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- For this question assume that technological progress does not occur. The rate of saving in Canada has generally been greater than the saving rate in the U.S. Given this information, we know that in the long run A) Canada's growth rate will be greater than the U.S. growth rate. B) capital per worker in Canada will be no different than U.S. capital per worker. C) investment per worker in Canada will be no different than U.S. investment per worker. D) all of these E) none of thesePlease no written by hand and graph Consider a small world that consists of two different countries, a developed and a developing country. In both countries, assume that the production function takes the following form: Y = F (K, LE) = K¹/4 (LE) 3/4, where Y is output, K is capital stock, L is total employment and E is labour augmenting technology. (a) Does this production function exhibit constant returns to scale in K and L? Explain. (b) Express the above production function in its intensive form (i.e., output per-effective worker y as a function of capital per effective worker k). (c) Solve for the steady-state value of y as a function of saving rate s, population growth rate n, technological progress g, and capital depreciation rate 6. (d) The developed country has a savings rate of 30% and a population growth rate of 2% per year. Meanwhile, the developing country has a savings rate of 15% and population growth rate of 5% a year. Technology evolves at the rate of 8% and 2% in…Population Growth and Technological Progress – Work It Out PLEASE WRITE ANSWERS CLEARLY An economy has a Cobb-Douglas production function: Y = K“(LE)'-a The economy has a capital share of 0.30, a saving rate of 42 percent, a depreciation rate of 4.00 percent, a rate of population growth of 5.25 percent, and a rate of labor-augmenting technological change of 3.5 percent. It is in steady state. b. Solve for capital per effective worker (k*), output per effective worker (y*), and the marginal product of capital. k* = y* = marginal product of capital =
- The economy has grown by 4% per year over the past 30 years. During the same period, the labor force has grown by 1% per year and the quantity of physical capital has grown by 5% per year. Each 1% increase in physical capital per worker is estimated to increase productivity by 0.4%. Assume that human capital has not changed during the past 30 years. What is the growth rate of productivity? A) 5% B) 4% C) 3% D) 1.6%1.1. Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of its log to show: (a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) = X(t)Y(t), then Ż(t)/Z(t) = [X(t)/X(t)] + [Ÿ(t)/Y(t)]. (b) The growth rate of the ratio of two variables equals the difference of their growth rates. That is, if Z(t) = X(t)/Y(t), then Ż(t)/Z(t) = [X(t)/X(t)]-[Y(t)/Y(t)]. (c) If Z(t) = aX(t)a, then Ż(t)/Z(t) = aX(t)/X(t).Regard x and y as continuous variables. If x grows at 3% rate and y grows at 2% rate, what is the growth rate of z = x2y2? a. 0.5% b. 1.5% c. 2.5% d. None of above.
- 5) Suppose that an economy starts off with a per capita real GDP of $5,000. How large will the per capita GDP of this country be if it grows at an annual rate of 6% for 40 years? Use compound growth rate formula. Show your calculations and the unit of account of your answer. Answer: 6) The graph below represents per-worker production functions for the same country. Answer the following questions using this graph. Real GDP per hour worked, Y/L $17,000 16,400 16,000 15,000 Production function3 B Production function2 E Production function1 a) Answer: $50,000 60,000 70,000 Capital per hour worked, K/L Which concept is illustrated by the movement from point A to B or from point B to C?Small differences in growth rates in the size of the economy, over several decades, will result in big differences in the size of the economy. Pretend we start in 1950 and the U.S. growth in real GDP has been around 3.15%. This has resulted in real GDP growing 8 times over this 70-year period (1950 to 2020). If real GDP growth had been 4.0%, real GDP would be times larger. a. 8 (about the same growth as with 3.15% growth) b. 10 С. 14 d. 16An economy's production function as follows Y = 8 (K)¹/2 (EL)¹/2 If depreciation rate is 10%, population growth rate is 4%, tech progress grows 6%, and saving rate is 20%. a. b. C. d. e. f. Write production function in term of per effective worker variables. Find steady state capital per effective worker, output per effective worker, consumption per effective worker, investment per effective worker. Find growth rate of capital per worker and output per worker at steady state. Find growth rate of capital stock and total output at steady state. Propose policies to encourage long run growth of total output and living standard? Draw relevant graph for the above questions.
- Suppose in the economy in question 4) there is an increase in the saving rate from 6% up to 10%.Briefly explain how this will affect the following variables in the steady-state.capital per workera)b)investment per workerc)growth rate of output per workerd)growth rate of output5. The real GDP per capita in Colombia was $3,692 in 2000 and $5,889 in 2020. What is the average annual growth rate of the real GDP per capita from 2000 to 2020? Please use the log formula.QUESTION 20 Refer to the information to answer this question. What is the percentage increase in productivity between 2020 and 2021? Output Labour Inputs 1,300 units 1,350 units A. 3.8% B. 5.2% C. 8.3% OD. 12.5% Year 2020 2021 15,600 tonnes 17,550 tonnes
