Consider a Cobb-Douglas production function with three inputs. K is capital (the numbe achines), L is labor (the number of workers), and H is human capital (the number of coll =grees among the workers). The production function is Y=K2/6 L3/6 H1/6 Derive an expression for the marginal product of labor. How does an increase in the amoun man capital affect the marginal product of labor? (Hint: The marginal product of labor MP und by differentiating the production function (Y) with respect to labor (L)) Derive an expression for the marginal product of capital. How does an increase in the amo human capital affect the marginal product of capital? (Hint: The marginal product of capita

Consider a Cobb-Douglas production function with three inputs. K is capital (the numbe achines), L is labor (the number of workers), and H is human capital (the number of coll =grees among the workers). The production function is Y=K2/6 L3/6 H1/6 Derive an expression for the marginal product of labor. How does an increase in the amoun man capital affect the marginal product of labor? (Hint: The marginal product of labor MP und by differentiating the production function (Y) with respect to labor (L)) Derive an expression for the marginal product of capital. How does an increase in the amo human capital affect the marginal product of capital? (Hint: The marginal product of capita

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Suppose that the price of labor (the wage rate) is $100 a day and that the rental price of capital is $50 a day. Currently the Jedie Weapons Corporation is using ten units of capital and five units of labor to produce 500 lightsabers a day. Each lightsaber sells for $2. At the current input use levels, the marginal product of capital is 40 lightsabers per day and the marginal product of labor is 60 lightsabers a day. Is the firm making an economic profit at its current levels of operation? 2. Could the firm increase its profits at the current level of output by adjusting its use of labor and capital? If so, how should input use be adjusted?
During the 1920s, Charles Cobb and Paul Dougkas modeled totalproduction output P (of a firm, company or entire economy) as a function of labourhours involved x and capital invested y (each includes the monetary worth of allbuildings and equipment). The Cobb-Douglas production function isP(x, y) = k x^α y^(1−α),where k ad α are constants representative of a particular firm or economy.(1) Show that doubling of both labor and capital results in doubling productionP.(2) Suppose a particular firm has the production function for k = 120 andα =3/4. Assume each unit of labor costs $250 and each unit of capital costs$400, and that the total expense for all costs cannot exceed $100,000. Findthe maximum production level for the firm.(3) Compute the production level at x = 64 and y = 81. If the capital isdecreased by 3 units, by how many units the labor should be adjusted toso that there is not change in production level.
Joe owns a coffee house and produces coffee drinks under the production function q = 5KL where q is the number of cups generated per hour, K is the number of coffee machines (capital), and L is the number of employees hired per hour (labour). What is the marginal product of labour?A. 5B. 5KC. 5LD. 5K/L
Consider a production process where flowers are grown (the output) using gardeners (labor) and greenhouses (capital). The quantity of flowers grown per day with various combinations of labor and capital are shown in the table. Fill in the marginal product of labor in the table below. (Enter your responses as integers).
4. Ariel's T-shirt company hires labor at a rate of $8 per hour and rents capital (sewing machines) at a cost of $128 per machine per day. Throughout this question, you can think of Ariel renting fractions of sewing machines if necessary. Her production function is given by q = 6LK where q measures the number of T-shirts produced each day, L measures the total number of hours worked by all employees in a day and K measures the number of sewing machines. (a) Using the Lagrangian technique, find the cost-minimizing combination of labor and capital for the production of q T-shirts per day. (b) Write down an equation for Ariel's long-run expansion path. (c) Find Ariel's long-run total, average, and marginal cost as a function of the number of T-shirts she produces each day. (d) Sketch Ariel's long-run total expansion path in a diagram. Sketch at least two isoquants with the associated isocost lines. Using your diagram, determine how Ariel's long-run expansion path will shift if the cost of…
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1. Computing labor productivity and its relationship to the demand for labor Gopher Excavators produces shovels in a small factory and sells the shovels in a competitive market. The following table shows the company's production function: Labor Output (Number of workers) (Shovels) 1 90 175. 245 4 300 325 Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the following graph. ?) 400 360 Production Function 320 280 240 200 160 120 80 1 3. 4 5. LABOR (Number of workers) Calculate marginal product of labor (MPL) of each worker, and then plot the MPL curve on the following graph using the blue points (circle symbol). Note: Remember to plot each point halfway between two integers. For example, when the number of workers increases from 0 to 1, the MPL of the first worker should be plotted with a horizontal coordinate of 0.5, the value halfway between 0 and 1. Line segments will automatically connect the points. OUTPUT (Shovels) 40
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Suppose you find that at a given input bundle the TRS=-2. Then you can conclude that at that input bundle: labour is more productive than capital O capital is more productive than labour labour and capital are equally productive O there is not enough information to answer
Please only answer d Consider the following Cobb-Douglas production function: Y = 10 L^0.4 K^0.4. Suppose that the price of labor is w = 20 and the price of capital if r = 40. a- Derive the total cost curve for this production function. b- Derive the marginal cost curve for this production function. c- Plot the marginal and total cost curves for q = 1,2,3,4,5. What does it tell you about economies of scale for the production function? d- Suppose that the wage rate went up from 20 to 30. What would happen to the total wage bill relative to total costs wL/(wL+rK) What would happen to total costs?
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