In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing a items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is z items with cost C (æ), then the cost of computing h additionial (C(z+h)-C(x)) . As we analyze the items is C ( + h). The average cost of those h items is cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (z). Problem Set question: The cost, in dollars, of producing a units of a certain item is given by C(z) = 0.02m3 – 10z + 450. (a) Find the marginal cost function. MC (x) - 固助 (b) Find the marginal cost when 50 units of item are produced. The marginal cost when 50 units are produced is $ Number (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ Number

In the previous Problem Set question, we started looking at the cost function C (æ), the cost of a firm producing a items. An important microeconomics concept is the marginal cost, defined in (non- mathematical introductory) economics as the cost of producing one additional item. If the current production level is z items with cost C (æ), then the cost of computing h additionial (C(z+h)-C(x)) . As we analyze the items is C ( + h). The average cost of those h items is cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (z). Problem Set question: The cost, in dollars, of producing a units of a certain item is given by C(z) = 0.02m3 – 10z + 450. (a) Find the marginal cost function. MC (x) - 固助 (b) Find the marginal cost when 50 units of item are produced. The marginal cost when 50 units are produced is $ Number (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ Number

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

After running a successful pineapple business, Diddy looks for a new business venture. Now he wants to run gold mining business named "Diddy Bling Bling" which produces/sells raw gold. For simplicity, two types of inputs are required to produce raw gold (workers and gold mine). In short- run production, the size of gold mine is fixed while the number or workers can vary. After consulting his business consultant, Diddy computes the following cost table. The quantity of raw gold (kilograms) Averaged Total Cost (gold mine size=small) Averaged Total Cost (gold mine size-medium) Averaged Total Cost (gold mine size-Large) 1 700 1400 1800 2 600 1300 1700 3 500 1200 1600 4 400 1100 1500 5 300 1000 1400 6 400 900 1300 7 500 800 1200 8 610 600 1100 9 700 500 1000 10 800 400 900 11 900 375 800 12 1100 250 700 13 1200 400 600 14 1300 490 500 15 1400 600 400 16 1500 700 350 17 1600 800 300 18 1700 900 350 19 1800 1000 400 20 1900 1100 500 21 2000 1200 600 22 2100 1300 700 Draw Diddy Bling Bling's…
Ten-year old Sarah is starting a lemonade stand, she uses baskets of lemons (L) and other ingredients (O). She is able to produce lemonade according to the production function f(L, O) = 1 2 L 2O. The cost of a basket of lemons is $10 and the average cost of the other goods is $4. (a) Derive MPL and MPO. (b) Currently Sarah is using 4 baskets of lemons and 40 units of the other goods. Using this information, calculate MPL and MPO. (c) True/False. At her current use of inputs Sarah is minimizing costs. If true, explain why. If false, what would you recommend Sarah do? (d) Sarah wants to produce 320 units of lemonade. Determine the cost minimizing combination of inputs to use. (e) Assuming no changes in the market price of lemonade nor in the prices of the inputs, if Sarah continues to produce 320 units of lemonade in the long run, what will Sarah’s long run costs be.
Craig and Javad run a paper company. Each week they need to produce 1,000 reams of paper to ship to their customers. The paper plant's longrun production function is Q = 4KL, where Q is the number of reams produced, K is the quantity of capital rented, and L is the quantity of labor hired. The weekly cost function for the paper plant is C = 20K + 4L, where C is the total weekly cost. (a) What ratio of capital to labor minimizes Craig and Javad's total costs? (b) How much capital and labor will Craig and Javad need to rent and hire in order to produce 1,000 reams of paper each week? (c) How much will hiring these inputs cost them?
Suppose you run a factory whose short-run production function is given by f (L) = 180L² – 3L³. (a) Find mathematical expressions for the total product of labor, the average product of labor and the marginal product of labor. (b) On two separate axes, graph TPL, APL, and M PL. The diagrams do not need to be scale, but be sure they are internally consistent. In other words, make sure that all relevant relationships between the three lines are correct. If you have trouble figuring out what the graph looks like, feel free to use a graphing calculator or an online graphing tool to find the basic shape. Find the quantity of labor associated with each of the following points and label it on your diagram: (i) the maximum value of TPL, (ii) the maximum value of APL, (iii) the maximum value of MPL. (c) For what values of L does the production function exhibit each of the following: i. increasing marginal labor productivity ii. diminishing marginal labor productivity iii. negative marginal labor…
Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q=F(L,K) Q=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $ b. What is their long-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $
Consider an airline's decision about whether to cancel a particular flight that hasn't sold out. The following table provides data on the total cost of operating a 100-seat plane for various numbers of passengers. Total Cost Number of Passengers (Dollars per flight) 40,000 10 60,000 20 65,000 30 68,000 40 70,000 50 71,000 60 72,500 70 73,500 80 74,000 90 74,300 100 74,500 Given the information presented in the previous table, the fixed cost to operate this flight is s At each ticket price, a different number of consumers will be willing to purchase tickets for this flight. Assume that the price of a flight is fixed for the duration of ticket sales. Use the previous table as well as the following demand schedule to complete the questions that follow. Price Quantity Demanded (Dollars per ticket) (Tickets per flight) 1,000 700 30 400 90 200 100
Label each of the following as sunk cost, opportunity cost, or incremental costs and briefly explain why: (Chapter 2) You are deciding which car to buy. Car A is $24,000 and car B is $32,000. The difference in price is $8,000. What kind of cost does this represent? Answer: Your company invested $300,000 into a study to determine the feasibility of introducing a new product line into the business. The study recommended 2 mutually exclusive feasible alternatives. What kind of cost does the $300K represent? Answer: You have 2 alternatives for a $10,000 investment. Investment A provides a $500 return and investment B provides a $700 return. If you choose Alternative B, what does the $500 return from Alternative A represent? Answer:
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?
Calculate a cost function from a production function and explain how economic costs differ from accounting costs.
A firm produces plastic bins using labor (measured in man-hours) and capital (measured in machine-hours), according to the production function Q = f(L,K) = LK, where Q is the number of plastic bins produced. Suppose that the cost of labor is $20 per worker-hour and the cost of capital is $10 per machine-hour. What is the cost minimizing input combination if the firm wants to produce 28,800 plastic bins? Hint: The marginal products are MP, = K and MPg = L.
***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches 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?…
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether β is larger than, smaller than, or equal to one?