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- 1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.Show that, when using a traditional economic production function,doubling our population can double our output if capital stocks alsodouble. Use the production function: Q = AK L , where A representstechnology in an economy, K capital, and L labor. Double K and L andshow that Q also doubles, assuming α=β=1/2. Now show that, when we incorporate natural capital into thediscussion, doubling the population does not increase output in thesame way (since natural capital cannot also grow). Use theproduction function: Q = AK L N , where N is natural capital. DoubleK and L and show that Q less than doubles, assuming α=β=γ=1/3.1. O LounchPad • Country A and country B both have the production function Y = F(K, L) = K/³L²/3. 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 work- er 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?
- PER CAPITA OUTPUT to YEAR In the Romer model in figure above, at time to, a change in the shape of the production function can be explained by an increase in the: Select one: O a. ideas efficiency parameter. O b. population. O c. saving rate. O d. share of labor engaged in research. O e. growth rate.Economics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScannerA country faces diminishing marginal returns when increasing it's capital stock. If this country added 1,000 units of capital last year and saw their GDP rise by $500 per person, what would you expect to happen if they had added 2,000 units of capital instead? O GDP would increase by another $500 per person O GDP would increase by less than another $500 per person O GDP would increase by more than another $500 per person O It is impossible to tell what would happen What is a potential downside of using patents to promote the creation of new technology? Without a market test, patents might be given to technology which ends up being useless. O Government money may be directed towards unproductive goals. It slows the spread and development of those ideas by restricting competition. They prohibit competition forever. What is the law of diminishing marginal returns?
- Jtilizing the aggregate production functions to the right, Robert Solow asserted that the most significant or critical factor in driving long term economic growth is and is reflected in the movement from to O A. capital accumulation; "B" to C" Production function3 D B. technological change; "A" to "B" Production function2 O C. economies of scale; "D" to "C" O D. technological change; "B" to "C Production function, :B O E. capital accumulation; "A" to "C" $40 Capital per hour worked (K/L) 60 Click to select your answer. la 19 Lhednge SSS-76 DOCX cBook Air F9 F10 F11 F12 F7 F8 + 8 9 del Real GDP per houraorked (Y/L)The “per person” versions of production functions: Write each productionfunction given below in terms of output per person y ; Y/L and capital perperson k ; K/L. Show what these “per person” versions look like in a graphwith k on the horizontal axis and y on the vertical axis. (Assume A is somefxed positive number.)(a) Y = K 1/3L2/3 and Y = K 3/4L1/4 (on the same graph) (b) Y = K(c) Y = K + AL(d) Y = K − ALConsider the production functions shown here, which show the output of a bakery over time. Suppose that the bakery experiences significant wear and tear of its ovens and that this leads some of the ovens to break down, Which of the movements reflects this scenario? Real GDP per worker Physical Capital per worker O B to C O D to C O A to C O E to C
- Consider the economies of Hermes and Gobbledigook, both of which produce gobs of goo using only tools and workers. Suppose that, during the course of 20 years, the level of physical capital per worker rises by 4 tools per worker in each economy, but the size of each labour force remains the same. first dropdown question options are (larger or smaller), second dropdown question options are (the brain drain, inward orietned growth, diminishing returns, constant returns, increasing returns), the third dropdown question oprions are (more diffucult or easier)The following table shows the GDP per capita of various countries forthe years 1960 and 2010 in PPP-adjusted 2005 dollars. The table alsocontains the implied growth rates, which show how much on average eachcountry needed to grow each year to reach the 2010 level of GDP per capitastarting from the 1960 level of GDP per capita. Use the table to answer thefollowing questions. 1. Why have some countries reduced the gap between their incomes andthat of the United States and other countries failed to do so?Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?