Production function Capital equipment per worker ($ thousands) Which 2 of the following statements are correct? Select one or more: O a. The figure shows that higher capital per worker increases output per worker. b. The figure shows that each extra $ of capital per worker raises output per worker by an equal amount. O c. The function is "convex" (i.e., it has a slope which increases as capital per worker rises) O d. The slope of the function is the marginal product of capital. Output per worker ($ thousands)

Production function Capital equipment per worker ($ thousands) Which 2 of the following statements are correct? Select one or more: O a. The figure shows that higher capital per worker increases output per worker. b. The figure shows that each extra $ of capital per worker raises output per worker by an equal amount. O c. The function is "convex" (i.e., it has a slope which increases as capital per worker rises) O d. The slope of the function is the marginal product of capital. Output per worker ($ thousands)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.11P

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(a) Complete the following table and draw the corresponding graphs. Capital inputs Labor inputs Total product Average product Marginal product 20 0 0 20 1 15 20 2 34 20 3 51 20 4 65 20 5 74 20 6 80 20 7 80 20 8 75 (b) What is relationship between MP and AP? Explain why MP first rises, then declines and ultimately becomes negative? (c) Whether the above phenomenon is long run or short run and why? (d) Does law of diminishing marginal returns holds in above scenario? Why and why not.
Suppose that the production function is Cobb-Douglas. That is, the production function is . Further, assume that the parameter α = 0.3. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percentage change)? The real rental price of capital (in percentage change)? The real wage (in percentage change)? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Q5The rate of change of the function f(x) =x + 2 /1 − 8xwith respect to x when x = 1. (i) The number of units Q of a particular commodity that will be produced with K thousand dollars of capital expenditure is modeled by Q(K) = 500 K^2/3. Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure,whereK(t) =2t4 + 3t + 149 /t + 2 Required:(a) What will be the capital expenditure 3 months from now? How many units will be producedat this time? (b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
a) What are the determinants of production? Explain.b) Suppose that an economy’s production function is in the Cobb–Douglas form with parameter α = 0.3. What is the production function equation? What does each component stand for?
a. Based on only the first-order condition with respect to labor computed in part a (Based on the given Lagrangian, compute the representative consumer's first-order conditions with respect to consumption and with respect to labor). Qualitatively sketch two things in a diagram with the real wage on the vertical axis and labor on the horizontal axis. First, the general shape of the relation ship between w and n (perfectly vertical, perfectly horizontal, upward-sloping, downward-sloping, or impossible to tell). Second, how changes in / affect the relationship (shift it outward, shift it in inward, or impossible to determine). Briefly describe the economics of how you obtained your conclusions. (Note: In this question you are not to use the first-order condition with respect to consump tion nor any other conditions.) b. Now based on both of the two first-order conditions computed in part a, construct the consumption-leisure optimality condition. Clearly present the important steps and…
A company produces children's toys. The manager noticed the connection between the number of employed workers and the quantity of toys produced per month, which are presented in the table of following: a) In what period is this firm operating? Why? b) What is the average product when 5 workers are employed? c) What is the marginal product when 7 workers are employed? What does this value mean? d) Does the law of declining marginal income apply? If yes to which worker? e) In this production function do we have total declining revenues? If so, which worker happens? f) Graph the curves of total product (TP), marginal product (MP) and product average (AP).
3. First, do the following functions exhibit increasing, constant, or decreasing returns toscale? Why? Explain in detail. Second, calculate the marginal product of each factorand discuss what happens to the marginal product of each individual factor as that factoris increased and the other factor is held constant. a. q = 3L + 4Kb. q = (2L + 2K)1/3c. q = 2LK2d. q = L1/4K1/3e. q = 4L1/2 + 4K
QUESTION 1 Consider the following production functions, where q is the quantity produced of the good, Kis the quantity of capital used, and L is the quantity of labor used:Production function 1q (K, L) = K^αL^βProduction function 2q (K, L) = K^α + L^βa) What is production function? Explain by providing appropriate graph.b) Does Production function 1 have decreasing, constant, or increasing returns to scale?Explain.c) Suppose that α = 1 and β = 1. Does Production function 2 have decreasing, constant,or increasing returns to scale? Explain.d) Suppose that α = 1/2 and β = 1/2. Does Production function 1 have decreasing,constant, or increasing returns to scale? Explain
The Law of variable proportion describes three stages of production. In the first stage of production a. Both MP and AP rise O b. MP rises O c. AP Falls O d. MP is zero
8) Suppose the production function for good q is given by q=3 ∙K+2∙ L where K and Lare capital and labor inputs. Consider three statements about this function:I. The function exhibits constant returns to scaleII. The function exhibits diminishing marginal productivities to all inputsIII. The function has a constant marginal rate of technical substitutionWhich of these statements are true?A) All of themB) None of themC) I and II but not IIID) I and III but not IIE) Only I .
The table below shows the marginal benefit for various inputs. Assume that each level represents a $100 investment, and answer the following questions. (a) If you have an unlimited budget, how much would you spend on each input? Explain.(b) Now, assume you can spend a maximimum of $500. What would you spend on each inputnow? What order would you buy them in?(c) Finally, assume you can borrow as much as you want with an interest rate of 10%. How muchwill you borrow and how will you spend it if you have to pay back the loan within 1 year?
Explain the economic meaning of the ? matrix and ? vector