2. What is the relationship between the total cost curve, and the average cost per unit? Explain their relationship, and draw a diagram showing how the two are related. The total cost of production, in thousands of dollars, is C(q) = q³ - 12q² + 60q, where q is in thousands and 0 ≤ q ≤ 8. (a) Graph C(q). Estimate visually the quantity at which average cost is minimized. (b) Determine analytically the exact value of q at which average cost is minimized.

2. What is the relationship between the total cost curve, and the average cost per unit? Explain their relationship, and draw a diagram showing how the two are related. The total cost of production, in thousands of dollars, is C(q) = q³ - 12q² + 60q, where q is in thousands and 0 ≤ q ≤ 8. (a) Graph C(q). Estimate visually the quantity at which average cost is minimized. (b) Determine analytically the exact value of q at which average cost is minimized.

Essentials of Economics (MindTap Course List)

8th Edition

ISBN:9781337091992

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter12: The Cost Of Production

Section: Chapter Questions

Problem 4CQQ

See similar textbooks

Similar questions

Which costs are measured on per-unit basis: fixed costs, average cost, avenge variable cost, variable costs, and marginal cost?
What shapes would you generally expect each of the following cost curves to have: fixed costs, variable costs, marginal costs, average total costs, and average variable costs?
What are explicit and implicit costs?
Cost (thousands of $) The graph shown on the right represents the cost C (in thousands of dollars) of refining x gallons of gasoline per hour (in thousands). The vertical axis represents the cost, and the horizontal axis represents the number of gallons of gasoline refined. Cost of refining gasoline per hour 1000- 800- 600- 400- Answer the following questions below in parts (a) through (d). 200 O 100 200 300 400 500 600 700 800 Number of Gallorns (thousands) (a) What is the cost of refining 200 thousand gallons of gasoline per hour? thousand
C(x) = 0.01x-0.3x + 10x gives the cost, in thousands of dollars, to produce x thousand items. (a) Find a formula for the marginal cost. (b) Find C'(0). Give units. (c) Graph the marginal cost function. Use your graph to find the minimum marginal cost, the production level for which the marginal cost is the smallest. (d) For what value of x does the marginal cost return to C'(0)? (a) Find a formula for the marginal cost. c'(x) =D (b) Find C'(0). Give units. c'(0) = (c) Use the derivative of the marginal cost function to find the minimum marginal cost, the production level for which the marginal cost is the smallest. The minimum marginal cost of additional dollars per item produced occurs when thousand items are produced. d) Recall your answer to part b. For what value of x does the marginal cost return to C'(0)? Marginal cost returns to this value of C (x) when x = items are produced.
1. The cost of producing 5 gallon water bottles is given by C(q) = 0.005q2 + 2q + 1000. If 2000 5 gallon water bottles are produced find the: (a) total cost (b) average cost (c) marginal cost (d) marginal average cost
The total cost (in dollars) of producing x food processors is C(x) = 1600 + 40x-0.1x². (A) Find the exact cost of producing the 61st food processor. (B) Use the marginal cost to approximate the cost of producing the 61st food processor. CHEO (A) The exact cost of producing the 61st food processor is $ (B) Using the marginal cost, the approximate cost of producing the 61st food processor is $
It costs a baker a fixed cost of $420 and variable cost of $2.10 per cupcake. A cupcake issold for $4.90 each.(i) Make a table showing the total cost and the revenue obtained from producing 20,40,60,80 and 100 cupcakes.(ii) Write algebraic expressions representing the cost C and the revenue R as functions of the number of cupcakes X produced and number of cupcakes X sold respectively.(iii) Graph both functions on the same coordinate axes and from your graph determine the cordinate at which cost equals revenue.
A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?
Please I need help on the math question I don't ge it Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.005x3+0.07x2+15x+600, and currently 35 chairs are produced monthly. a) What is the current monthly cost? b) What is the marginal cost when x=35? c) Use the result from part (b) to estimate the monthly cost of increasing production to 37 chairs per month. d) What would be the actual additional monthly cost of increasing production to 37 chairs monthly?
4. The minimum value for average costs is$19which occurs atQ=1and the vertical intercept is$20. (a) Find the average cost equation. (b) Graph. (c) Find the level of average costs when 10 units of output are produced.
(a) Find the marginal cost function C'(x). C'(x) Use it to estimate how fast the cost is increasing when x = 60,000. | per game system Compare this with the exact cost of producing the 60,001st game system. The cost is increasing at the rate of $ | game system is $| the estimated cost of producing the 60,001st game system found using the marginal cost function. | per game system. The exact cost of producing the 60,001st J. The actual cost of producing the 60,001st game system is --Select-- (b) Find the average cost function C(x) and the average cost to produce the first 60,000 game systems. (Round your answer to the nearest cent.) C(x) C(60,000) - $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 60,000 game systems.