Homeworks - Exam 1

The Black Death in the fourteenth century decimated European populations and workforces by up to 50 percent. Assuming that the capital stock was unaffected (i.e. you can assume that K ¯ was constant), use the model of production to predict the effect of such a decline in the number of workers on output, output per worker, the marginal product of labor, and the marginal product of capital. Select all the correct answers below: A. Total GDP (Y) falls. B. The marginal product of capital rises. C. The marginal product of labor rises. D. Wages fall. E. GDP per worker ( Y L = y ) stays constant since both Y and L are falling.

A,C

Consider the following per capita production functions for the US and the USSR (the Soviet Union): Yus = Aus(K^a)us Yussr=Aussr(K^a)ussr You know that Yussr/Yus = 0.75, Aussr/Aus = 0.5, and (K^a)ussr/(K^a)us = 27/8. Put differently, the USSR produces less output (per capita) with a higher capital-labor ratio, simply because the US is more productive than the USSR. One piece of information is missing, however. You don't know the capital income share α, except you know that it's the same in both countries. What value of α reconciles the three pieces of information you have for these two countries? (Hint: Take the ratio of the two equations, take natural logs, and then solve for α.) A. α=1/3 B. α=1 C. α=1/2 D. No positive value of α can reconcile the given information

A

If the population doubles every 40 years, then the annual growth rate of the population is ______. A. 1.75 percent B. 2 percent C. 3 percent D. 0.57 percent

A

Suppose the variable a grows at a constant rate ga, the variable b grows at a constant rate gb, the variable c grows at a constant rate gc, and the variable d grows at a constant rate gd. If we know that ga = 1/2 ( gb − gd ) + 3/4 gc, what is the relationship between variables a, b, c, and d? A. a=[(b^1/2)/(d^1/2)]c^3/4 B. a=[(b^1/2)/(c^1/2)]d^3/4 C. a=1/2b+3/4c+1/2d D. a=1/2b+3/4d-1/2c

A

How quickly GDP doubles will depend on: A. the initial value of GDP. B. the growth rate of GDP. C. the current value of GDP. D. all of these

B

Let the production function be Y = K^1 − δ L^δ. Then the ratio MPK/APK =______. (Recall, MPK = ∂ Y/∂ K and APK = Y/K.) A.§ B. 1-§ C. 1 D. Not enough information is given

B

Which of the following is an example of labels for equidistant tick marks on a ratio scale? A. 1, 3, 5, 7, 9... B. 1, 3, 6, 9, 12... C. 1, 3, 9, 27, 81... D. All of these choices are correct.

C

Which of the following questions does the Solow model NOT help to explain? A. Why do countries have different growth rates in the same time periods? B. Why are some countries richer than other countries? C. Why do countries sustain growth in the long run? D. Will a country be richer if the investment rate is higher than another country, all else being equal?

C

According to figure 3.7, the fastest growing country during 1960-2014 had a level of per capita GDP approximately equal to _____ of the U.S. level in 2014: A. 1/16 B. 1/8 C. 1/4 D. 1/2

C.

According to the principle of transition dynamics in the Solow model, which economy will have the highest growth rate of GDP per capita? A. A poor country in steady state. B. A country 100 years after the Black Death wiped out half the population. C. The same country 1 year after the Black Death wiped out half the population. D. A country 1 year after a natural disaster destroyed a large amount of capital.

D

Consider Figure 4.1. (Half rainbow) For given L, the shape of this production function suggests that α in the production function Y = K ^α L^1 − α is: A. equal to one. B. greater than one. C. equal to zero. D. less than one. E. Not enough information is given.

D

Which of the following are NOT discussed in Jones and Klenow's alternative measure of economic welfare? (Note: there may be more than one correct answer. Select all that apply.) A. inequality B. leisure C. life expectancy D. child mortality rates E. consumption share of GDP F. environmental degradation

D,F

A production function has inputs X, Y, and Z and a productivity parameter A. The production function A^2 X^1/4 Y^1/2 Z^1/4 exhibits ________. (More than one answer may be correct.) A. constant returns to scale with respect to X, Y, and Z. B. decreasing returns to scale with respect to X, Y, and Z. C. diminishing marginal returns to scale with respect to X, Y, and Z, individually. D. increasing returns to scale with respect to X, Y, and Z.

A,B

Which of the following is an explanation for why a Solow economy eventually settles in steady state? Select all that apply. A. The marginal product of capital is infinite when evaluated at K=0 and approaches 0 as K approaches infinity. B. The capital stock depreciates at a constant rate. C. Eventually, investment generated is equal to the amount of capital depreciated. D. None of these answers is correct.

A,B,C

If the productivity parameter is assumed to equal 1, the production model ______. (More than one answer may be correct.) A. correctly identifies that countries are richer if they have more capital. B. predicts that countries with low capital-labor ratios countries are substantially poorer than they are in reality. C. predicts that some countries are richer than the United States. D. predicts that differences in the capital-labor ratio can account for the entire gap in income per person across countries.

A,C

Which of the following increases the U.S. GDP? A. The U.S. government purchases a tank from a U.S. company. B. The U.S. government increases social security payments. C. The U.S. government increases funding for tax policy at a U.S. university. D. The U.S. government purchases protective medical equipment from China.

A,C

If total depreciation exceeds gross investment, the economy is ______________ its steady state and output per person is growing at a ______________ rate.

above; negative

In the long run, the Solow model predicts that consumption per capita is maximized when s ¯ is ___________.

Between 0 and 1

Consider a simple economy producing 2 goods: coffee and TVs. In 2014 the economy produced 2000 pounds of coffee and 10 TVs. In 2015 the economy produced 1000 pounds of coffee and 12 TVs. The price of one TV was $1,000 in both years while the price of coffee decreased from $6/pound in 2014 to $5/pound in 2015. Based on this information the percentage change in real GDP in chained prices benchmarked to 2015 is: A. 22% B. 16.5% C. -16.5% D. -22%

C

If nominal GDP grew by 7% in year 2 relative to year 1, the price level increased by 2% during the same period and the real GDP in year 1 was $1,000, what was real GDP in year 2? Use the properties of growth rates in section 3.5 of the textbook to answer your question. A. $1,000 B. $1,020 C. $1,050 D. $1,100

C

In the standard production model's production function, the productivity parameter enters the equation with an exponent of one, while in the Solow model's equation for the steady-state stock of capital it is greater than one because: A. the long-run level of the capital stock does not on productivity in the Solow model, only output does. B. the productivity measure is negative in the Solow model. C. the long-run level of output depends on the capital stock, which, in turn, depends on productivity in the Solow model. D. productivity measure is zero in the production function model.

C

According to the Solow model two countries will grow at different rates if: A. both have the same steady-state level of output and the same capital stock below the steady-state level B. both have different steady-state level of output and the same capital stock below the steady-state level C. both have the same steady-state level of output and the same capital stock above the steady-state level D. they are both in their steady states

B

In the Cobb-Douglas production function Y = AK^α L^1 − α, defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is: A. y = Ak^ − α B. y = Ak^α C. y = Ak^1 − α D. y = Ak^1 − α E. None of these answers is correct.

B

Professor Nordhaus' light example in the Economist article "The trouble with GDP" highlights a major shortcoming of GDP as a measure of welfare. Which of the answers below best captures the essence of his argument? A. Pollution caused by candles isn't taken into account. B. Quality improvements as a source of well-being are ignored. C. GDP doesn't capture the soothing effect of candlelight. D. The marginal cost of light is zero, and by convention zero-priced goods and services are excluded from GDP.

B

The equation sF(Kt ,L) + ( 1 − d) Kt describes A. gross investment. B. tomorrow's capital stock Kt + 1. C. net investment. D. today's capital stock Kt. E. depreciation.

B

This year a real estate agent helped you buy a house for $200,000 which was originally built in 1985. The agent's commission was $12,000. How will this transaction affect this year's GDP? A. Consumption expenditures will increase by $212,000. B. Consumption expenditures will increase by $12,000. C. Investment expenditures will increase by $212,000. D. Investment expenditures will increase by $12,000.

B

Which of the following counts as consumption? A. You buy your neighbor's gas grill. B. You buy a computer to use for fun at home. C. You buy a new house. D. All of these choices are correct.

B

Assume that GDP per capita for two countries is displayed in plot with a ratio scale on the y-axis and a linear time scale (in years) on the x-axis. If the two times series are straight lines in this plot, then the growth rates are _________ over time. If in addition, the two lines are parallel and upward-sloping, then the income gap | y high − y low | (where the vertical bars are the symbol for "absolute value") is __________ over time.

constant;increasing

One example of an inclusive institution discussed by Acemoglu and Robinson in their book "Why Nations Fail" (and in a large number of other publications) is the so-called commenda contract in Medieval Venice (and other parts of the Mediterranean). These contracts are discussed in some additional detail in the book excerpt available in the Chapter 4 module on Canvas. Acemoglu and Robinson claim that this type of contract offered emerging traders a pathway to commercial success and wealth. What feature best captures the "inclusiveness" of this type of contract? A. The contracts were written on cheap paper rather than expensive parchment, which lowered the entry costs substantially. B. The contract offered novice traders a line of credit to finance new commercial ventures. C. The commenda contract enabled up-and-coming traders to acquire equity stakes in risky, but potentially lucrative commercial voyages without requiring them to supply capital in the same proportion as their profit share. D. The term "commenda" refers to the use of a common language, which was crucial in overcoming cultural and linguistic barriers to trade in the Mediterranean around the 14th century.

C

Suppose we compare GDP per person in Uganda and the United States in two ways: first using the nominal exchange rate and then again using the relative price-based conversion. The GDP per person in Uganda calculated using the exchange rate method is $643 while that calculated using the relative price-based conversion is $1,102. Which of the following is true about the relative price ratio between Uganda and the U.S. (i.e., the price level for Uganda relative to the United States)? A. Greater than 1. B. Equal to 1. C. Less than 1. D. Not enough information is given

C

The United States and Chile have both grown at about 2 percent per year for the last 40 years. By the principle of transition dynamics, what does this imply? A. Both countries are below their steady states. B. Both countries are above their steady states. C. Both countries are at their steady states. D. It implies nothing, because transition dynamics only tell us how an economy moves over time.

C

The production function Y = K^1/3L^2/3 − G exhibits________ returns to scale in K and L. (Assume G is some fixed positive number.) A. constant B. decreasing C. increasing D. None of these answers is correct.

C

Using the same production function as in the previous question, you know that if K and L are both multiplied by the same scalar λ, then y = Y L(output per person) will ______ A. change by the same factor λ. B. change by factor 1 λ. C. remain constant. D. will change, but it's impossible to tell by how much.

C

What is the paradox that Diane Coyle (the author of "GDP: A Brief but Affectionate History") highlights in the NPR Planet Money podcast "Beyond GDP"? A. Even though GDP has become more useful over time, we haven't payed enough attention to it recently. B. People and GDP are both "shortsighted". We should pay more attention to the long run. C. Natural disasters lead to a rise in GDP since reconstruction efforts are included, but the destruction of infrastructure, property,... that triggers the recovery effort is not. GDP tends to understate the welfare costs of natural disasters.

C

Which of the following characteristics below does the Cobb-Douglas production function Y = K^α L^1 − α − β X^β satisfy? (There may be more than one correct answer. Select all of them.) A. Increasing returns to scale. B. Decreasing returns to scale. C. Constant returns to scale. D. Constant labor share of income. E. It is an exact replication of a firm's production function.

C,D

A country that, since 1980, has shown convergence to the United States is Japan. China. South Africa. Germany.

China

A country starts in steady state. Due to a lost war, the country has to give up territory containing 10% of its capital stock and 50% of its population. This will cause A. the economy to converge to a new higher steady-state level of capital k ∗. B. the growth rate of output to rise initially as the economy begins to converge to the old steady-state level of output per capita y ∗. C. the growth rate of output to rise initially as the economy begins to converge to a new lower steady-state level of output. D. the economy to enter a period of negative growth of output per person (y t).

D

Consider the production function Y = K^αL^β X^γ, where X denotes the quantity of intermediate goods used in the production of the final good Y. You know that α + β = 1 and β + γ = 1. Moreover, you know that α , β , γ are strictly positive real numbers. From this conclude that: A. Y has constant returns to scale with respect to all three inputs. B. if you double the amount of K, L, and X, you will produce 2^2 = 4 times the amount of output. You know this since ( α + β ) + ( β + γ ) = 2. C. the production function has constant returns to scale with respect to K and X. D. the production function has decreasing returns to scale with respect to K alone.

D

In the Solow model, net investment is defined as: A. investment plus capital depreciation. B. the saving rate minus the depreciation rate. C. the saving rate plus the depreciation rate. D. investment net of capital depreciation. E. All of these answers are correct.

D

Output per person is higher when A. a country is more efficient in adopting a technology. B. a country has a higher capital-to-population ratio. C. a country has stronger property rights and contract enforcement. D. All of these choices are correct.

D

Suppose you are given the data for Brazil and Portugal. In Brazil, the saving rate is 0.1 and the depreciation rate is 0.1, while in Portugal the saving rate is 0.2 and the depreciation rate is 0.1. Using the Solow model, you conclude that in the steady state: A. Brazil has a higher level of output than Portugal. B. Brazil has a higher capital-output ratio than Portugal. C. Portugal has a higher level of output than Brazil. D. Portugal has a higher capital-output ratio than Brazil. E. Portugal and Brazil have the same capital-output ratio.

D

Under national income accounting, if GDP in a given country equals $2,000, then we know for sure that A. the goods and services produced in the economy equal $2,000. B. the income earned in the economy equals $2,000. C. the total purchases in the economy equal $2,000. D. All of these choices are correct.

D

Use the version of the Solow model with population growth to answer the following question. Suppose the current capital-labor ratio in South Korea is greater than the current capital-labor ratio in China. Moreover, assume that productivity is constant (i.e. it doesn't grow over time), but it needn't be the same in the two countries. Lastly, the two countries have the same population growth and depreciation rates and the same labor income share. If GDP per capita grows at the same rate in China and South Korea, it must be the case that A. steady-state output per person is higher in China, provided they have the same investment rate. B. China and South Korea have the same steady state. C. neither of the two countries has reached its respective steady state yet. D. s^α/1 − α A^1/1 − α is higher in South Korea than in China.

D

When comparing real rates of economic growth it is best to use ( ___ ) variables. When comparing shares of consumption in GDP it is best to use ( ___ ) variables. A. nominal; nominal B. chain-weighted; chain-weighted C. nominal; chain-weighted D. chain-weighted; nominal

D

Consider an economy described by the textbook Solow model with the following Cobb-Douglas production function: Y = AK^α L^1 − α, where α = 1/3. The economy is producing 100 units of output and the productivity parameter is equal to 1. If the depreciation rate is 6%, the investment rate is 24%, and there are 64 workers, the growth rate of total output Y t is ______________ and the economy is ____________________ its steady-state output per capita of __ units.

positive; converging to; 2

Starting from steady state, a permanent decrease in the rate of depreciation in the Solow model causes output per capita to ______________ in the short run. In the long run, the growth rate of the economy ____________________________.

rise; remains unchanged

According to Joel Mokyr's "Progress Isn't Natural" article, a consensus emerged in the 18th century that ____________ and ____________ were the fundamental causes of economic progress.

science;technology

If we define s1 and s2 as the saving rates, d1 = d2 as the depreciation rates, and A1 and A2 as productivity in Countries 1 and 2, respectively, and the production function per capita is given by y t = Akt^1/3 in both countries, the Solow model predicts that the ratio of steady-state GDP per worker in Country 1 relative to Country 2 is:

y1/y2 = (A1/A2)^3/2 x (s1/s2)^1/2

In the year 2014, the five richest countries had a per capita GDP that was ________ times higher than the five poorest countries. Capital per worker varies by a factor of about ________ while total factor productivity is about ________ times higher in the top-5 compared to the bottom-5. A. 60; 6; 10 B. 45; 10; 4.5 C. 1.25; 0.25; 5 D. 18; 108; 6 E. 70; 5; 14

E

The law of diminishing marginal product to capital means that as we add additional units of capital: A. and labor, output will increase, but at a constant rate. B. and labor, output will increase, but at a decreasing rate. C. but hold labor constant, output will increase, but at an increasing rate. D. but hold labor constant, output will increase, but at a constant rate. E. but hold labor constant, output will increase, but at a decreasing rate

E

Finally, assume that real GDP in year 1 (Y 1) equals nominal GDP in year 1 and compute the chain-weighted GDP (Y 2) for year 2 using the following formula: Y 2 = √(L × P) × Y 1. The growth rate of chain-weighted real GDP between year 1 and 2 is ______ percent.

9

Considering the figure below, the transitional dynamics best describe (select all that apply): Y* drops to Y** A. a decrease in the depreciation rate. B. a negative and permanent productivity shock. C. a decrease in the saving rate. D. a decrease in the capital stock. E. an increase in the population.

B,C

Consider Table 2.3. Using the Laspeyres index, the real GDP in 2018 is $______.

8600

Which of the following is NOT included in the investment category of the national income accounts? A. Installation of new robots at an automobile factory B. The purchase of a new family car. C. Screws and fasteners used in the production of a new car. D. The purchase of a new computer for the auto plant manager.

B,C

Steady state output goes from: Steady state consumption goes from:

Y to bottom line; Y to sY

In a production model where the production function is Y = AK^1/3L ^2/3 the equilibrium wage rate is equal to 2, labor supply is 27 workers and the productivity parameter is equal to 1. What is the equilibrium level of capital?

729

The real growth rate of this same economy using the Paasche index is ______ percent.

8

Using the same Table 2.3 , real GDP in 2017 based on the Paasche index is $______.

8875

A U.S. citizen resides in Germany where she works for a U.S. company and gets paid $80,000 in 2020. By how many U.S. $ does U.S. GDP change as a result?

0

Using the Solow model, if, in time t = 0, the capital stock is K0 = 100, and in time t = 1, the capital stock is K 1 = 75, d= 0.25 is the depreciation rate, then gross investment I0 between periods 0 and 1 is ______.

0

Using the same version of the Solow model as in the previous question, you know that the growth rate of output per person is ________ percent.

0

Using the same production function as in the previous question, compute the marginal product of capital. Round your answer to the nearest hundredth after the decimal point.

0.07

Using the same production function as in the previous question, compute the marginal product of labor. Round your answer to the nearest hundredth after the decimal point.

0.28

If Y = AK1/3L2/3 and A grows at a rate of 1 percent per year, K grows at a rate of negative 6 percent per year and L grows at a rate of 3 percent per year, then the growth rate of Y is ______ percent. (Hint: Use the "properties of growth rates" from section 3.5 to answer this question.)

1

Use the numbers in the table above to compute nominal GDP for years 1 and 2 in a spreadsheet application of your choice (Excel, Numbers,...). Next, recall that the formula for a Laspeyres index is L = ∑ p t − 1 q t ∑ p t − 1 q t − 1 and the formula for a Paasche index is P = ∑ p t q t ∑ p t q t − 1. The real growth rate of this economy using the Laspeyres index is ______ percent.

10

A construction company produces a $200,000 house using $55,000 worth of wood and steel in addition to $95,000 worth of labor hours and $40,000 in rental (or usage) fees for construction equipment (jackhammer, compressor, backhoe,...). The project generates $10,000 in profits. The value added generated by this new dwelling is $_______.

145,000

Using the Solow model, if, in time t = 0, the initial capital stock is K0 = 100, investment is I0 = 25, and d= 0.1 is the depreciation rate, capital accumulation from period 0 to period 1 is ______.

15

The United States is running a $419 billion trade deficit with China. Suppose the Phase One Deal leads to a decrease in U.S. computer imports from China by $11 billion and, at the same time, China agrees to purchase additional soybeans worth $5.5 billion from the U.S. The resulting change in U.S.'s trade deficit with China is $ _______ billion.

16.5

You are a staff economist for your local bank and the bank manager asks you to calculate whether United Arab Emirates (UAE), Luxembourg (LUX), Canada (CAN), or the United States (USA) is biggest in per capita terms when adjusted for price differences. She gives you the following data table and asks you to fill in the missing values. Population (column A) and GDP (D) are in millions. GDP in column D is in local currency units (LCU): the euro for Luxembourg, the dirham for the UAE, the Canadian dollar, and the U.S. dollar. The exchange rate (B) is units of foreign currency per U.S. dollar, and Pi /PUS is the price level for other countries relative to the United States. Luckily, there's a whole team assigned to this task and you only have compute PPP Per Capita GDP ($US) for the UAE in 2014 (someone else will take care of the rest). This is done most easily in a spreadsheet application like Excel. Round your answer to the nearest dollar. For instance, if your numerical spreadsheet result is 58367.76511, you enter 58368 in the space below (no need for a currency symbol). UAE: Pop: 9.09 Exchange rate: 3.67 Pi/Pus: 2.4 GDP(millions LCU): 1,466,000 LCU Per Capita GDP: - Per Capita GDP ($US): - PPP Per Capita GDP($US): -

18,310

After graduating college, you start a job making $40,000. Your earnings grow at a constant growth rate of 4 percent per year. When you retire 40 years later, you are earning approximately $________. (Use equation (3.7) in the text book and round your answer to the nearest US Dollar.)

192,041

Consider the version of the Solow model where the population grows at an exogenous rate n = .02 (that is, Lt+1 = ( 1 + n ) Lt = 1.02 Lt), A = 5, s = .2, d = .06, and α = 1 4. Based on this information you know that in the long run the growth rate of output is ________ percent.

2

Using the same information as in the previous question, calculate the growth rate of capital per person between time 0 and 1 (again in percent, rounded to the nearest tenth).

21.2

In addition to the information from the two previous questions, you know that the economy has K0 = 81 and L0 = 16 at time 0. Using a calculator or a spreadsheet application, calculate the growth rate (in percent) of K between time 0 and 1. Round to the nearest tenth. (Note: If the capital stock grows at a rate of 7.47%, enter 7.5 in the answer box. Omit the percentage symbol.)

23.6

The production function is given by Y = K^1 / 4 L^3 / 4. Moreover, K = 81 and L = 16. Calculate total output. Round your answer to the nearest tenth after the decimal point.

24

Consider an economy characterized by the production function Y = AK^1/2^L1/2 where the productivity parameter is equal to 0.75. How many units of output can be produced with 36 units of capital and 64 workers?

36

Consider a perfectly competitive economy with a production function Y = AK^1/3L^2/3. There are 27 workers who produce cream cheese (a numéraire good) with 125 units of capital. If the productivity parameter is equal to 1, the economy produces ___ units of cream cheese. Assuming perfect competition and price-taking behavior by producers total payments to capital _________ _______________.

45; equal; 15 units of cream cheese

You can use equation (2.3) on page 33 in the textbook and the corresponding "percentage change equation" two paragraphs below to calculate the inflation rate in this economy. Using the Laspeyres index to calculate the growth rate of real GDP, the inflation rate is ______ percent (round to the nearest tenth).

5

According to the World Bank, income per capita in Austria in 2019 was Int$59,110 while income per capita in Rwanda in the same year was Int$2318. If Austria's investment rate is 30% and Rwanda's investment rate is 10%, what is the productivity ratio AAustria/ARwanda? Assume that both countries are in their steady states, that they have a common depreciation rate, and that α = 1/3. Round to the nearest tenth.

6

With an average annual growth rate of 7 percent per year, per capita income will increase by a factor of _____ over a period of six decades.

64

In 1994, your parents made an investment of $4,000. By 2014 the investment grew to $16,000. Assuming a constant rate of growth and using the Rule of 70, the average annual return (or growth rate) of this investment is _______ percent.

7

China: Observed percapita GDP: 0.24 Predicted per capita output y=k^a: 0.67 Considering the data in Table 4.1, the explanation for the difference between the predicted and actual level of output is called _______ . The value that reconciles the data with the predicted GDP per capita for China is _________ .

TFP; 2.79