Concept explainers
Problems 25–26 involve the average cost of manufacturing a quantity q of a good, which is defined to be
The average cost per item to produce q items is given by
- (a) What is the total cost, C(q), of producing q goods?
- (b) What is the minimum marginal cost? What is the practical interpretation of this result?
- (c) At what production level is the average cost a minimum? What is the lowest average cost?
- (d) Compute the marginal cost at q = 30. How does this relate to your answer to part (c)? Explain this relationship both analytically and in words.
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Calculus: Single And Multivariable
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus: Mathematics for Calculus (Standalone Book)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus & Its Applications (14th Edition)
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardWith fixed costs of Ksh. 400,000, a firm has average total costs of Ksh. 3,000 and average variable costs of Ksh. 2,500. Its output is?arrow_forwardIf, in a monopoly market, the demand function for a product is p = 150 – 0.20x and the revenue function is R = px, where x is the number of units sold and p is the price per unit, what price will maximize revenue?arrow_forward
- tion are given. (a) Sketch the first-quadrant portions of In Problems 1–4, a supply function and a demand func- market equilibrium point. (c) Algebraically determine the those functions on the same set of axes. (b) Label the market equilibrium point. (c) Algebraically determine the market equilibrium point. 1 q2 +10 1. Supply: p 4 Demand: p = 86 – 6q – 3g² 2. Supply: p = q² + 89 + 16 Demand: p = 216 - 29 3. Supply: p = 0.2q² + 0.4q + 1.8 Demand: p = 9 – 0.2q – 0.1q² 4. Supply: p q² + 8g + 22 %3D %3D %3D 1 198 4g 4 Demand: p %3D 5. If the supply function for a commodity is p = q? + 8q + 16 and the demand function is p = -3q2 + 6q + 436, find the equilibrium quantity and equilibrium price. 6. If the supply function for a commodity is p = q? + 8q + 20 and the demand function is p = 100 – 49 – q², find the equilibrium quantity and equilibrium price. 7. If the demand function for a commodity is given by the equation p? + 4q = 1600 and the supply function is given by the equation 300 – p² +…arrow_forward1. For the profit function P(x) = –x³ + (3x+2)², where x represents an amount invested in thousands of dollars, determine (a) The maximum profit and the value of x which achieves it, (b) The point of diminishing returns and the marginal profit at this point. Answers should be given to the nearest dollar.arrow_forwardSuppose that a cost–benefit function is given by f (x) = 50x105 - x, 0 … x … 100, where x is the percentage of some pollutant to be removed and f (x) is the associated cost (in millions of dollars). Find the cost to remove 70%, 95%, and 100% of the pollutant.arrow_forward
- Suppose that "q" is quantity of outputs produced, L is labour employed, and K is the capital invested. Say, for the function q = f (L, K), if L = 3 and K = 5 then q = 10. Question: Is it possible that L = 3 and K = 6 also yields q = 10 for this production function? Why or why not?arrow_forward2) A production function for a business follows the model P(L, K) = 0.1 L0.4K0.6 over the course of one year, where P represents the total value of all products the company makes, L represents the value of the labor from employees, and K represents the value of all the company's assets (buildings, machines, etc.), where everything is measured in millions of dollars. ap a. Find and ƏL ap ак' , and explain what they represent in this context. b. Evaluate the partial derivatives from part a when (L, K) = (3,4). If this was your business and your values, if you wanted to expand would it be better to expand in workforce (increase L) or expand in assets (increase K)?arrow_forwardA firm's short-run cost curve for any given level of capital K is C(K,Q) K+K-1/2Q2: Find the equation of the long-run average cost curve and sketch its graph. Explain why this curve is different from the curve traced out by the minimum points of the short- run average cost curves.arrow_forward
- 4. Salary (pesos) f 1001-2000 7 2001-3000 12 3001-4000 10 4001-5000 5001-6000 Compute the following: a. average weekly salary of the employees Solution: Salary (pesos) Xm fXm 1001-2000 2001-3000 12 3001-4000 10 4001-5000 5001-6000 5 N= 48 Efxm = _arrow_forward1. In economics, a Cobb-Douglas production function takes the form Y = AL³ Ka, where Y the output of goods produced by a company in a year, A is a variable capturing technological progress called Total Factor Productiv- ity, L captures the amount of labor going into production (measured in thousands of person-years), and K captures the amount of capital (e.g. machinery, raw material) going into production. Assume throughout this problem that a and 3 are both greater than or equal to zero. dy dt (a) Your company's production goals include making equal to .5. Suppose a and ß are fixed at 0.5 each, and furthermore right now dA dk dL you have L = K = A = 1 and = .1. What value of do dt dt dt you need to meet your company's production goals? (b) In words, what does the answer to the previous question mean? (c) Suppose the production function displays constant returns to scale, meaning that a +ß = 1. Suppose further that we have L = K = A = dA dK dy dL = 1. Which value of a will maximize dt…arrow_forwardIf the demand curve for a particularly commodity is p=-0.09×+51 and the titakcist function C(×)=1.32×+11.7×+101.4, where is the level of production. Find (a) The revenue R(×) and profit II(×). (b) All values of × for which production of the commodity is profitable.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning