Principles of Economics (12th Edition)
12th Edition
ISBN: 9780134078779
Author: Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher: PEARSON
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Chapter 7.A, Problem 4P
To determine
Isoquant/isocost diagram.
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Using the information from the isoquant/isocost diagram to the right and assuming that PL = P = $2,
complete the table below. (Enter your responses as integers.)
Output Units
100
200
300
Total Cost of Output
$100
$
$300
Units of
Labor
Demanded
25
50
Units of Capital Demanded
4
50
75
Units of capital (K)
200
175-
150-
125-
8100-
75-
50-
25+
0+
0
25 50
9=100 9 200
100 125 150
q=300
75
Units of labor (L)
175 200
Q
Q
Isoquant curves and isocost curves are tools that can explain how a firm might best respond to changes in the production environment. Present an example of an isocost curve where labor and capital are the two inputs, and explain what it is using language someone not trained in economics could understand. Present an example of an isoquant in the same diagram you used for your isocost curve, and draw the isoquant so it cuts the isocost curve twice. Explain what an isoquant is using language someone not trained in economics could understand. Label the two points A and B, where the isocost and isoquant curves intersect. Present a logical argument that explains why the firm should operate neither at point A nor point B, and present a point that would be optimal by drawing a new isoquant curve in the diagram. Add a second isocost curve to your diagram such that the firm is spending more money on inputs. Add a third isoquant to your diagram to show a firm that would become more capital…
WickCo makes decorative candles, and its
production function is given as Q = K+ L,
where K is the units of capital, and L is the
units of labor used in the production process.
a. In the diagram below, draw the isoquant
for WickCo. for output level Q = 10.
The diagram below is a 10x10 grid
b. Suppose the wage rate is $50 per unit of
labor and the rental rate of capital is $55 per
unit. In the diagram given in part (a), show the
cost minimizing input combination for Q = 10
and draw the associated isocost line. What is
the total cost of production at the cost
minimizing input combination?
Chapter 7 Solutions
Principles of Economics (12th Edition)
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- Instructions: Move the slider at the bottom of the diagram to change the quantity of labor hired for both graphs and the table. Move the production slider to 6 units of labor. Suppose you had the information for the L=2 row and the L=6 row, but the row(s) in between them were missing and you didn't have any information in the Marginal Product column. If you wanted to estimate the marginal product, you might assume the marginal products of each of the 4 additional workers are equal. a. Estimate the marginal product of each additional worker if L were to increase from 2 to 6. b. Calculate the slope of the total production function between L=2 and L=6.arrow_forwardExhibited in the table below are the two isoquants and the isocost for a hypothetical firm A B C D E F Labor 40 28 18 10 4 0 Capital 1 2 3 4 5 6 Labor 80 38 28 20 14 10 Capital 1 2 3 4 5 6 Labor (P2/unit) 25 20 15 10 5 0 Capital (P5/unit) 0 2 4 6 8 10 In a single graph, please perform the following: A. Draw the Isoquant curve B. Draw the isocost C. Identify the optimal point which is tangent to the isoquant line. Please mark the spot as X. D. How many units of capital and labor is the optimal combinationarrow_forward***There are FOUR parts to the question, all based around the same given data...please answer and explain each and note where graphs are needed*** Given: A farmer raises apples using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor? d. In the long run, the farmer can change both his…arrow_forward
- Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}.If he uses 1 kg of wool and 3 hours of labour, he can produce 1 t-shirt.1. Draw isoquants for q = 1 and q = 2 on a diagram with labour on the horizontal axis and wool on the vertical. 2. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the optimal bundle of that he can produce in order to minimise costs? Draw the isocost lines.arrow_forward***QUESTION HAS FOUR PARTS - ALL PARTS MUST BE ANSWERED TOGETHER AS THEY ARE DEPENDENT ON EACH OTHER*** 1. A farmer raises apples using land (K) and labor (L), and has an output of ? (?,?) = ? 0.5 ? 0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor? d. In the long run, the farmer can change both his amount of land and his amount of labor. Suppose…arrow_forwardPrunella raises peaches. She uses L units of labor, and T units of land to produce peaches. Her production function is f(L, T)= L1/2T 1/2 A: Write the equation and plot the isoquant for the output quantity 4. B: What is the returns to scale of this production function? C: Find the marginal products of labor and land. What is the rate of technical substitution between land and labor? D: In the short-run, Prunella cannot vary the amount of land she uses. Plot the output as a function of labor only for the fixed level of land of T=1. E: Find the marginal product of labor from L=4 and show it on the graph. Is the marginal product of labor diminishing, constant or increasing in labor? F: Suppose wages are constant and equal w, fixed costs are zero. Find the short-run profit maximizing level of labor for T=1. Please see the attached photoarrow_forward
- Q3) A chair manufacturer hires its assembly-line labor for $30 an hour and calculates that the rental cost of its machinery is $15 per hour. Suppose that a chair can be produced using 4 hours of labor or machinery in any combination. Graphically illustrate the isoquant and the two isocost lines for the current combination of labor and capital and for the optimal combination of labor and capital.arrow_forwardWhen analyzing isoquants, if the marginal product of all inputs double, how would that change the input mix you would use to produce a given level of output?arrow_forwardThe following table gives the output achievable for various combinations of inputs. There are only two inputs used in production, labour and capital. labor input capital input 1 2 3 4 5 1 20 40 55 60 65 2 40 50 65 70 75 3 55 65 75 80 85 4 60 70 80 90 95 5 65 75 85 95 100 Explain the meaning of an isoquant . Draw the isoquants for the output level of 65 and 75 on the same graph.Define and explain the returns to scale for production with those inputs given above table.arrow_forward
- Cheburashka uses kiwi fruits (K) and labour (L) to produce juice (q). His production function is: q=min{L/3, K0.5}, where labour is measured in hours, kiwi fruits in kg, and juice in (large) bottles. For example, if he uses 4 kg of kiwi fruits and 6 hours of labour, he can produce 2 bottles of juice. a) Draw isoquants for q = 1, q = 2 and q = 3 on a graph with labour on the horizontal axis and kiwi fruits on the vertical one. = $5 per kg. b) Let the price of labour-hour be given by w = $18 and the price of fruit by p What is the optimal amount of labour and fruit to produce q bottles of juice if Cheburashka strives to minimise costs? (Note that you need to provide expressions L(q) and K(q)). Illustrate on the graph from a) by drawing corresponding isocost lines. c) Draw the Cheburashka's expansion path on a graph from a). Derive an expression for the expansion path, i.e., K as a function of L. How does it depend on the wage and the price of kiwi?arrow_forward2. Inputs and outputs Aneesha's Pizzas is a takeout-only pizza parlor servicing the college campus of Tallahassee that specializes in vegan pizzas. Aneesha's small shop has barely enough room for customers to stand and wait, let alone the five pizza ovens necessary to keep up with the hungry student customers. Aneesha signed a lease renting both the five ovens and the storefront for the next year. Due to the terms of the lease and the building's size constraint, Aneesha is unable to change the store's number of pizza ovens in the short run. However, Aneesha does face a decision regarding the number of employees to schedule on a weekly basis. Every Sunday, Aneesha contacts the staff to communicate the amount of workers needed on each day of the upcoming week. In the short run, the store employees are inputs, and pizza ovens are inputs. The following table presents Aneesha's daily production schedule. Fill in the blanks to complete the Marginal Product of Labor column for each worker.…arrow_forwardA firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?arrow_forward
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