Economics:
10th Edition
ISBN: 9781285859460
Author: BOYES, William
Publisher: Cengage Learning
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Question
Chapter 29, Problem 2E
To determine
To compute:
The marginal revenue product.
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What is the marginal Physical Productivty (MPP) of the inputs given the function Q= 18x21+2x1x2+2x22 ?
Q = 4L + 8K
Q = 50K04L0.6
Q = [K0510.5]3
i)
Calculate the marginal products of labor and capital
Calculate the 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.
100
06
MPL
80
70
60
50
40
30
20
10
4
5
LABOR (Number of workers)
The following graph shows the demand for labor for three different prices per shovel:
150
135
120
105
75
60
2.5, 40
45
30
15
3
LABOR (Number of workers)
Given the company's marginal product of labor curve shown on the second graph, line
graph shows Gopher's demand for labor when the price of a shovel is $0.50, and line
Gopher's demand for labor when the price of a shovel is $1.50.
on this
shows
MPL (Shovels per worker)
WAGE (Dollars per worker)
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- Suppose that you are starting up a lawn-raking business. All of your workers are required to supply their own rakes, so the only cost to you is hiring labor at an hourty rate. Suppose that the market price of raking someone's yard is $50 per lawn and the hourly wage is $25 per hour. The following graph shows the production function (PF) for your business. On the following graph, use the green line (triangle symbol) to plot the daily isoprofit curve that indicates the profit-maximizing level of output. (Hint: Derive the slope of the isoprofit curve and then move the curve up or down until it's in the position you warnt; this is because you do not know the amount of profit that will yield the desired curve.) Then use the black point (plus symbol) to indicate the profit-maximizing level of labor and output per day. Note: You will not be graded on any adjustments made to the graph. 100 90 Isoprofit 30 Profit Max 40 FF 20 LABOR Hours per day LAWNS RAKED PER DAYarrow_forwardWhat is the marginal physical productivity (MPP) of the inputs given the function Q=12x21+2x1x2+2x22?arrow_forwardQuestion What will be the demand of inputs when the input price depends on the demandarrow_forward
- Consider the following production function: Q = (6L + 3K)¹/2 1. What is the Marginal Product of Labor (MPL)? What is the Marginal Product of Capital (MPK)? Are they diminishing? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (MPK)? 3. What is the TRSL,K? Is the absolute value of TRSLK diminishing in L or K? 4. Are there constant, decreasing, or increasing returns to scale?arrow_forwardArgue using a graph that the elasticity of substitution for a linear production function, f(1, k) = al + bk, is infinite. Hint: dividing by something really small makes the quotient really big.arrow_forwardSuppose 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?arrow_forward
- A commercial fisherman notices the following relationship between hours spent fishing and the quantity of fish caught: Hours Quantity of Fish (in pounds) 0 hours 0 lb. 1 10 2 18 3 24 4 28 5 30 What is the marginal product of each hour spent fishing? Use these data to graph the fisherman’s production function. Explain its shape. The fisherman has a fixed cost of $10 (his pole). The opportunity cost of his time is $5 per hour. Graph the fisherman’s total-cost curve. Explain its shape.arrow_forwardGopher Excavators produces shovels in a small factory and sells the shovels in a competitive market. The following table shows the company's production function: Output (Number of workers) (Shovels) Labor 1 100 195 275 4 340 380 Use the blue points (circle symbol) to plot the production function for Gopher Excavators on the following graph. 40 Producion Function 340 100 130 40 LABOR (Number of workana) Calculate the 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. (genoygl indinoarrow_forwardCalculate the Marginal Product (MP) at each input level. If the price of printer is $100 each, calculate the Value of the Marginal of labor (VMPL). If the wage rate (per week) is $1800 , how many workers will be employed? If the firm decides to hire 14 workers, what is the maximum wage the firm would be willing to pay?arrow_forward
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