Intermediate Macroeconomic Theory Unit 2
3.5%
If the number of workers is growing at 2% and the efficiency of worker is growing by 1.5%, the growth rate of the effective number of workers is:
Falls but the steady-state growth rate of y is unchanged.
If the population growth rises, the level of output per worker
The steady state level of k* but not its growth rate.
If the saving rate fell, then in the steady state which of the following would be lower?
s*f(k) - δk
If there is no population growth or technological progress, net investment per worker always equals:
k is below k* and k is rising.
If there is no technological progress and no population growth, and s*f(k) > δk, then:
36
If there is no technological progress or population growth, f(k) = k^1/2, s = 0.12 and δ = 0.02, what is k*?
Conditionally Converge
If two countries are the same except that one has a lower saving rate than according to the Solow growth model these two countries could:
Output is below its natural rate creating downward pressures on prices.
If velocity decreases, then in the short run:
Firms do not change their prices in the short-run (prices are sticky). The SRAS is horizontal.
In chapter 10, what do we assume about firms' responses to changes in demand in the short run? What does this imply about the slope of the short-run aggregate supply curve?
g+n, and output per worker grows at the rate of g.
In the Solow growth model output grows at the rate of:
The growth rate of the real wage rate is the growth in technological progress or the variable, g, in the model.
In the Solow growth model with population growth and technological progress what is the growth rate of the real wage rate?
Capital per worker and capital, but not capital per effective worker.
In the Solow growth model with technological progress and population growth, which of the following is growing at a rate greater than zero?
(n+δ+g)k
In the Solow growth model with technological progress, break-even investment equals:
MPK = (g+n+δ)
In the Solow growth model with technological progress, the Golden Rule level of capital is where:
Both K/L and Y/L
In the Solow growth model with technological progress, which, if either, of the following grows at the same rate as technological progress?
The real wage rate but not the real rental rate of capital
In the Solow growth model with technological progress, which, if either, of the following grows at the same rate as technological progress?
An increase in population growth reduces the steady-state levels of capital per worker and output per worker. In the Solow growth model population growth does not explain growth in capital per worker or output per worker. However, an increase in the population growth rate increases the growth rate of capital and output (note these are not per worker). However, Michael Kremer finds some evidence that population growth leads to greater technological progress and so leads to growth of output per worker.
In the Solow growth model, how does the rate of population growth affect the steady-state level of income? How does it affect the steady-state rate of growth?
A country with a higher saving rate will have higher levels of capital per worker and output per worker but will not have a higher growth rate of either capital per worker or output per worker. An increase in the saving rate causes capital per worker and output per worker to grow at a faster rate, but only temporarily until the new steady state is reached.
In the Solow model, how does the saving rate affect the steady-state level of income? How does it affect the steady-state rate of growth?
The growth rate of real output per worker equals the growth rate of technological progress (g). The production of output generates income so in macroeconomics income and output are sometimes used interchangeably.
In the Solow model, what determines the steady-state rate of growth of income per worker?
*Index of supplier deliveries *Money Supply M2 *Difference between the interest rate on a 10-year Treasury note and a 3-month Treasury bill
List economic indicators given in the text but not in the notes.
A decrease in the population growth rate increases the steady-state level of capital per worker and so increases the steady-state level of output per worker. Capital per worker and output per worker will grow as the economy moves to the steady state. However, once the steady state is reached, they will not grow. As population growth slows, the growth of total output slows.
Many demographers predict that the United States will have zero population growth in the coming decades, in contrast to the historical average population growth of about 1% per year. Use the Solow model to forecast the effect of this slowdown in population growth on the growth of total output and the growth of output per person. Consider the effects both in the steady state and in the transition between steady states.
In the short run only.
Most economists believe that prices are sticky:
Increase prices by less than 1% in the short run and increase prices by 1% in the long run.
Most economists would agree that a 1% increase in the money supply will:
Prices are flexible, the AS curve is vertical, and changes in AD affect the price level but not output.
Over long periods of time,
Prices are sticky, the AS curve is flat, and changes in AD do affect the economy's output of goods and services.
Over short periods of time,
Stabilization Policy
Policy used to reduce the duration and severity of recessions by shifting AD in the opposite direction.
DONE
Show the Effects of a Decrease in the Population Growth Rate
If the FED responds, both the price level and real GDP return to the original level. If it does not respond, firms will eventually reduce their prices, the SRAS curve will shift down, and real GDP will return to its original level, but the price level will be lower than if the FED responds.
Suppose that AD shifts left. In the long run what does it matter if the Fed responds to this shock or not?
Saving per worker = s*f(k) = s*y = 0.05 * 200 = 10 Depreciation per worker = δk = 0.08*100 = 8 Net Investment (∆k) = s*f(k) - δk = 10-8 = 2 Thus, the capital stock is rising.
Suppose that k = 100, that output per worker is 200, that the saving rate is 0.05, and that the depreciation rate is 0.08. Which is greater saving per worker or depreciation per worker? What is net investment per worker? Given the level of net investment per worker, what is happening to the level of capital per worker?
Other things the same, output per worker will converge at the same level. That is the real output per person in country A will "catch up" to the level of real GDP per person in country B. Other things the same, a country with a higher saving rate will have a higher steady state level of real GDP per person. So, the countries will not converge. However, since country A starts further away from its steady state it should grow faster until it reaches it new steady state. This second case is called conditional convergence. Empirical evidence finds that countries which are further from their steady state grow faster.
Suppose that other things the same country A has a lower level of real GDP per person. According to empirical evidence will output per worker converge for these two countries? Now suppose that country A raises its saving rate. According to empirical evidence will output per worker converge for these two countries?
A) If the Fed decreases the money supply AD shifts left. B) In the short run, prices are unchanged and real output is lower. When output is below its natural level, firms are producing less than they desire and will reduce prices. As they reduce prices, the SRAS curve shifts down. The SRAS curve continues to shift down until output returns to its natural rate where firms are producing the desired quantity. So, in the long run the price level falls by 5%, but real output is unchanged. C) In the short run as output falls, unemployment rises. In the long run as output rises back to its natural rate, unemployment falls back to its natural rate. (And vice versa)
Suppose the Fed reduces the money supply by 5%. Assume the velocity of money is constant. A) What happens to the AD curve? B) What happens to output and the price level in the short run and in the long run? Give a precise numerical answer. C) In light of your answer to part (B), what happens to unemployment in the short run and in the long run according to Okun's Law? Again, give a precise numerical answer.
The Golden Rule Level of Capital
The steady-state value of k that maximizes consumption.
It implies that the money supply does not affect output.
The vertical AS curve satisfies the classical dichotomy because:
Larger populations put a strain on an economy's food-producing capacity.
Thomas Malthus believed that:
The capital that wears out is replaced and new workers are equipped with the same amount of capital as existing workers.
To keep capital per worker constant,
The amounts of labor and capital as well as the level of technology and institutions. No. There is no change.
What determines the position of the long-run aggregate supply curve? Is the position of the LRAS curve determined by the money supply? If the price level rises what happens to the quantity of goods and services supplied in the long run?
f(k) - s*f(k)
What is consumption per worker always equal to?
Advantage: Real GDP levels are restored and the unemployment level is unaffected. Disadvantage: Prices will be forever increased.
What is the advantage and what is the disadvantage of accommodative monetary policy in response to an adverse supply shock?
Investment and Depreciation
What two forces influence the capital stock?
The money supply and the amount of money people want to hold per dollar of income.
When deriving the aggregate demand curve, which variables are held constant?
Investment is just enough to cover depreciation and population growth.
When investment equals break-even investment,
Aggregate demand shifts right and output rises.
If the money supply rises, then in the short-run:
Productivity is output per worker, the standard of living is output per person. An increase in the saving rate raises the steady state level of output per worker. If the labor force is a constant fraction of the population, then the increase in the saving rate also raises the steady state level of output per person. As the economy moves to the new steady state, productivity and the standard of living will be growing to reach the new steady state level. However, the increase in growth is only temporary. It stops when the new steady state levels are reached. Further, the increase in the saving rate initially requires that consumption is lower. If the saving rate increases enough that k rises above its golden rule level, consumption per worker in the steady state could fall.
"Devoting a larger share of national output to investment would help restore rapid productivity growth and rising living standards." Do you agree with this claim? Explain, using the Solow model.
Leading Economic Factors
*Average weekly hours in manufacturing *Average weekly initial claims for unemployment insurance *Manufacturers' new orders for consumer goods and materials *Manufacturers' new orders for non defense capital goods, excluding aircraft *ISM new orders index *Building permits for new private housing units *Index of stock prices *Leading credit index *Interest rate spread: The yield on a 10-year Treasury bond minus the federal funds rate *Average consumer expectations for business and economic conditions
As the economy moves to the new steady state, but not in the steady state.
A decrease in the saving rate would decrease the growth rate of k:
Up and so reduce output
A drought would shift the short-run aggregate supply curve:
Solow Growth Model
A model showing how saving, population growth, and technological progress determine the level of and growth in the standard of living.
50%
A survey of firms found that about what percentage of firms adjust their prices once a year or less than once a year?
A) Y = 4800/10 = 480 Y = 5600/10 = 560 B) Yes, because for a given price level an increase in the money supply raises Y. C) The curve shifts right. D) Because at each price level, which is on the vertical axis, output is higher when the money supply is higher.
A) Suppose that M=1200, V=4, and P=10, what is Y? Now suppose that M rises to 1,400, what is Y? B) Would the direction of the change in Y be the same if we started at a different price level say 8 or 12? C) Is the effect of a change in the money supply shown as a movement along the curve or a shift of the curve? D) How do we know?
A) MV = PY, so Y = MV/P 4800/10 = 480. So Y is 480 if P =10. 4800/12 = 400. So Y is 400 if P =12. B) Shown as a movement along the AD curve because the price level is on the vertical axis of the AD curve.
A) Suppose that M=1200, V=4, and P=10, what is Y? Now suppose that P rises to 12, and that M and V are fixed. Now what is Y? B) Is this change shown as a movement along the AD curve or a shift of the AD curve? How do we know?
A) Y = 4800/10 = 480 Y = 4200/10 = 420 B) V goes down if people want to hold more money. C) Yes. D) The decrease in velocity reduces the aggregate quantity of goods and services demanded at each price level, so the curve shifts left.
A) Suppose that M=1200, V=4, and P=10, what is Y? Now suppose that V falls to 3.5, what is Y? B) Does the decline in V mean that people want to hold more or less money per dollar of income? C) Would the direction of the change in Y be the same if we started at a different price level say 8 or 12? D) Is the effect of a decrease in the velocity shown as a movement along the curve or a shift of the curve?
Lower ; The Same
According to the Solow model, if an economy increases its saving rate, then in the new steady state, compared with the old one, the marginal product of capital is _________ and the growth rate is __________.
Below the steady state level of capital per worker and so has positive net investment.
An economy has 100,000 units of capital per worker, a depreciation rate of 0.02 and saving per worker of 2,500. It is:
6%
An economy has the production function y=20k^1/2. The current capital stock is 100, the depreciation rate is 10 percent, and the population growth is 2 percent. For income per person to grow, the saving rate must exceed:
Supply Shock
An increase in the cost of production
No. Some types of industries may have positive externalities and so provide benefits to society for which the industries do not receive revenue. However, the positive externalities are difficult to find and measure.
Are governments able to easily and accurately identify which industries should receive subsidies in order to increaser the efficient use of capital?
Total output will increase by 5%. Output and capital per worker are unchanged.
Assume constant returns to scale. If capital and labor each increase by 5%, what happens to total output? What happens to output per worker?
MPK = δ
Assuming no population growth or technological progress, the steady state level of k which maximizes consumption per worker is where:
That net investment = Change in k = 0. Which requires that gross investment per worker = depreciation per worker, so: s*f(k) - δk = 0 OR s*f(k) = δk
Assuming no population growth or technological progress, what is the condition for an economy to be at its steady state level of capital per worker?
s*f(k) - δk
Assuming no technological progress or population growth, which of the following is always equal to the change in the capital stock per worker?
The SRAS curve, but not the AD curve
Assuming the economy self corrects, which curves shift as the economy moves back to the natural rate of output?
Level of investment needed to keep capital per worker constant.
Break even investment is the:
Country A has the lower standard of living but both countries will move to the same standard of living as they reach their steady state.
Country A and Country B are the same except that Country A has a lower level of capital per worker. According to the Solow growth model:
Output will increase more in country A. It has less capital per worker and so a higher marginal product of k (MPK).
Country A and country B are the same except country A has 100 units of capital per worker, Country B has 150 units of capital per worker. If each country adds one more unit of capital per worker, will output per worker increase by more in one country than the other?
Less capital per worker and use it less efficiently.
Data shows that as compared to rich countries, poor countries have:
Solow Growth Model
Designed to show how growth in the capital stock, growth in the labor force, and advances in technology interact in an economy as well as how they affect a nation's total output of goods and services.
Less and use it less efficiently. A small amount of capital may mean that it is used inefficiently because larger amounts of capital are more likely to lead to better spillovers as users will have more access to information about the capital and how to use it and may be able to get it repaired more quickly. Or, efficiency use of capital may make its accumulation more desirable. Or, institutions and government policies may both discourage capital accumulation and reduce the efficiency with which it is used.
Do countries that are poor tend to have less capital per worker, use it less efficiently, or both? Why might this be?
DONE
Draw a graph and identify output, saving, and consumption per worker.
DONE
Draw a graph of the Solow model to show the effect of a decrease in the saving rate.
DONE
Draw a graph that shows the effects of an increase in the savings rate
DONE
Draw and Explain a decrease in AD through the short and long run.
DONE
Draw and Explain the Effects of an Increase in the Money Supply
5%
During 2014, the unemployment rate fell by about 1% point. According to Okun's Law, output growth in 2014 should have been about:
Is smaller than the percentage decline in investment spending.
During recessions the percentage decline in consumption:
3.8%
During the first six months of 2019, the unemployment rate fell by 0.2% points. What was the growth rate of GDP in 2019 according to Okun's Law?
Natural Disaster, A Rise in the Price of Oil, Strikes
Examples of Supply Shocks
In the short run, an increase in the money supply shifts the AD curve to the right. Since prices are sticky in the short run, producers increase production to meet increased demand. As output is above the natural rate, firms are producing more than they desire and so will raise their prices. The increase in prices is shown by shifting the SRAS curve up and so moving along the AD curve to the left. As prices rise the aggregate quantity of output demanded falls. The SRAS curve continues shifting up until the economy has reached long-run equilibrium. So, output returns to its natural rate and the price level is higher.
Explain the impact of an increase in the money supply in the short run and in the long run.
The amount of capital per worker changes, change in k = net investment, equals saving per worker, s*f(k) = gross investment per worker, minus depreciation per worker (δk).
Explain what the following means: Change in k = s*f(k) - δk
Output is above its natural rate, and there are upward pressures on prices.
If the aggregate demand shifts to the right, then in the short run:
Y grows at 3% and y does not grow.
If the depreciation rate = 1%, the saving rate is 10%, the population growth rate is 3%, and there is no technological progress, which of the following is correct in the steady state?
Decrease steady-state income but increase steady-state consumption
If the economy has more capital than in the Golden Rule steady state, reducing the saving rate will:
A) Falls B) Rises C) Stays the Same
For each of the following, state if it rises, falls, or stays the same after the decrease in population growth. A) The growth rate of the effective labor force. B) The steady-state level of capital per effective worker. C) The steady-state growth rate of output per worker.
A) f(k) = 200 B) s*f(k) = 40 C) δk = 32 D) s*f(k) = 40 E) ∆k = 8 F) Rising G) Below
For the following exercises assume that the saving rate, s, equals .20, that the depreciation rate, δ, equals .02, f(k) = 5k1/2, that k = 1600, and that there is no population growth or technological progress. A) What is output per worker? B) What is saving per worker? C) What is depreciation per worker? D) What is gross investment per worker? E) What is net investment per worker? F) Is k rising, steady, or falling? G) Is this economy currently above, at, or below the steady state?
MPK = δ
Golden Rule Equation
Saving will be higher if the government reduces its budget deficit. Some economists think that reducing the tax rate on saving will raise saving. Protecting property rights and maintaining a well-functioning and honest legal system make the financial system work better and so increase saving and investment. Reducing barriers to foreign investment acts as an increase in the saving rate.
How can policymakers influence a nation's saving rate?
In endogenous growth models growth in the physical capital stock leads to growth in knowledge about how best to use capital. This increase in knowledge raises human capital and offsets the tendency of the marginal product of physical capital to diminish. In endogenous growth models, the marginal product is assumed to be constant and an increase in the saving rate permanently increases growth of output per worker. In the Solow growth model, the MPK is diminishing so that an increase in the saving rate raises the growth of capital per worker and output per worker temporarily, not permanently.
How does endogenous growth theory explain persistent growth without the assumption of exogenous technological progress? How does this differ from the Solow model?
Increases in capital decrease consumption, so k* must be above the Golden Rule Level.
If MPK - δ < 0,
Increases in capital increase consumption, so k* must be below the Golden Rule Level.
If MPK - δ > 0,
2K^1/3
If Y = 2K^1/3L^2/3 which of the following is equal to output per worker?
In response to lower demand, firms initially reduce production, but the decrease in marginal cost eventually results in firms reducing their prices. This is shown by shifting the SRAS curve down. Firms are pursuing self-interest. They are trying to maximize profits.
If aggregate demand shifts left what happens that moves the economy back to the long run? Do you think this happens because firms want to move the economy back to the long run, or because firms are each following their own self interest?
Horizontal
If all firms fix their prices, then the short-run aggregate supply curve is:
Investment is less than break-even investment, so k falls.
If k is greater than k*
Investment is greater than break-even investment, so k rises.
If k is less than k*,
Initially reduces consumption per worker but increases its steady state value.
If k* is less than its Golden Rule level, an increase in the saving rate that doesn't move the economy past the Golden Rule level:
Falls but the steady-state growth rate of Y rises.
If population growth rises, the level of output per worker:
Increase production but eventually raise their prices.
If short-run aggregate supply shifts down, then firms with fixed prices initially:
A) Since L is lower total output falls. Since L is lower and K is unchanged, K/L increases and so output per worker rises (on average each worker has more capital). B) The decrease in L temporarily raises K/L above its steady-state level. As labor rises, capital per worker falls and the economy moves back to the steady-state level of output per worker. As labor rises, output rises.
In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital stock is destroyed in a war. By contrast, suppose that a war does not directly affect the capital stock but that casualties reduce the labor force. Assume that the economy was in a steady state before the war, the saving rate is unchanged, and the rate of population growth after the war is the same as it was before the war. A) What is the immediate impact of the war on total output and on output per person? B) What happens subsequently to output per worker in the postwar economy? Is the growth rate of output per worker after the war smaller or greater than it was before the war?
Prices are flexible and can respond to changes in supply and demand.
In the long run,
Capital, labor, available technology, and its institutions
In the long run, the rate of output is determined by a country's:
Many prices are "sticky" at some predetermined level.
In the short run,
Output and capital per person both grow at the rate of technological progress (g) in the Solow model. This result is consistent with the US date which show that all have grown at a rate of about 2% per year on average.
In the steady state of the Solow model, at what rate does output per person grow? At what rate does capital per person grow? How does this compare with the US experience?
Lower ; Higher
In the steady state of the Solow model, higher population growth leads to a ___________ level of income per worker and ____________ growth in total income.
n+g
In the steady state with technological progress, K and Y grow at a rate of:
g
In the steady state with technological progress, K/L and Y/L grow at a rate of:
0
In the steady state with technological progress, K/LE and Y/LE grow at a rate of:
The endogenous growth model but not the Solow model.
In which model, if either, does an increase in the saving rate permanently raise the growth rate of output per worker?
Immediately after the change in population growth rate, net investment is positive which drives the level of k up to the new k* level.
Just after a decrease in the population growth rate what happens to net investment per effective worker?
Rise: Unemployment Claims Fall: Stock Prices, New Building Permits, Orders for Consumer Durables, Orders for Non-defense Capital Goods, Consumer Expectations
Leading Economic Indicators According to Professor Kanago
A) A decrease in velocity means that people desire to hold more money per dollar of income so money demand increases. This increase in money demand reduces spending and so shifts the AD curve to the left. If the Fed wants to stabilize output, it increases the money supply so that AD shifts back to the right. If the Fed wants to stabilize prices, which if the Fed does nothing will fall as the economy moves to long-run equilibrium, it should increase the money supply so that AD shifts back to the right. B) An increase in the price of oil means that the SRAS curve shifts up as firms raise prices in response to the increase in the costs of production. In the short run, output falls and the price level rises. To move the economy back to long-run equilibrium, the Fed should should increase the money supply which shifts the AD curve to the right and returns the economy to its natural level of output but at a permanently higher price level. If the Fed wants to stabilize prices, it does nothing. Prices will remain higher for a while, but eventually firms will lower prices and the SRAS will shift down to the original long-run equilibrium. However, while the economy is adjusting, it will be in recession.
Let's examine how the goals of the Fed influence its response to shocks. Suppose that in scenario A the Fed cares only about keeping the price level stable and in scenario B the Fed cares only about keeping output and unemployment at their natural levels. Explain how in each scenario the Fed would respond to the following. A) An exogenous decrease in the velocity of money. B) An exogenous increase in the price of oil.
*Reduce the government budget deficit *Reduce barriers on foreign investment *Perhaps by reducing tax rates on capital and property *Reduce government corruption and burdensome regulations *Improve the integrity and efficiency of the justice system *Alter laws that heavily favor lenders over borrowers
List a couple of ways that a country might raise its saving rate.
The saving rate rises or the population growth rate falls.
The steady-state level of capital per worker rises if:
3% - 2 (Annualized Change in the Unemployment Rate)
The data says we can estimate the growth rate of real GDP by using the following equation:
Vertical
The long run aggregate supply curve is:
The number of workers and the efficiency of workers.
The number of effective workers takes into account:
Consistent with the classical dichotomy because it does not depend on the money supply.
The position of the long run aggregate supply curve is:
Aggregate supply shifted down
The price level falls and output rises. Assuming this is the short-run effect of a shock, which of the following could have caused this?
The efficiency of labor.
The rate of labor-augmenting technological progress equals the growth rate of:
A) The growth rate of output per worker is higher as the level of capital per worker moves to its new steady state. B) The level of output per worker is higher in the new steady state. C) The steady state growth rate of output per worker is unchanged. D) The steady state growth rate of output, Y, will fall.
When population growth falls what happens to: A) The growth rate of output per worker until the economy reaches the steady state? B) The level of output per worker once the economy reaches the steady state? C) The growth rate of output per worker once the economy reaches the steady state? D) The growth rate of output once the population reaches the steady state?
When real GDP falls, consumption and investment fall and unemployment rises. The percentage decrease in consumption is smaller than the percentage decrease in real GDP while the percentage decrease in investment is much larger than the percentage decrease in real GDP. Unemployment rises when real GDP falls. The rule of thumb provided by Okun's Law says that real GDP growth = 3% - 2(Annualized change in the unemployment rate).
When real GDP declines during a recession, what typically happens to consumption, investment, and the unemployment rate?
Investment
Which declines by a large percentage during recessions, consumption or investment?
The LRAS only.
Which if either is consistent with monetary neutrality, the short-run aggregate supply curve or the long-run aggregate supply curve?
Lower tax rates on saving could potentially increase national saving.
Which of the following is correct?
A decrease in the money demanded per unit of income.
Which of the following shifts aggregate demand to the right?
Neither the steady-state growth rate of k nor y.
Which of the following would an increase in the population growth rate increase?
It is easier for the Fed to deal with demand shocks than with supply shocks, because monetary policy affects the AD curve. So, monetary policy can shift the AD curve back towards long-run equilibrium which moves both prices and output back to their original level. Supply shocks, created by changes in the cost of production, move the SRAS curve along the AD curve and so move price and output in the opposite directions. So, there is no way for the Fed to return both output and the price level to their original values. If, for example, the Fed wishes to stabilize output in response to an adverse supply shock it would increase the money supply to shift AD right. This accommodative policy moves output back toward its natural rate, but keeps the price level permanently higher. If the Fed does nothing, the economy is below the natural rate which creates downward pressure on prices. As prices fall the SRAS curve shifts down and the economy returns to the natural rate of output at its original price level.
Why is it easier for the Fed to deal with demand shocks than with supply shocks?
The growth rate of Y equals the growth rate of population (n) + the growth rate of technology (g) + the growth rate of Y/LE. Since Y/LE is constant in the steady state, the steady state growth rate of Y = n+g With g=0, the steady state growth rate of Y = n. With g=0 and n=0, the steady state growth rate of Y = 0.
Y = LE(Y/LE). What does this tell us about the steady state growth rate of output? What is the steady state growth rate of output if the growth rates of L>0, but the growth rate of E = 0? What is the steady state growth rate of output if the growth rates of both L and E are 0?
The growth rate of a product equals the sum of the growth rates of each part of the product. Y/LE is fixed in the steady state, and E, the effectiveness of labor grows at the rate of technological progress, g. So, Y/L grows at the same rate as technological progress.
Y/L = E(Y/LE). What does this tell us about the steady state growth rate of output per worker?
Notation for Output
f(k)
Notation for Consumption
f(k) - s* f(k)
Notation for Saving (Investment)
s * f(k)
Notation for Net Investment
s*f(k) - δk
Notation for Depreciation per Worker
δk