Population Growth and Technological Progress- Work It Out In the nation of Winknam, the capital share of GDP is 35 percent, the average growth in output is 3.0 percent per year, the depreciation rate is 5.5 percent per year, and the capital-output ratio is 3.0. Suppose that the production function is Cobb- Douglas and that Winknam has been in a steady state. Round answers to two places after the decimal when necessary. b. In the initial steady state, what is the marginal product of capital (MPK)? MPK =
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- Population Growth Population growth in the US has, for a very long time been about 1% per year.Take the production function to be y = k0.5, where y and k are output andcapital per capita. The depreciation rate is about 10% per year and the savingsrate is about 20%. 1. What is the steady state capital per capita rate?2. From one period to the next, at what rate does total capital (not percapita) grow.3. If the population growth rate grew to 1.5%, how much would steady statecapital per capita change? Then how much is total capital changing atthis steady state?A) Suppose there are two countries that are identical in every way with the following exception: Country A has a higher saving rate than country B. Given this information, we know with certainty that A) Country A will experience capital widening b) growth rate of output per sopita in the steady state is same in two countries c) K/N is higher in country B d) growth rate of output per capita in the steady state is higher in country A B) When expectations are taken into account, a policy to reduce budget deficit may not lead to a fall in output in the current period. Which of the followings cannot be listed as factor that offsets the detrimental impact of fiscal contraction on the output in the short run? a) Increasing tax rates harshly to finance deficit. b) Credibility of the deficit reduction program. c) Cutting wasteful spending and leaving room for future tax cuts. d) Backloading the deficit reduction, leaving larger cuts in government spending to the future while only small cuts…3 Assume a closed economy, perfectly elastic labor supply, and linear technology. Suppose the incremental capital-output ratio (ICOR) is 3, the depreciation rate is 3%, and the gross savings rate is 10%. Use the Harrod-Domar growth equation to determine the rate of growth. What would the gross savings rate have to be to achieve 5% growth? Assuming a perfectly elastic labour supply, state one criticism of this model from an exogenous growth theory viewpoint and another criticism of this model from an endogenous growth theory viewpoint.
- Assume an economy without population growth or technological progress. Their production function is given by ? = 35?0.5. Their currency capital stock is 100, and the depreciation rate is 17.5%. Give a savings rate such that: Income per worker will grow over the current period Income per worker stay the same over the current period Income per worker will fall over the current periodSuppose that for a particular country, the savings rate is 20%, the capital–output ratio is 4, the depreciation rate is 1%, and the rate of growth of the population is 2% per year. a) Calculate the rate of growth of overall GDP. b. What is the rate of per capita GDP growth? c. What should the savings rate be to get the growth rate of overall GDP to 8%?Social infrastructure and the investment rate. Suppose that rates of return to capital are equalized across countries because the world is an open economy, and suppose that all countries are on their balanced growth paths. Assume the production function looks like Y = IKaL1-a, where I reflects differences in social infrastructure. (a) Show that differences in I across countries do not lead to differences in investment rates. (b) How might social infrastructure in general still explain differences in investment rates?
- Consider a closed economy in which the population grows at the rate of 1% per year. The per-worker production function is yt = 2.2kt^0.5, where y is output per worker and k is capital per worker. The depreciation rate of capital is 10% per year a- Households initially consume 80% of income and save the remaining 20% of income. There is no government spending. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker? b-Suppose saving rate decreases to 10% permanently. What are the steady-state values of capital per worker, output per worker, consumption per worker, and investment per worker?7 Assume a Cobb-Douglas production function, where © =0.5 and A = 1. If AN/N = 0.06, d = 0.04, and s = 0.2, what is the steady state value of capital per capita ??Given a saving rate of 5%, a depreciation rate of 1%, and a production function in which y = k0.5where y is output per worker and k is capital per worker, calculate the steady state values forii. output per worker, iii. consumption per worker, iv. Calculate the golden rule steady state level of capital
- Question 1:In Ghana, the capital share of GDP is about 40 percent, the average growth in output is about2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratiois about 1.5. Suppose that the production function is Cobb–Douglas and that Ghana has beenin a steady state.a. What must the saving rate be in the initial steady state? [Hint: Use the steady-staterelationship, sy = (δ + n + g)k.]b. What is the marginal product of capital in the initial steady state?c. Suppose that public policy alters the saving rate so that the economy reaches the GoldenRule level of capital. What will the marginal product of capital be at the Golden Rule steadystate? Compare the marginal product at the Golden Rule steady state to the marginal productin the initial steady state. Explain.d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product…Q7 An economy has a Cobb–Douglas production function: Y = Kα(LE)1−α The economy has a capital share of 1/3, a saving rate of 24 percent, a depreciation rate of 3 percent, a rate of population growth of 2 percent, and a rate of labor-augmenting technological change of 1 percent. It is in a steady state. a. At what rates do total output, output per worker, and output per effective worker grow?b. Solve for capital per effective worker, output per effective worker, and the marginal product of capital. c. Does the economy have more or less capital than at the Golden Rule steady state? How do you know? To reach the Golden Rule steady state, does the saving rate need to increase or decrease?d. Suppose the change in the saving rate you described in part (c) occurs. During the transition to the Golden Rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)? After the economy reaches its new steady state, will the growth rate of…Which of the following statements are correct? state which ones are definitely incorrect and why. a. Capital grows when investment is higher than depreciation b. The growth rate of capital increases when investment is higher than depreciation c. For a given rate of depreciation of capital, a rise in the ratio of investment to capital will raise the growth rate of capital d. There are no rich countries wth low investment ratios, and no poor countries with high investment ratios e. A country can only invest more than it saves if it borrows from abroad. f. The scatter diagram of capital output ratios vs investment rates does not show a perfect correlation. Therefore there is something wrong with the model of the way capital grows g. A country that increases its saving rate will be able to have more rapid growth of capital for as long as it maintains this higher savig rate h. A country that increases its saving rate will be able to have more rapid…
