EBK MICROECONOMICS
2nd Edition
ISBN: 9780100254138
Author: BERNHEIM
Publisher: YUZU
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Chapter 3, Problem 1CP
To determine
Calculate the marginal benefit and marginal cost when H is equal to 4.
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Assume that it costs a company approximately
C(x) = 400,000 + 160x + 0.003x²
dollars to manufacture x smartphones in an hour.
(a) Find the marginal cost function.
Use it to estimate how fast the cost is increasing when x = 10,000.
$
per smartphone
Compare this with the exact cost of producing the 10,001st smartphone.
The cost is increasing at a rate of $
(b) Find the average cost function C and the average cost to produce the first 10,000 smartphones.
C(x)
(10,000)
=
=
per smartphone. The exact cost of producing the 10,001st smartphone is $
$
(c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones.
The marginal cost from (a) is ---Select--- than the average cost from (b). This means that the average cost is ---Select---
Thus, there is a difference of $
at a production level of 10,000 smartphones.
Production function of a company is given by f(x;y)= root of x + root of y where x is labor and y is capital. Cost of labor is 2 currency units, while the cost of capital is 1 currency unit. What are the minimal cost to produce 10 units of the product? What is the change in the costs, if the production volume would increase by 50 %?
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- Assume that it costs a company approximately C(x) = 400,000 + 180x + 0.001x² dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. Use it to estimate how fast the cost is increasing when x = 10,000. $ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) C(10,000) $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. The marginal cost from (a) is ---Select--- O than the average cost from (b). This means that the average cost is ---Select--- O at a production level of 10,000 smartphones.arrow_forwardK Drilling of an oil well has a fixed cost of $40,000 and a marginal cost of M'(x) = 5000+56x dollars per foot, where x is the depth in feet. Find the expression for M(x), the total cost of drilling x feet. [Note M(0) = 40,000] M(x)=arrow_forwardMake sure you write out all your work with all the steps. Don't type it.arrow_forward
- The function C(x)=−24x+1936 represents the cost to produce x items. What is the least number of items that can be produced so that the average cost is no more than $20?arrow_forwardWhen a firm produces 600 widgets with total cost of $1,300 and fixed cost of $800, what is the average variable cost?arrow_forwardCost, revenue, and profit are in dollars and x is the number of units.If the daily marginal cost for a product is MC = 4x + 150, with fixed costs amounting to $600, find the total cost function for each day. C(x) =arrow_forward
- The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 150 + 2,600x – 0.06x2. (a) Find the marginal cost function C'(x). C'(x) = (b) Use the marginal cost to approximate the cost to air the 5th commercial. Convert your answer to dollars. The cost to air the 5th commercial is approximately X dollars. (c) What is the exact cost to air the 5th commercial? Convert your answer to dollars. The exact cost to air the 5th commercial is x dollars.arrow_forward1. For each of the cost functions given below, do the following things: C(T) = = 10 + 2T. C(T) = T0.8 (a) Draw the graph for C(T), with T on the horizontal axis. Explicitly the values for the intercepts. (b) Derive AC and MC respectively, and draw their curves. (c) Determine whether the cost function exhibits IRTS or DRTS or CRTS.arrow_forwardhow to calculate total cost analysisarrow_forward
- Suppose that a company has determined that a 70% experience curve accurately describes the evolution of its production costs for a new line. If the first unit costs $200 to produce, what should the 1,000th unit cost based on the experience curve?arrow_forward$150 125 100 75 50 Cost per Unit 25 0 5 e 15 25 30 MC ATC AVC Units per day Use the graph above to answer the following question: What is the total cost of producing 15 units? Note: enter answer with only numerical values and round up to the nearest tenth. For example, if you think the answer is "$101.58" then enter the answer "101.6" in the space below.arrow_forwardAs a producer and seller of some commodity, you have learned that, if you produce and sell x itmes in a particular month, the following functions can be used to find the cost and revenue: Revenue: R(x)=150x-x^2 and Cost: C(x)=3000+20x. (a) Write a simplified formula for your profit in a particular month, P(x)=R(x)- C(x) (b) Find the "break-even" point(s) (c) How many items should you produce and sell in a month in order to achieve a maximum profit? (d) What is the maximum possible monthly profit? This is the problem and I cannot solve the c and d, could you please help me?arrow_forward
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