Macroeconomics
If wages and the rental prices of capital are determined by their marginal products, what would be the impact on wages and rental prices of each of the following events:( a) A wave of immigration increases the labour force. (b) An earthquake destroys some of the capital stock. (c) A technological advance improves the production function. (d) High inflation doubles the prices of all factors and outputs in the economy.
(a) According to the neoclassical theory of distribution, the real wage equals the marginal product of labour. Because of diminishing returns to labour, an increase in the labour force causes the marginal product of labour to fall. Hence, the real wage falls. Given a Cobb-Douglas production function, the increase in the labour force will increase the marginal product of capital and will increase the real rental price of capital. With more workers, the capital will be used more intensively and will be more productive. (b) The real rental price equals the marginal product of capital. If an earthquake destroys some of the capital stock (yet miraculously does not kill anyone and lower the labour force), the marginal product of capital rises and, hence, the real rental price rises. Given a Cobb-Douglas production function, the decrease in the capital stock will decrease the marginal product of labour and will decrease the real wage. With less capital, each worker becomes less productive (c) If a technological advance improves the production function, this is likely to increase the marginal products of both capital and labour. Hence, the real wage and the real rental price both increase. (d) High inflation that doubles the nominal wage and the price level will have no impact on the real wage. Similarly, high inflation that doubles the nominal rental price of capital and the price level will have no impact on the real rental price of capital.
In the solow model, how does the savings rate affect the steady state level of income? How does it affect the steady state affect of growth?
1. In the Solow growth model, a high saving rate leads to a large steady-state capital stock and a high level of steady-state output. A low saving rate leads to a small steady- state capital stock and a low level of steady-state output. Higher saving leads to faster economic growth only in the short run.
what determines the amount of output an economy produces?
Factors of production are the inputs used to produce goods and services (capital, and labor).
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 percent 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.
First, consider steady states. In Figure 8-7, the slower population growth rate shifts the linerepresenting population growth and depreciation downward. The new steady state has a higher level ofcapital per worker, k*2, and hence a higher level of output per worker.What about steady-state growth rates? In steady state, total output grows at rate n, whereas output perworkergrows at rate 0. Hence, slower population growth will lower total output growth, but perworkeroutput growth will be the same.Now consider the transition. We know that the steady-state level of output per worker is higherwith low population growth. Hence, during the transition to the new steady state, output per workermust grow at a rate faster than 0 for a while. In the decades after the fall in population growth, growthin total output will transition to its new lower level while growth in output per worker will jump up butthen transition back to zero.
explain what happens to consumption, investment, and the interest rate when the government increases taxes
Increase of taxes equals the decrease in consumption. Increased taxes that created decrease of consumption must be followed by increase of investments, but in order for that to happened interest rate must be decreased also.
Why might an economic policymaker choose the Golden Rule level of capital?
It is reasonable to assume that the objective of an economic policymaker is to maximize the economicwell-being of the individual members of society. Since economic well-being depends on the amount ofconsumption, the policymaker should choose the steady state with the highest level of consumption.The Golden Rule level of capital represents the level that maximizes consumption in the steady state.Suppose, for example, that there is no population growth or technological change. If the steadystatecapital stock increases by one unit, then output increases by the marginal product of capital MPK;depreciation, however, increases by an amount δ, so that the net amount of extra output available forconsumption is MPK - δ. The Golden Rule capital stock is the level at which MPK = δ, so that themarginal product of capital equals the depreciation rate.
suppose consumption depends on the interest rate, how if it all does this assumption alter the conclusions reahced in the chapter about the impact of an increase in government purchases on investment, consumption, national svings, and interest rate?
The conclusion is that savings will increase while consumption will decrease. Government purchases will also decrease.In general, higher interest rates discourage consumption and encourage saving. In general, higher interest rates discourage consumption and encourage saving.
In the Solow 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?
The higher the population growth rate is, the lower the steady-state level of capital per worker, andtherefore there is a lower level of steady-state income per worker. For example, Figure 8-1 shows thesteady state for two levels of population growth, a low level n1 and a higher level n2. The higherpopulation growth n2 means that the line representing population growth and depreciation is higher, sothe steady-state level of capital per worker is lowerIn a model with no technological change, the steady-state growth rate of total income is n: the higherthe population growth rate n is, the higher the growth rate of total income. Income per worker,however, grows at rate zero in steady state and, thus, is not affected by population growth
explain what happens to consumption investment and the interest rate when the government increases taxes
When government increases taxes then households have less income for consumption. Increase of taxes equals the decrease in consumption. Increased taxes that created decrease of consumption must be followed by increase of investments, but in order for that to happened interest rate must be decreased also.
the government raises taxes by 100 billion dollars. if the marginal propensity to consume is 0.6 what happens to the following? By what amounts? Private, Public, National, Investment
a) Increase in taxes will lead to the increase in public saving by the same amount - 100 billion euro. b) The increase in taxes will affect disposable income by the same amount - 100 billion euro. With the marginal prosperity to consume 0.6 we can calculate the following: Private saving=100 billion-(0.6-100 billion)= 100 billion-60 billion=40 billion. The private savings fall for 40 billion euro. c) National saving is sum of both private and public savings, so the national savings will increase for 60 billion euro. d) National income is described as Y=C(Y-T)+I(r)+G. When we substitute the consumption function and the investment function into national income identity we get :Y-C(Y-T)-G=I(r). From this formula we can see that national savings are equal to the investments. Since national savings increased for 60 billion then investments also increased for the same amount 60 billion.
Country A and country B both have the production functionY = F(K, L) = K^1/3L^2/3.a. Does this production function have constant returns to scale? Explain .b. What is the per-worker production function, y = f(k)? c. Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker.d. Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?
a. A production function has constant returns to scale if increasing all factors of production by anequal percentage causes output to increase by the same percentage. Mathematically, a productionfunction has constant returns to scale if zY = F(zK, zL) for any positive number z. That is, if wemultiply both the amount of capital and the amount of labor by some amount z, then the amount ofoutput is multiplied by z. For example, if we double the amounts of capital and labor we use(setting z = 2), then output also doubles.To see if the production function Y = F(K, L) = K^1/3L^2/3 has constant returns to scale, we write:F(zK, zL) = (zK)^1/3(zL)^2/3 = zK^1/3L^2/3 = zY.Therefore, the production functionY = K^1/3 L^2/3 has constant returns to scale. b. To find the per-worker production function, divide the production functionY = K1/3L2/3 by L:Y/L = (K^1/3 L^2/3)/ LIf we define y = Y/L, we can rewrite the above expression as:y = K^1/3) / (L1/3Defining k = K/L, we can rewrite the above expression as:y = k^1/3 c. We know the following facts about countries A and B:δ = depreciation rate = 0.20,sa = saving rate of country A = 0.1,sb = saving rate of country B = 0.3, andy = k1/3 is the per-worker production function derived in part (b) for countries A and B.The growth of the capital stock Δk equals the amount of investment sf(k), minus the amountof depreciation δk. That is, Δk = sf(k) - δk. In steady state, the capital stock does not grow, so wecan write this as sf(k) = δk.To find the steady-state level of capital per worker, plug the per-worker production functioninto the steady-state investment condition, and solve for k*:sk^1/3 = δk.
Consider an economy described as follows: Y=C+ I+G Y = 8000 G = 2500 T = 2000 C = 1000 + (2/3)*(Y-T) I = 1200 - 100r a. In this economy, compute private saving, public saving, and national saving. b. Find the equilibrium interest rate. c. Now suppose that G is reduced by 500. Compute private saving, public saving, and national saving. d. Find the new equilibrium interest rate.
a. Private Saving = 1000; Public Saving = -500; and National saving = 500. b. Equilibrium interest rate = r = 7 c. Private Saving = 1000; Public Saving = 0; and National saving = 1000. d. New equilibrium interest rate = 2 Explanation: Y=C+ I+G Y = 8000 G = 2500 T = 2000 C = 1000 + (2/3)*(Y-T) = 1000 + (2/3)*(8000-2000) = 5000 I = 1200 - 100r 8000 = [1000 + (2/3)*(8000-2000)] + [1200 - 100r] + 2500 a. In this economy, compute private saving, public saving, and national saving. Private Saving = Y - T - C = 8000 - 2000 - 5000 = 1000 Public Saving = T - G = 2000 - 2500 = -500. This implies a budget deficit or a borrowing by the government from the private saving. National saving = Y - C - G = 8000 - 5000 - 2500 = 500 b. Find the equilibrium interest rate. National saving = I Therefore, we have: 500 = 1200 - 100r 500 - 1200 = - 100r - 700 = - 100r r = -700/-100) = 7 c. Now suppose that G is reduced by 500. Compute private saving, public saving, and national saving. Private Saving = Y - T - C = 8000 - 2000 - 5000 = 1000 Public Saving = T - G = 2000 - 2000 = 0. This a balanced budget. National saving = Y - C - G = 8000 - 5000 - 2000 = 1000 d. Find the new equilibrium interest rate. New national saving = I Therefore, we have: 1000 = 1200 - 100r 1000 - 1200 = - 100r - 200 = - 100r r = - 200/-100 = 2
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 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. 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?
a. The production function in the Solow growth model is Y = F(K, L), or expressed in terms of outputper worker, y = f(k). If a war reduces the labor force through casualties, then L falls but k = K/Lrises. The production function tells us that total output falls because there are fewer workers.Output per worker increases, however, since each worker has more capital. b. The reduction in the labor force means that the capital stock per worker is higher after the war.Therefore, if the economy were in a steady state prior to the war, then after the war the economyhas a capital stock that is higher than the steady-state level. This is shown in Figure 8-2 as anincrease in capital per worker from k* to k1. As the economy returns to the steady state, the capitalstock per worker falls from k1 back to k*, so output per worker also falls.Hence, in the transition to the new steady state, the growth of output per worker is slower thannormal. In the steady state, we know that the growth rate of output per worker is equal to zero,given there is no technological change in this model. Therefore, in this case, the growth rate ofoutput per worker must be less than zero until the new steady state is reached.
explain how a competitive. profit maximizing firm decides how much of each factor of production to demand
based on how it will affects its profits. In order to get higher profit it must analyze the cost and the benefits of an additional unit.
how can policy makers influence a nation's saving rate
increasing public saving or providing incentives to stimulate private saving. Public saving is the difference between government revenue and government spending.
