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- Consider the augmented production function Y equals A K to the power of 1 divided by 3 end exponent open parentheses H N close parentheses to the power of 2 divided by 3 end exponent, where Y is output, A is total factor productivity, K is capital, N is the number of workers, and H is average years of education. Suppose that A=2, K=8, and N=1000. What is the average product of labor (or output per worker) if H is 15.7?Suppose the US total output is represented by the standard Cobb-Douglas production function with capital and labor inputs. If all inputs are tripled (and TFP is unchanged), then output per worker Exactly triples B. Increases but not exactly triples C. Is unchanged D. Decreases E. None of the other optionsLet be a production function. The average product of factor L (labour force) is equal to:
- Is it possible to increase the labor productivity (output per unit of labor) in a given production process which exhibits diminishing returns to labor? If so, how?3. Capital labor ratio is denoted by the equation K/L where K=capital and L=labor. If the total amount of capital remains constant over a certain period of time but the number of workers L grows in the same period, will the value of K/L rise or fall? Justify your answer.Suppose that production q, capital k and labour 1 satisfy g(q, k, 1) = O. In other words, the production function q(k, I) is defined implicitly, and it satisfies g(q(k, I),k, 1) = 0 identically. How do you think we might calculate the partial derivatives in a manner similar to that developed in this chapter for functions g of only two variables? Illustrate your method by working out the partial derivatives when q is defined by the equation q3k2 +l3 +qkl = O.
- Assuming labor is the only variable factor and paid at a constant wage rate ? show that the average variable cost (AVC) is inversely related to productivity?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 ).. Determine the average products of capital (K) and labour (L)
- 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 FalseTechnological progress decreases the marginal product of labor if a new input is developed that is complementary with labor. True FalseCan you Solve the solution below A. Complete the Column for MRS. Show your solution for each answer,Number each solution that corresponds to each unknown MRS.B. Graph the Labor-Capital function, making sure that Labor units are in the horizontal axis