Midterm 1
After graduating college, you start a job making $40,000. Your earnings grow at a constant growth rate of 3 percent per year. When you retire 40 years later, you are earning approximately:
130,000. -Apply formula y(t)=y(0)(1+g)^t where y(0)=40,000, g=0.03, and t=40
Luckily, there's a whole team assigned to this task and you only have compute PPP Per Capita GDP ($US) for the UAE in 2014:
18322.49 -((GDP/Pop.)/Price level comparison)/Exchange rate
With an average annual growth rate of 3.5 percent per year, per capita income will increase by what factor over a century?
32 -Applying the Rule of 70 implies 70/3.5 = 20. Thus, income will double in 20 years. In a century, per capita income will double 5 times, which is 100/20. Thus, GDP per capital will increase by a factor of 2^5.
In the Romer model presented in class, the change at time t = 0 in the path of GDP per capita(dip in the graph the increasing) can be explained by:
share of labor engaged in research.
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
s¯^(α/1-α) A¯^(1/1-α) is higher in South Korea than in China.
Which of the following is an example of labels for equidistant tick marks on a ratio scale?
1, 5, 25, 125, 625... -A ratio scale is one where the numbers exhibit a constant ratio. The ratio scale here has a constant ratio of 5.
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?
Both countries are at their steady states. -The fact that most rich and poor countries grow at the same rate suggests that most countries have already reached their steady states. If a relatively poorer country like Chile were poor because of a bad shock, we would expect it to grow faster.
Recently, the largest share of GDP is
Consumption
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?
Consumption expenditures will increase by $12,000. -GDP measures the market value of final goods and services produced in an economy over a certain period. Thus, the value of a house built earlier does not get counted in this year's GDP. The only new production is the service by the real estate agent who got paid a commission for that service.
Imagine increases in the parameters of the Solow model that are all identical in magnitude. Which one of the following parameters will result in the largest increase in steady-state output?
The productivity parameter -Notice that the investment rate is raised to the power of .5, the labor force to the power of 1, and the productivity parameter to the power of 1.5. Thus, if the magnitudes of the increases are identical, the productivity parameter will have the largest impact on output in steady state.
If real GDP increases by 2 percent and nominal GDP increases by 4 percent, then inflation is approximately 2 percent.
True
Which of the following questions does the Solow model NOT help to explain?
Why do countries sustain growth in the long run? -The Solow model helps us explain why some countries are richer than others are (different parameters) and why growth rates differ (transition dynamics). The Solow model does not generate long-run economic growth because the economy rests in steady state.
According to Figure 4.5, does the production model accurately predict the level of per capita GDP for Singapore?
Yes, because the predicted value of per capita GDP for Singapore is close to the actual value of its per capita GDP -Figure 4.5. If we extend the solid line on Figure 4.5, Singapore would lie very close to it, suggesting that the predicted and the actual values of per capita GDP for this country are almost equal to each other. This means the model successfully predicts Singapore's per capita GDP.
Which of the following counts as investment?
You buy a new house. -Investment includes purchases of structures and equipment by businesses in addition to purchases of new homes. A computer for home counts as consumption.
If we define the saving rate as mc038-1.jpg, output as F ( K t , L ¯ ) , and the depreciation rate as δ , and if s ¯ F ( K t , L ¯ ) − δ K t = 0 , the economy is:
at the steady state.
Let s¯ be the investment rate, δ the depreciation rate, A¯ aggregate productivity (or TFP), L¯ the population, and α capital's income share in a Solow economy. What is the steady-state level of consumption per person c^*?
c^*=(1-s)A^(1/1-α) (s/∂)^(α/1-α)
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 constant over time. If in addition, the two lines are parallel and upward-sloping, then the income gap is constant in absolute terms.
constant and increasing
One of the key characteristics of the Cobb-Douglas production function is:
constant returns to scale.
The growth rate of per capita GDP in the Romer model depends on the number of workers engaged in research. However, the country of Luxemburg, which has far fewer researchers than the U.S., grows at a rate faster than the U.S. and has a higher per capita GDP. How can the Romer model explain this difference in growth rates?
Due to the nonrivalry of ideas, the economy of Luxemburg grows because the model is based on ideas created throughout the world not just within that country.
If net investment is negative:
the economy is above its steady state and growth of output is negative. -Negative net investment implies depreciation is greater than investment. Thus, the economy has a capital stock that is decreasing because it is above steady state.
Starting from steady state, a permanent increase in the rate of depreciation in the Solow model causes
the growth rate of output to fall temporarily and the level of GDP to fall permanently. -An increase in the depreciation rate causes the depreciation curve to pivot upward, resulting in a new lower steady state. Thus, the growth rate of output is rapidly negative at first and converges to zero as it approaches steady state.
An economy starts in steady state. A war causes a massive destruction of the capital stock. This shock will cause
the growth rate of output to rise initially as the economy begins to converge to the old steady state. -The diagram in Figure 5.1 indicates that if the capital stock is below the steady-state level of capital, the economy will proceed to the old steady-state level. Note that a shock to the level of capital will not shift any of the curves, and that the steady state remains unchanged in the long run. Because the economy is below steady state, growth is positive.
Consider the production function Y = K^α L^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 . From this conclude that:
the production function has decreasing returns to scale with respect to K alone.
the explanation for the difference between the predicted and actual level of output is called ________. If you compare South Africa's observed and predicted output, this difference is equal to ________.
total factor productivity; 0.37
In the Solow model, net investment is defined as:
investment minus capital depreciation.
The level of consumption:
is largest when the economy is above its steady state. -Figure 5.2. Consumption is the difference between the amount produced and the amount invested. The amount invested depends on the investment rate and the production function, none of which depend on the depreciation rate. We can see from the figure that the difference between the output line and the investment line grows as capital increases.
In the Solow model, the steady-state level of output per worker is a function of:
productivity, the depreciation rate, and the saving rate.
When comparing shares of consumption in GDP it is best to use ( ___ ) variables. When comparing real rates of economic growth it is best to use ( ___ ) variables.
nominal; chain-weighted -Nominal variables are best for comparing shares of GDP because the nominal variables will add up, but chain-weighted real variables are best for measuring economic growth because it produces a more accurate portrayal of how real GDP changes over time.
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.
$1,050 -Nominal GDP = Real GDP x Price level. Applying the second property of growth rates: growth rate of nominal GDP = growth rate of real GDP + growth rate of the price level. Growth rate of real GDP = growth rate of nominal GDP - growth rate of the price level. Growth rate of real GDP = 7% - 2% = 5%. The growth rate is the percentage change from year 1 to year 2: 5% = (real GDP in year 2 - 1,000)/1,000. Real GDP in year 2 = $1,050.
A construction company produces a $200,000 house using $50,000 worth of wood and steel in addition to $50,000 of labor hours. The value added by the construction company is?
$150,000
What is the marginal product of capital (MPK) for the production function LaTeX: Y = bar{A} K^{1/2} L^{1/2}
(1/2)*(A^barK^1/2L^1/2)/K -The marginal product of capital for a Cobb-Douglas production function is proportional to the average amount produced by each unit of capital where the factor of proportionality is equal to the exponent on capital.
What is an explanation for why an economy eventually settles in steady state?
-The production function exhibits diminishing returns to capital. -The capital stock depreciates at a constant rate. -Eventually, investment generated is equal to the amount of capital depreciated. The first two arguments taken together imply the third argument. Diminishing returns implies the slope of the investment curve becomes smaller, while depreciation remains constant. At the intersection of the two curves, net investment is zero.
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 LaTeX: \bar{K} K ¯ was constant), use the model of production to predict the effect of such a decline of 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:
-Total GDP (LaTeX: Y Y ) falls. -The marginal product of labor rises.
Output per person is higher when
-a country is more efficient in adopting a technology. -a country has a higher capital-to-population ratio. -a country has stronger property rights and contract enforcement. A country has higher per capita output if capital per person and the productivity parameter are higher. The productivity parameter is higher under better institutions and when technologies are adopted more efficiently.
If the productivity parameter is assumed to equal 1, the production model
-correctly identifies that countries are richer if they have more capital. -incorrectly predicts that poor countries are substantially richer than they are. -correctly predicts that some countries are richer than the United States. The model implies that more capital implies more output per person but incorrectly overestimates the value of per capita output.
Which of the following can be used to give firms incentive to innovate?
-patents -copyrights -prizes -trade secrets
Suppose India has a per capita GDP that is .074 times the United States GDP. It has a capital-per-person ratio that is .035 times that of the United States. Compared to the United States, the implied value of total factor productivity for India is approximately
.23 -The United States is standardized to a value of 1 in this problem. The implied value of TFP is equal to the ratio of output per person divided by the capital-to-labor ratio raised to the 1/3 power.
For the years 1995-2007, if output per person in the private sector grew 2.7 percent, the contribution of the capital-labor ratio was 1.1 percent, and the change in the labor composition accounted for 0.2 percent of that growth, what was the growth rate of total factor productivity?
1.4 percent -We can decompose the growth rate of per capita GDP into the growth rate of TFP, the growth rate of capital, and the growth rate of workers. Therefore, in this example the contribution of TFP is equal to 2.7%-1.1%-0.2%=1.4%
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:
1/4 -The fastest growing country during 1960-2014 was Botswana with an average annual growth rate of above 6%. Its level of per capita GDP is slightly above 1/4 of the U.S. level.
In 1994 your parents made an investment of $4,000. By 2015 the investment grew to $32,000. Assuming a constant rate of growth, what was the average annual growth rate of this investment?
10% -The data above are plotted using a ratio scale. Since this is a straight line we can conclude that the growth rate is constant. We see that the investment doubles every 7 years (i.e. for 1994 - 2001 the investment grew from $4,000 to $8,000; or use formula 3.9 to verify). Therefore, we can estimate the growth rate using the rule of 70: 70/7 = 10%.
In a production model where the production function is Y = \bar{A} K^{1/3} L^{2/3} the equilibrium wage rate is equal to (30/27), labor supply is 27 workers and the productivity parameter is equal to 1. What is the equilibrium level of capital?
125 -The equilibrium wage rate is given by w^*=(2/3)*(Y^*/L^*)and is equal to {30}/{27} in this case. We know that in equilibrium, quantity of labor supplied is equal to the quantity of labor demanded, so L* = 27. Set the equilibrium wage rate equal to the analytical solution for w* in Table 4.2 and solve for K; frac{30}/{27} = frac{2}/{3} frac{K^{1/3}27^{2/3}}/{27} K=125
If population doubles every 35 years, then the growth rate of population is
2% -The Rule of 70 implies that the growth rate equals 70/35 = 2%.
If Y = AK^1/3L^2/3 and A grows at a rate of 1 percent per year, K grows at a rate of negative 3 percent per year and L grows at a rate of 3 percent per year, then the growth rate of Y is
2% -The growth rate formula for such a production function is g(Yt) = g(At) + (1/3)*g(Kt) + (2/3)*g(Lt). The first two terms cancel and we are left with (2/3)*(3).
According to the International Monetary Fund, income per capita in Bhutan in 2015 was Int$8,201 while income per capita in Chad in the same year was Int$1,214. If Bhutan's investment rate is 40% and Chad's investment rate is 10%, what is the productivity ratio (A¯of Bhutan)/(A¯ of Chad)? Round to the nearest tenth. Assume both countries are in their steady states.
2.3 -.LaTeX: \frac{y^*_{\textrm{Bhutan}}}{y^*_{\textrm{Chad}}} = \frac{Int\$ 8,201}{Int\$ 1,214} = 6.8 y Bhutan ∗ y Chad ∗ = I n t $ 8 , 201 I n t $ 1 , 214 = 6.8 . LaTeX: \frac{\bar{s}_{\textrm{Bhutan}}}{\bar{s}_{\textrm{Chad}}} = 4 s ¯ Bhutan s ¯ Chad = 4 . Using equation 5.12, LaTeX: 6.8 = \bigg(\frac{\bar{A}_{\textrm{Bhutan}}}{\bar{A}_{\textrm{Chad}}} \bigg)^\frac{3}{2} 4^\frac{1}{2} \Rightarrow \bigg(\frac{\bar{A}_{\textrm{Bhutan}}}{\bar{A}_{\textrm{Chad}}} \bigg)^\frac{3}{2} = 3.4 6.8 = ( A ¯ Bhutan A ¯ Chad ) 3 2 4 1 2 ⇒ ( A ¯ Bhutan A ¯ Chad ) 3 2 = 3.4 and LaTeX: \bigg(\frac{\bar{A}_{\textrm{Bhutan}}}{\bar{A}_{\textrm{Chad}}} \bigg)^\frac{3}{2} = 3.4^\frac{2}{3} =2.3 ( A ¯ Bhutan A ¯ Chad ) 3 2 = 3.4 2 3 = 2.3 .
Consider a perfectly competitive economy with a production function Y = bar{A} K^{1/3} L^{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 and the economy produces 40 tons of cream cheese in equilibrium, what is the sum of the total payments to capital and labor?
40 tons of cream cheese -Since the numéraire good is cream cheese, all prices are expressed in tons of cream cheese. Total payments to capital and labor (w*L + r*K) are also expressed in tons of cream cheese. In equilibrium the sum of payments to capital and labor is equal to total production.
Consider an economy characterized by the production function Y = \bar{A} K^{1/2} L^{1/2} where the productivity parameter is equal to 1.2. How many units of output can be produced with 25 units of capital and 64 workers?
48 -A production function is a mathematical representation of the relationship between inputs and output, i.e. how much output can be produced with any input combination. Replacing bar{A}=1.2 A ¯ = 1.2 , K = 25, and L = 64 yields Y = 48
If the production function is given by Y=K^1/4L^3/4, and K = 81 and L = 2.5, total output equals about:
6.0
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.
70; 5; 14
A firm uses capital and labor to produce a good. Which of the following is greatest?
Accounting profit. -Economic profit equals total revenue minus payments to all inputs. Accounting profit equals total revenue minus payments to inputs other than capital.
Which of the following production functions exhibits constant returns to scale?
All where exponents of K and L add up to 1
A production function has inputs X, Y, and Z and a productivity parameter A¯ . The production function A^-1/3X^1/3Y^1/3Z^1/3 exhibits?
Constant returns to scale with respect to X, Y, and Z. -Doubling each input X, Y, and Z, will result in a doubling of output. If the exponents on the inputs sum to 1, it has constant returns to scale.
A country that, since 1980, has shown convergence to the United States is
China
A U.S. citizen works for a U.S. company in Germany. The income earned by the citizen increases U.S. GDP.
False
Patents are unambiguously beneficial to society because they create profits for firms, which generate incentives to produce new ideas.
False - Patents also distort the economy by generating welfare loss.
The standard replication argument implies that Italy can double its per capita GDP by doubling the amount of capital per person.
False -Capital per person is subject to diminishing returns to capital. Thus, because the exponent on capital per person is less than 1, doubling only the amount of capital per person will not double per capita output.
If an economy has a higher investment rate and a higher depreciation rate, the economy will have a higher level of output.
False -Imagine an economy with a given rate of depreciation and investment. An economy with higher rates will have depreciation and investment curves that are both higher in the Solow diagram. Whether the steady state is higher or lower depends on the magnitudes of the parameters. Thus, we cannot determine the output definitively—it may be higher, lower, or the same.
When the trade balance is negative, domestic producers are exporting more goods than are being imported.
False -The trade balance is exports minus imports. The trade balance is negative when imports exceeds exports.
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:
Portugal has a higher capital-output ratio than Brazil.
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:
Real GDP 2014 using 2014 prices = 2,000x6 + 10x1,000=22,000 Real GDP 2015 using 2014 prices = 1,000x6 + 12x1,000=18,000 Percentage change = (18,000-22,000)/22,000= -18% Real GDP 2014 using 2015 prices = 2,000x5 + 10x1,000=20,000 Real GDP 2015 using 2015 prices = 1,000x5 + 12x1,000=17,000 Percentage change = (17,000-20,000)/20,000= -15% Percentage change in real GDP in chained prices benchmarked to 2015 is the average of the two growth rates = (-18 -15)/2 = - 16.5%
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 inflation rate is approximately:
Real GDP 2014 using 2014 prices = 2,000x6 + 10x1,000=22,000 Real GDP 2015 using 2014 prices = 1,000x6 + 12x1,000=18,000 Percentage change = (18,000-22,000)/22,000= -18% Real GDP 2014 using 2015 prices = 2,000x5 + 10x1,000=20,000 Real GDP 2015 using 2015 prices = 1,000x5 + 12x1,000=17,000 Percentage change = (17,000-20,000)/20,000= -15% Percentage change in real GDP in chained prices benchmarked to 2015 is the average of the two growth rates = (-18 -15)/2 = - 16.5% Nominal GDP 2014 = 2,000x6 + 10x1,000=22,000 Nominal GDP 2015 = 1,000x5 + 12x1,000=17,000 Percentage change in nominal GDP = (17,000-22,000)/22,000 = -22.7% Percentage change in price level (inflation) = -22.7%+16.5%=-6.2%
Which of the following is NOT an example of capital?
Screws and bolts used for making cars at an automobile factory -Screws and bolts are an intermediate good. Inputs used in the production process are not capital.
Which of the following does NOT increase the U.S. GDP?
The U.S. government increases social security payments. -Transfer payments do not increase GDP because nothing new is purchased. When the U.S. government purchases a tank from a U.S. company, this is a government purchase, which counts towards GDP. When the French government purchases a tank produced in America, this increases U.S. GDP as it is exported out of the country. Increasing funding for tax policy at a U.S. university is government-funded research, which also counts towards GDP.
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?
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.
Suppose that the economy is on a balanced growth path. Use the equations of the Romer model with λ = 1 − ϕ presented in class to describe what happens after a one-time immigration wave that raises L t by 10 percent. Before and after the "jump", the population growth rate is n and s R is constant throughout.
The rise in L t leads to a rise in Δ At/At in the short run, but the growth rate of the economy is unchanged in the long run (i.e. along the Balanced Growth Path).
According to the principle of transition dynamics, which economy will grow fastest?
The same country 1 year after the natural disaster destroyed most of the capital stock -The principle of transition dynamics says that an economy that is farther below its steady state will grow faster. The destruction of the capital stock places the economy further below its steady state 1 year after the destruction took place.
If population and GDP are growing at the same rates, then per capita GDP does not grow.
True -Growth rate formulas imply that the growth rate of per capita GDP is the growth rate of GDP minus the growth rate of population, which in this example is 0.
Suppose we compare GDP per person in Uganda and the United States in two ways: first using the exchange rate method and second using the relative price-based conversion as well. Then, Uganda appears to be richer under the relative price-based conversion than with the exchange rate conversion.
True Wages in poorer countries are usually lower than wages in rich countries. Thus, prices are lower in Uganda. This implies that adjusting by the ratio of U.S. to Ugandan prices will make Uganda's GDP appear larger than if using only an exchange rate adjustment.
According to the Solow model two countries will grow at different rates if:
both have different steady-state level of output and the same capital stock below the steady-state level -If two countries have different steady-state levels of output and the same capital stock then through the process of transition dynamics the country with the higher steady-state level of output will grow faster as it tries to reach that higher steady state.
The law of diminishing marginal product to capital means that as we add additional units of capital:
but hold labor constant, output will increase, but at a decreasing rate.
If there are large fixed costs due to research and development, perfect competition does not generate new ideas because:
firms need to recoup these costs through higher profits.
In the Solow model, if investment is ________ depreciation, the capital stock ________.
greater than; grows
A balanced growth path is defined as a situation in which the:
growth rates of all endogenous variables are constant.
Nonrivalry of ideas and the standard replication argument imply the production function will have
increasing returns to scale. -The standard replication argument implies we can double output by doubling objects, but ideas are nonrivalrous and can be used in two duplicate factories simultaneously.
Consider an economy described by the textbook Solow model with a production function. 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 6%, and there are 125 workers, the growth rate of the economy_____:
is positive because the economy is below its steady state. - Replace the given numbers in equation 5.7 and solve for the steady state level of capital: K* = 125. Therefore, Y* = 5 * 25 = 125. If the economy currently produces 100 units of output according to the Solow diagram it is below its steady state and the growth rate of the economy is positive.
In the Cobb-Douglas production function Y=K^a L^(1-a) , if a = 1/3, then:
labor's share of GDP is two-thirds.
A production function displaying a shape of diminishing returns suggests that alpha is
less than one
The equation (s¯)F(Kt ,L¯) − ∂Kt is called:
net investment
Under national income accounting, GDP equals
the goods produced in the economy. the income earned in the economy. the total purchases in the economy. -Under national income accounting, production equals expenditure equals income.
How quickly GDP doubles will depend on:
the growth rate of GDP. -The Rule of 70 implies that the time it takes for a variable to double depends only on its growth rate.
Imagine a two-good economy where the quantity of the goods produced is unchanged over time, but where prices have increased. Then, in the most recent year, real GDP will be
the largest number when using the Paasche index. -In a two-good economy, real GDP depends on which year is selected for the prices. The Paasche index uses most recent prices and will give the largest number for real GDP when there is inflation—even though the actual quantity amounts are unchanged.
An example of a good that is both non-rivalrous and excludable is
the source code for Microsoft Word. -Nonrivalry implies one person's use of a good does not reduce the usefulness to someone else. The park is rivalrous because you may go there to enjoy quiet, but if it is crowded and no park benches are available, the park has become less useful to you. Excludability is a restriction on the use of a particular idea. While, in principle, multiple consumers can use the same piece of software, access may be restricted by a license purchase requirement, for instance.
In the Cobb-Douglas production functionY = A¯ K^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:
y=A¯(k^α)
