Suppose in an economy the production function is defined by the following equation: Y(t) = 20K(t)04L(t)0.6 where Y(t) stands for production level at time t, 20 `is the technological level that will affect positively all inputs, K(t) is the physical capital, and L(t) is the used labor force. 1- Deduce the productivity function. 2- Suppose that K(t) and L(t) increase by the same rate 0% . Find the growth rate of production and productivity. Interpret your result. 3- Suppose that the physical capital starts at 120 and the labor force at 60, find the new production level in terms of 0 after inputs' growth of 0%. 4- What is the growth rate of production using result from 3? Link this to the concept of constant returns to scale. 5- The marginal productivity of capital is given by the first derivative of productivity with respect to capital. Economically, this function captures the returns of an extra unit of capital. a. For L = 243, find the marginal productivity of capital for the 80th unit and the 120th unit of physical capital. b. Compare the marginal productivities found in (a) and explain.

Suppose in an economy the production function is defined by the following equation: Y(t) = 20K(t)04L(t)0.6 where Y(t) stands for production level at time t, 20 `is the technological level that will affect positively all inputs, K(t) is the physical capital, and L(t) is the used labor force. 1- Deduce the productivity function. 2- Suppose that K(t) and L(t) increase by the same rate 0% . Find the growth rate of production and productivity. Interpret your result. 3- Suppose that the physical capital starts at 120 and the labor force at 60, find the new production level in terms of 0 after inputs' growth of 0%. 4- What is the growth rate of production using result from 3? Link this to the concept of constant returns to scale. 5- The marginal productivity of capital is given by the first derivative of productivity with respect to capital. Economically, this function captures the returns of an extra unit of capital. a. For L = 243, find the marginal productivity of capital for the 80th unit and the 120th unit of physical capital. b. Compare the marginal productivities found in (a) and explain.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

See similar textbooks

Similar questions

Suppose the production function for widgets is given byq = kl - 0.8k2 - 0.2l2where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.a. Suppose k = 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?b. Again assuming that k = 10, graph the MPl curve. At what level of labor input does MPl = 0?c. Suppose capital inputs were increased to k = 20. How would your answers to parts (a) and (b) change?d. Does the widget production function exhibit constant, increasing, or decreasing returns to scale?
Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the graph we know that for the corresponding K: APL(L1,K)=MPL(L1,K) APL(L2,K)>MPL(L2,K)…
Explain in details and steps
Question 19 Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) From the graph we know that for the corresponding K: MPL(L2,K)=MPL(L3,K) MPL(L1,K)>MPL(L2,K) MPL(L1,K)=MPL(L2,K) MPL(L1,K)<MPL(L2,K) MPL(L3,K)>MPL(L2,K)
6. Consider a hypothetical economy that has the production function Y = = F (K, LE) = K¹/3 (LE) 2/3, where Y is output, K is capital, and LE is the number of effective workers. Suppose the saving rate is 20%, the capital depreciates by 3%, the population grows at the rate of 1%, and the rate of labor-augmenting technological change is 1%. a. Solve for the per-effective-worker production function.
Assume instead that pharmacists and robots dispense prescriptions according to the following production function: Y = 10*KO.8L0.2 where Y is the number of prescriptions dispensed; L is the number pharmacist hours, and K is the number of robot hours. In addition, $10 worth of materials is used for each prescription. a. What is this type of production function called, and what are we assuming about the relationship between robots and pharmacists by using this production function? b. Derive the cost - minimizing demands for K and L as a function of output, the wage rate and the rental rate of capital. c. Use these results to derive the total cost function: costs as a function of y, r, w, and the $10 materials cost. d. Pharmacists earn $32 per hour. The rental rate for robots is $64 per hour. What are total costs as a function of Y? e. Does this technology exhibit decreasing, constant, or increasing returns to scale?f. The pharmacy plans to produce 40,000 prescriptions per week. At the…
Suppose that the economy's production function is given by Y=K²N¹-a where Y is output, K is capital, and N is labor. Assume that a = 1/3. The production function transformed into output per worker is (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with N character.)
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.
Suppose the production function is given by a = 3k - 41. what is the average product of capital when 10 units of capital and 10 units of labor are employed? A. 3 B. 4 C. 7 D. 45
The table below shows various values of labour (L), capital (K), and technology (T) for Economies A, B, and C. In each case, the aggregate production function takes the following form: Y = T x KL Economy A Economy B Economy C L. K LK I L K T on 100 50 100 50 100 50 2 110 50 110 55 110 55 4 120 50 2 120 60 120 60 130 50 130 65 2 130 65 8. 140 50 2. 140 70 140 70 10 150 50 150 75 150 75 12 TABLE 25-4 Refer to Table 25-4. The production function that applies to Economies A, B, and C displays Select one: O a. constant returns to scale. O b. diminishing marginal returns to capital. O c increasing returns to scale. O d. increasing marginal returns to capital. O e. Both C and D are correct. 6 2.
Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?
Suppose the production function is given by q = 3k - 41. what is the average product of capital when 10 units of capital and 10 units of labor are employed? A. 3 B. 4 C. 7 D. 45