Homework #3
Economic 204

1. According to the growth accounting approach, what are the three sources of economic growth? From what basic economic relationship is the growth accounting approach derived?
2. Of the three sources of growth identified by growth accounting, which one is primarily responsible for the slowdown in the U.S. economic growth after 1973?
3. According to the model of economic growth, if there is no technology growth, what will happen to output per worker, consumption per worker, and capital per worker in the long run?
4. True or False? The higher the steady state capital to labor ratio is, the more consumption each worker can enjoy in the long run.
5. What effect should each of the following have on long-run living standards, according to the economic growth model?

• An increase in the saving rate.
• An increase in the population growth rate.
• A one-time improvement in technology.

6. What types of policies are available to a government that wants to promote economic growth? For each type of policy you identify, explain briefly how the policy is supposed to work and list its costs or disadvantages.

Below are some mathematical notes to assist you.

1. The sources of economic growth : The Growth Accounting Approach
1. The production function Y=A*F(K,L)

For the quantity of output to increase one of the factors of production must increase otherwise output will stay constant and there will be no growth in the economy.

1. The rate of growth of output can be represented by:



Where: D Y/Y = the rate of growth of output

D A/A = the rate of growth of technology

D K/K = the rate of growth of capital

D L/L = the rate of growth of labor

.7 = the elasticity of output with respect to capital

.3 = the elasticity of output with respect to labor

Both elasticities are less than one due to diminishing marginal returns

2. Growth Accounting: Measuring the relative importance of the different factors of growth. Need to break the growth in output into its components: capital input growth, and labor input growth. What is left over is attributed to growth in growth in total factor productivity also know as the growth in technology or D A/A

Procedure to find this:

• Get data on D Y/Y, D K/K, and D L/L. (Adjust for quality changes.)
• Estimate the elasticities from the data using regression analysis.
• Calculate the contribution of K and N by multiplying the elasticities by the percent change in the inputs
• Calculate technology growth as the residual:

1. Growth Dynamics: The Second Economic Growth Model

Allows capital to vary and attempts to explain how economic growth and capital accumulation are interrelated. We will use it to explain three basic questions

• What is the relationship between a nations long-run standard of living and fundamental factors such as its saving rate, its population growth rate, and its rate of technological progress?

• Do economic forces exist that will ultimately allow poorer countries to catch up with the richest countries in terms of standard of living?

1. Setup of the Economic Growth model
1. Basic assumptions
1. Population and work force grow at the same rate n.
2. Closed economy and there are no government purchases of goods and services therefore C_t = Y_t - I_t
3. Rewrite the equation in per capita (per worker) terms by dividing by the size of the labor force N_t. Denote per worker values in lower cases y_t = Y/N_t; c_t=C_t/N_t; k_t = K_t/N_t
4. k_t is the capital -labor ratio
2. The supply side, the production function ,can also be represented in per worker terms
1. y_t =a f(k_t)
2. Plot the per- worker production function assuming no technology growth.
1. Same shape as the original production function
3. Steady states
1. The steady state exists when the economy is growing at a constant rate. In the growth model, the previous statement implies that there is no growth in technology. What are the conditions that underlie the steady state.
1. In the steady-state the per-capita levels of output, capital and consumption will be constant over time. (labor force and capital grow at the same rate)
2. Change in capital stock :
1. Replace worn out capital, which decreases at the depreciation rate (d K,)
2. Expand so the capital stock will grow as the population grows (nK,)
3. Gross investment
4. D k_t= i_t - (n + d)k_t
3. In per worker terms in the steady state c = f(k) - i_t
4. Plot a f(k) and (n + d)k

 

3. Reaching the Steady State
1. Assume saving is dependent upon current income Saving per capita = sY, s is the saving rate between 0 and I
2. In closed economy Saving equals investment St = sY, = (n + d)k = It

s a f(k) = (n + d)k

3. Add s a f(k) to the graph.
4. k* is the only possible steady state capital labor ratio it is where saving is equal to the steady state level of investment.
1. If k does not equal k*, then the economy will converge to the steady state level If k < k*, then saving > investment needed to keep k constant so k increases. If k > k*, then saving < investment needed to keep k constant so k decreases.
2. The economy reaches a long run steady state if there is no technology growth.
2. The fundamental determinants of long -run living standards
1. The Saving Rate
1. Higher saving rate leads to a higher capital labor ratio, higher output per worker, and consumption per worker
2. Should policy increase the saving rate
1. Lowers consumption in the short run
2. Trade-off between future and present consumption
2. Population Growth
1. Population growth lowers the capital output ratio and lowers consumption per worker
2. Policy to lower population growth
1. Raises the consumption per worker
2. Reduce total output and consumption, lowering a nations ability to defend itself or influence world events
3. The economic growth model also assumes that the population of working age is fixed may not be true as the population grows
1. Social security and health care issues
3. Technology growth
1. The key factor in determining economic growth -- increases the output per worker for a given level of the capital labor ratio
2. In equilibrium, technology improvements increase the capital labor ratio, output per worker and consumption per worker
1. Increase in output per worker will increase the capital-labor ratio which will increase the supply of saving causing the long-run capital-labor ratio to rise
3. Is there a limit? Can consumption per worker grow indefinitely?
1. Saving rate cannot rise forever ... population growth rate can not fall forever .....
2. However technology and innovation can always occur, so living standard can rise continuously
4. Do Economies converge?
1. Unconditional convergence
2. Conditional Convergence
3. No convergence
4. Evidence and international financial markets
3. The new growth theory -- Explaining the sources of technology growth
1. Human Capital
1. Knowledge, skills and training
2. Richer countries invest in more human capital
3. Higher levels of human capital are linked to economic growth and output per worker
2. Technological innovation
1. Research and development
2. Learning by doing
3. Policy issues
4. Government Policy to Raise Long Run Living Standards
1. Policies to affect the saving rate
1. Should the government try to change the saving rate? -- Depends on whether the saving market is efficient or not.
2. How can saving be increased?
1. Raise interest rate, but in practice the response of saving to the real interest rate appears to be small
2. Increase Government Saving --Reduce Deficit or Increase Surplus -- difficult to do since it requires taxes to increase or spending to decrease.
2. Improve infrastructure:
1. US spending on infrastructure has decreased in last 20 years
2. Does it increase technology?
1. ,Do richer countries spend more on infrastructure or odes infrastructure increase a nations wealth?
2. Decisions are political
3. Building Human Capital
4. Encouraging research and development
3. Industrial Policy
1. Should governments intervene in allocating resources to technology enhancing industry?