x+2(1) Find the rate of change of the function f(x)(ii) The number of units Q of a particular commodity that will be produced with Kwith respect to x when x = 1.1- 8xthousand dollars of capital expenditure is modeled by Q(K) = 500 Kố.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, where2t* + 3t + 149K(t)t+2(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?

Hi, thank you for the question. As per the Honor code, we are allowed to attempt only first…

Answered: x+2 (1) Find the rate of change of the…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.6P

See similar textbooks

Similar questions

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?
Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.
Q5 The rate of change of the function f(x) =x + 2 /1 − 8xwith respect to x when x = 1. (ii) 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 now there will be K(t) thousand dollars of capital expenditure,where K(t) =2t4 + 3t + 149 /t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be produced at 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?
Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.
Anation with fixed quantities of resources is able to produce any of the following combinations of carpet and carpet looms: Yards of Carpet (Millions) Carpet Looms (Thousands) 75 60 20 45 35 30 45 15 50 50 These figures assume that a certain number of previously produced looms are available in the current period for producing carpet. To answer this question, assume carpet looms is on the y-axis and yards of carpet is on the x-ais The plot of these points that make up the PPF has a vertical intercept of and a horizontal intercept of This PPF would be (Enter your responses as a wvhole number) bowed out a straight line
Q4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.
100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t = 50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP) is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ MPy character.)
A Iqbal production function takes the form: Q = min [5L, 6K]. What are the optimum values for L and K to produce an output level (Q) of 30 units? A. L = 6 and K = 0 B. K = 5 and L = 0 C. K = 5 and L = 6 D. Answer cannot be established without knowing the cost of L and K inputs
Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =
A firm has the following production function: Q = 9L2/3K1/3 Where Q is output, L is labor and K is Capital. Where Q is output, L is labor and K is Capital. (a) What sort of returns to scale characterize this production function? (b) Derive the marginal product of labor and capital. (c) What do we mean when we say the production function is linearly homogenous?
10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?

SEE MORE QUESTIONS

Recommended textbooks for you

Microeconomic Theory

Economics

ISBN:

9781337517942

Author:

NICHOLSON

Publisher:

Cengage

Managerial Economics: Applications, Strategies an…

Economics

ISBN:

9781305506381

Author:

James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:

Cengage Learning

Microeconomic Theory

Economics

ISBN:

9781337517942

Author:

NICHOLSON

Publisher:

Cengage

Managerial Economics: Applications, Strategies an…

Economics

ISBN:

9781305506381

Author:

James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS