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Determining Cost Estimating Function

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A product plant is being considered for a new booming market. Total fixed cost for design, land, and plant construction is $105. The variable cost of producing product is a function C (n) = 100n - 3 x 10-3 n2 + 10-7 n3 where n = number of product produced.

(a) Determine the total cost function C (T). (Hint: It includes the cost of producing the product and fixed cost.)

(b) Find the marginal cost function Cm for producing the product.

(c) Find the number of product for minimum marginal cost. What is the marginal cost at this point? What is the average cost per unit at this level of production?

(d) Total revenue is given by S (n) = 250 n. Find the marginal price. Determine the functions for total profit, and marginal profit.

(e) Find the point to maximize profit.

(f) Graph these cost equations.

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Solution Summary

The solution determines a cost estimating function. The total cost function for producing the product and fixed costs are determined.

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TC Equation - Economics and Management

Please refer to attached word document for instructions.

1)
A monopoly firm in a small island country produces and supplies to the country. It faces a market demand curve for its products. The demand equation is linear, so is the firm's total cost (TC) function. The following table exhibits the data for Quantity, Price, and TC.

(1) (1) Estimate the demand equation.
[Show the estimated equation.]
(2) (2) Estimate the TC function.
[Show the estimated TC equation.]
(3) (3) What is the profit-maximizing quantity?
[Profit-max quantity is determined at the level where MC = MR. Hence, Derive MC function from the estimated TC function. Derive MR from TR function which is PQ, where P = P(Q). In other words, P is the estimated demand equation expressed by Q. But, since the demand function is linear, the MR function is linear with a twice steeper slope than the demand equation and with the same intercept.]
(4) (4) What is the profit-maximizing price?
[Once the quantity is determined, find the corresponding price at the demand curve.]
(5) (5) What is the monopoly profit? [Profit = TR - TC.]

Q P TC
1 100 11
2 97 19
3 98 31
4 95 39
5 96 51
6 93 59
7 94 71
8 91 79
9 92 91
10 89 99
11 90 111
12 87 119
13 88 131
14 85 139
15 86 151
16 83 159
17 84 171
18 81 179
19 82 191
20 79 199
21 80 211
22 77 219
23 78 231
24 75 239
25 76 251

2)
A manufacturing firm operating in a perfectly-competitive market has the following cost function:
TC = a + b Q + c Q2 + d Q3
The TC data with respect to Q are provided in the table below.

(1) (1) Estimate the TC equation and show the estimated equation.
[a = round up to a whole number (no decimal), b = round up and no decimal, c = round up to the first decimal (one decimal), and d = round up to the first decimal (one decimal)]
(2) (2) What are the equations for AC and MC?
(3) (3) The market price is $637.5. What is the firm's profit-maximizing level of output?
(4) (4) Does the firm make profit or loss? Show either the profit or loss?
(5) (5) The market price changes. At which price will the firm shut down the operation?

TC Q
1780 1
2021 2
2238 3
2435 4
2626 5
2814 6
3013 7
3227 8
3472 9
3750 10
4074 11
4451 12
4893 13
5405 14
6001 15
6684 16
7468 17
8357 18
9366 19
10500 20
11770 21
13182 22
14749 23
16475 24
18375 25

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