The Ali Baba Co. is the only supplier of a particular type of Oriental carpet. T
ID: 1194618 • Letter: T
Question
The Ali Baba Co. is the only supplier of a particular type of Oriental carpet. The estimated demant for its carpets is
Q = 112,000 – 500P + 5M
Where Q = number of carpets, P = price of carpets (dollars per unit), and M = consumers’ income per capita. The estimated average variable cost function for Ali Baba’s carpets is
AVC = 200 – 0.012Q + 0.000002Q2
Consumer’s income per capita is expected to be $20,000 and total fixed cost is $100,0000.
a-d are answered but need help finding out how to get numbers
a.How many carpets should the firm produce in order to maximize profit?
b. What is the profit maximizing price of carpets?
c. What is the maximum amount of profit that the firm can earn selling carpets?
d. Answer parts a through c if consumers’ income per capita is expected to be $30,000 instead.
I need help figuring out how exactly where the following numbers came from 0.024Q, 0.000006Q(sq), 0.004 the square root of 0.005776, square root of 0.008176, 0.002 and 0.024 they are in the answer sheet provided, please explain
Explanation / Answer
The estimated demand equation is Q = 112,000 – 500P + 5(20,000) = 212,000 – 500P.
The inverse demand function is P = 424 – 0.002Q
The marginal revenue is MR = 424 – 0.004Q
The average variable cost is AVC = 200 – 0.012Q + 0.000002Q2
The marginal cost is SMC = 200 – 0.024Q + 0.000006Q2
a. How many carpets should the firm produce in order to maximize profit?
To maximize profit, marginal revenue is set to equal marginal cost.
MR = SMC = 424 – 0.004Q = 200 – 0.024Q + 0.000006Q2 = 224 + 0.020Q – 0.000006Q2
Solving for Q, it is equal to 4666.67 and –8000. Since there can be no negative output, the firm should produce 4667 carpets.
b. What is the profit-maximizing price of carpets?
The profit maximizing price P = 424 – 0.002Q, when Q = 4667, the price is $414.33.
c. What is the maximum amount of profit that the firm can earn selling carpets?
The maximum amount of profit the firm can earn selling carpets is:
(P * Q) – [(AVC * Q) + TFC] = (414.33 * 4667) – [(187.56 * 4667) + 100,000)] = $958,341.48
d. Answer parts a through c if consumer’s income per capita is expected to be $30,000 instead.
The estimated demand equation is Q = 112,000 – 500P + 5(30,000) = 262,000 – 500P.
The inverse demand function is P = 524 – 0.002Q
The marginal revenue is MR = 524 – 0.004Q
The average variable cost is AVC = 200 – 0.012Q + 0.000002Q2
The marginal cost is SMC = 200 – 0.024Q + 0.000006Q2
To maximize profit, marginal revenue is set to equal marginal cost.
MR = SMC = 524 – 0.004Q = 200 – 0.024Q + 0.000006Q2 = 1476 – 0.020Q + 0.000006Q2
Solving for Q, it is equal to 5833.33 and –9166.67. Since there can be no negative output, the firm should produce 5834 carpets.
The profit maximizing price P = 524 – 0.002Q, when Q = 5834, the price is $512.33.
The maximum amount of profit the firm can earn selling carpets is:
(P * Q) – [(AVC * Q) + TFC] = (512.33 * 5834) – [(198 * 5834) + 100,000)] = $1,733,801.22.
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