Suppose the process of producing lightweight parkas by Polly's Parkas is described by the functionq=40K04(L-40)0.6where q is the number of parkas produced, K the number of computerized stitching-machine hours, and L thenumber of person-hours of labor. In addition to capital and labor, $40 worth of raw materials is used in theproduction of each parka.Note thatandдаак=40(0.4)K 0.60 (L-40)0.6да=40K04 (0.6)(L-40) 0.4-0.40aLBy minimizing cost subject to the production function, derive the cost-minimizing demands for K and L as a functiof output (q), wage rates (w), and rental rates on machines (r).The cost-minimizing demands for K and Lare

Answered: Suppose the process of producing…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Qc = K0.1 L0.9. 3.1 Show that both additional labour and additional capital increase production at a decreasing rate by computing and referring to some of the second derivatives of Qe. 3.2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg = K0.6 L0.4. Show, using the Jacobian derivative matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units, would approximately change production of both goods. Start from an initial combination of K = 100 and L = 50. 3.3 Suppose that demand for capital and labour are in turn determined by the interest rate 125. Use the Jacobian r and wages paid to workers w, as follows: K = derivative matrix of Qe and Qeg to calculate how production changes in response to an and L = 10r3 ar increase in interest rates: when r = 2 and w = 1000. Or
3) If we duplicate all the production factors of the production function f (L,K) = L 2/3. K1/3, where L are working hours, k the capital then the amount of product will be multiplied by: Choose one: A) 4 B) 2 C) 1 D) 8 E) 0.5
For the Cobb-Douglas production function P and isocost line (budget constraint, in dollars), find the amounts of labor L and capital K that maximize production, and also find the maximum production. Then evaluate and give an interpretation for |å| and use it to answer the question. (a) Maximize P = 2000L3/5K2/5 with budget constraint 15L + 32OK = 8000. L = K = P = (b) Evaluate and give an interpretation for |21. Each additional dollar of budget increases production by this amount. (c) Approximate the increase in production if the budget is increased by $80. units
Show using math and logic that for constant returns to scale production functions, MRTS between labor and capital depends only on the K/L ratio, and not the scale of production.
complete the table
Consider the production function of gadgets: Q = 2.9K12 L0.5 where Q is units of output per month, K is hours of capital and L is hours of labour. Capital can be rented at $66 per hour, and labour %3D can be hired at $33 per hour. What is the maximum output for a monthly production budget of $18600? Answer: units DO NOT ROUND YOUR CALCULATIONS UNTIL YOU REACH HE FINAL ANSWER. ENTER YOUR RESPONSE ROUNDED TO VO DECIMAL PLACES, AND NO SEPARATOR FOR OUSANDS.)
Kris wants to open a BBQ restaraunt. He has signed a 12- month lease at $6,000 per month. The lease enabled him to rent a restaraunt with all the equipment he needs to make BBQ; therefore, K equals 1. Kris must pay his workers a monthly salary of $2,400 each. His production function is q = 100L1/2K1/2 where q is the quantity of BBQ prepared per month in pounds, L is the number of workers employed per month, and K is the quantity of capital employed, and, as previously indicated, K is assumed to equal 1. What does Kris's monthly total cost expressed as a function of quantity equal?
What is the marginal physical productivity (MPP) of the inputs given the function Q=18x21+2x1x2+2x22 ? Select one: а. МPPx1336х1+2x1MPPx2-2x1+4х1 b. МPPX1336x1+2x1MPPx2-2x2+4х2 С. MPPX1=36+2x2+2MPP×2=2x1+4x2 d. MPPX1=36x1+2×2MPPX2=2x1+4x2
Given the production function per hour Q(x, y) = 2x² - 4y² + 40x + 40y, where x is a worker receiving $1 per hour and y is a worker receiving $2 per hour. The budget constraint is $410. What is the value of ? (given that your bordered hessian (or variable vector) is in the order of X, x and y, respectively)
Question 37 [ DIFFICULT] Consider two firms, both producing the same product, using the same production technology given by: q = √√K This production technology implies the following MRTS: K MRTS=AY ΔΧ L where K is the amount of capital used and L is the amount of labour used to produce output. It can be shown that this production technology implies the following minimised total cost function: TC = 2q√w√r where w represents the per-unit cost of labour and r represents the per-unit cost of capital. Suppose each firm can hire labour at $1 per unit and capital at $9 per unit. Each firm produces 90 units of output. One firm (Firm 1) chooses its input combination to minimise costs of production. However, Firm 2 instead produces output using twice as much labour as Firm 1. Compared to Firm 1, how much higher are Firm 2's cost of production? a) $270 b) $67.50 c) $275 d) $135 e) $132 Hint: It can be shown that the cost-minimising quantities of capital and labour (chosen by Firm 1) are K = 30…
3 Consider the production function of candles, with capital (K) and labour (L) as inputs: Qc = K0.1 L0.9 3.1 Show that both additional labour and additional capital increase production at a decreasing rate by computing and referring to some of the second derivatives of Qe. 3.2 Now consider the production function of an additional product, electrical generators, de- fined by the following function: Qeg = K0.6 L0.4. Show, using the Jacobian derivative matrix of Qe and Qeg, how increasing capital by 10 units and decreasing labour by 5 units, would approximately change production of both goods. Start from an initial combination of K = 100 and L = 50. 3.3 Suppose that demand for capital and labour are in turn determined by the interest rate 125,2 r and wages paid to workers w, as follows: K = _8w and L = 10r3 Use the Jacobian derivative matrix of Qe and Qeg to calculate how production changes in response to an aQ. ar increase in interest rates: when r = 2 and w = 1000.
please show graphs and table thank you

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