state income ratio and the ratio observed in 2017. Use the actual 2017 ratio in the denominator. 3. a) Using the production function 𝑌𝑌𝑡𝑡 = 𝐴𝐴𝑡𝑡𝐾𝐾𝑡𝑡

1/3𝐿𝐿𝑡𝑡 1/3, write out the relationship between the growth rate

of per capita GDP and the growth rates of TFP, capital, and population (this is in chapter 3). How are the growth rates of GDP and capital related if productivity and population are both constant? b) Using the capital accumulation equation for the Solow growth model

∆𝐾𝐾𝑡𝑡+1 = �̅�𝑠𝑌𝑌𝑡𝑡 − 𝑑𝑑𝐾𝐾𝑡𝑡, we derived the expression for the growth rate of capital,

∆𝐾𝐾𝑡𝑡+1 𝐾𝐾𝑡𝑡

= �̅�𝑠 � 𝑌𝑌𝑡𝑡 𝐾𝐾𝑡𝑡 − 𝑌𝑌∗

𝐾𝐾∗ �.

Make sure you understand how we got this equation. Use this equation to express the growth rate of per capita GDP in terms of �𝑦𝑦

𝑘𝑘 − 𝑦𝑦

∗

𝑘𝑘∗ �.

c) Now you can use this equation to demonstrate the principle of transition dynamics. Use the solutions for per capita GDP in the steady state from your answer to problem 2, part c, to calculate the predicted growth rate of per capita GDP for each country in the table. Rank the countries from highest to lowest growth rate. d) In problem 2, you accounted for differences in TFP. Suppose TFP grows at different rates across the countries in the table. Could this change the rankings of the predicted growth rates across these countries? Can you give a brief explanation? 4. This is problem 9 of chapter 6. Consider the following variant of the Romer growth model:

𝑌𝑌𝑡𝑡 = 𝐴𝐴𝑡𝑡 1 2𝐿𝐿𝑦𝑦𝑡𝑡

∆𝐴𝐴𝑡𝑡+1 = 𝑧𝑧̅𝐴𝐴𝑡𝑡𝐿𝐿𝑎𝑎𝑡𝑡 𝐿𝐿� = 𝐿𝐿𝑦𝑦𝑡𝑡 + 𝐿𝐿𝑎𝑎𝑡𝑡 𝐿𝐿𝑎𝑎𝑡𝑡 = ℓ�𝐿𝐿�

Notice the only change is the exponent on productivity in the production function. There are now marginal diminishing returns to knowledge in the economy. a) Provide an economic interpretation for each of these equations.

b) Find the growth rate of knowledge in this economy.

c) Find the growth rate of output per capita.

d) Solve for the level of output per capita at any point in time.