Y = F(K, L) = A K0.6L0.4 Where Y is aggregate output, A is a measure of available technology, K is capital and L is labor. When graphed, the production function will be concave to the origin, exhibiting increasing Marginal Product of Capital (MPK) Select one: O True O False
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- Consider now the two-period model in general equilibrium, so that prices, investment and labour supply are endogenous, i.e. the production economy. Analyse and carefully explain graphically and in words the general equilibrium effects of a decrease in TFP(total factor production) for a benchmark economy with no frictions.Consider an economy in which the aggregate production function is given by the equation: Y = 3.6 K0.5 N0.5 where (Y) is aggregate production, (A) measures productivity, (K) is the stock of physical capital and (N) is the amount of labor, measured in millions of workers. Both Y and K are measured in billions of reais. K is given and is 10,000 (i.e., 10,000 billion reais), so K0.5 = 100. The aggregate labor supply is given by the following equation: NS = [(1-t).w]2 where (t) is the income tax rate on labor and (w) is the real wage, measured in reais per hour. t = 0.20 (20%). The equilibrium levels of the real wage (w) and employment (N) are, respectively, [ANSWER] and [ANSWER]. The full employment production level (Y) is [ANSWER]. Finally, the after-tax real wage that workers receive per hour in this economy iAssume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? d. Briefly explain why y'' ≤ 0 . e. Find the elasticity of substitution between K and L. What does expansion path look like?
- please answer the following, I have attached an image of the question for better format. Thanks! 2. Suppose that the production function of a country is given by Y=K3L0.7, where Y is output, L is labour, and K is capital. a)What is the return to scale property of the production function? B)What will happen to output if we double the use of capital and labour? C)Write the production function as a relationship between output per worker and capital per worker.Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lba. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or y- or dy/dk ? c. Briefly explain why y’>0 or =dy/dk >0 . Is it possible that dy/dk>0 ? Why? d. Briefly explain y’’ < 0 e. Find the elasticity of substitution between K and L. What does expansion path look like?Suppose the production function is given by Y = K0.4 L0.6, where K is amount of land and L is amount of labor used in the production process. In the beginning, the economy has equal amount of labor and land (K = L = 100 units). Answer the following questions: How much output does the economy produce with the given inputs? What are the real rental price of land and the real wage of labor at the optimum? What is the share labor income (WL/PY) in the economy? If a plague kills one-half of the population (i.e., labor), how much does the output of the economy, the rental price of land and the wage of labor change? Answer all four.
- David Ricardo ([1817] 1965) modified Smith’s model by introducing diminishing returns to land cultivation. Diminishing returns implies that as you apply more of a variable input (labor) to a fixed input (land), the productivity of each additional worker will eventually decline as long as technology isfixed. He claimed that land was of variable quality and finite. Thus, as an economy grows, population grows relative to land, and the productivity of the labor on the land will decline. According to Ricardo, the only way stagnation could be averted, at least temporarily, would be through the trade and imports of cheap food or wage goods. The essential doctrines of John Stuart Mill (1848) differed little, if at all, from those of Ricardo. He, like Smith, believed in the doctrine of laissez-faire , but he also recognized the possibility of modifying the system. He displayed a leaning to the socialist ideal, growing closer as his life advanced. He believed that we should sacrifice economic…Hey! Need help with the following Macroeconomics question, it is divided into three smaller sub-questions. Chart it attatched below. Thank you in advance! Assume that the country Lusitania has two industries, clothing production and computer chip production. At first, both industries have identical aggregate production functions. The following table shows how the output of each industry is affected by a change in efficiency units of labor. Using the data in the table, draw a graph showing how output (on the y-axis) changes with efficiency units of labor (on the x-axis). What explains the shape of the graph? Why is it valid in this case to plot output against the efficiency units of labor and leave the stock of physical capital in the background? A Lusitanian inventor has produced a new technology that doubles the output of computer chips for any combination of capital and labor. Explain, using an equation, how this invention affects the production of computer chips. Create a new…Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ?
- Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=WKr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ).Consider the production function Y = z * K^1/3 * N^1/3 * L^1/3 where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land. Question text If we double the technology factor, z, then output will double. Question 17Select one: True False Question text If we increase the population, and therefore the workforce, then if nothing else changes, the average product of labour must increase. Question 18Select one: True False Question text We would need to increase capital input by a factor of 8 to double output. Question 19Select one: True False Question text Increasing technology will increase labour productivity. Question 20Select one: True FalseConsider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Calculate GDP (Y) for this economy. Does the production function exhibit constant returns to scale? Demonstrate with examples. Determine if the production function exhibits diminishing marginal returns to capital. Demonstrate with calculus What is the real wage in this economy? What share of GDP will go to labor in this economy?