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To answer this question On a single graph draw the marginal cost curve, the average total cost curve, and the average variable cost curve for a...

To answer this question
On a single graph draw the marginal cost curve, the average total cost curve, and the average variable cost curve for a typical firm. Then, on the same graph draw a horizontal straight line that is in the same relation to the average total and average variable costs as calculated in question 5. On the same graph show the area that represents the profit or loss this firm will earn. Finally, show the shutdown point on the graph
use this data:5. As the manager of a custom automobile refinishing company, Custom Refinishing and Paint Company. You are concerned with determining the profit maximizing level of output. You have commissioned a market survey which has yielded the information that your total revenue is given by the equation
TR = 43,324Q - 7.75Q2
you also have studied your production process and know that CRAPCO=s total cost curve is given by
TC = 5Q2 +10,500Q + 25,625,125
A. Is this a perfect or an imperfect competitor? How do you know? HINT: Use the data given--not the industry.
In case of perfect competition, each firm is a price taker and faces a perfectly elastic demand curve such that P = MR = AR.
Here, TR = 43,324Q - 7.75Q2
Thus, MR = dTR/dQ = 43,324 – 15.5Q
This MR schedule shows that the MR curve is downward sloping and not a horizontal line as in case of perfect competition. Thus, this industry is not characterized by perfect competition. This is a case of imperfect competition.
The cost curves are same in case of both perfect and imperfect competition. So, the cost curves are not analyzed to arrive at this conclusion.




B. To the nearest whole automobile, at what quantity will profits be maximized? Remember that the profit maximizing quantity is found by equating at marginal revenue and marginal cost. Use this quantity in all remaining calculations where Q is required for this question.
Profit is maximized at the point where MR = MC
MR = dTR/dQ = 43,324 – 15.5Q
Given, TC = 5Q2 +10,500Q + 25,625,125
Thus, MC = dTC/dQ = 10Q + 10500
Equating MC = MR
10Q + 10500 = 43,324 – 15.5Q
25.5Q = 32824
Or, Q = 1287.216
Thus, profits will be maximized at Q = 1287 units approx.




C. To the nearest penny, what will be the profit maximizing Price that will be paid?
Given TR = 43,324Q - 7.75Q2
TR = PQ
Factoring out Q from TR equation,
TR = (43,324 - 7.75Q) Q = PQ
Thus, P = 43,324 - 7.75Q
The profit maximizing quantity is Q = 1287
Hence, the profit maximizing Price is
P = 43,324 - 7.75Q = 43,324 - 7.75*1287 = 33349.75




D. What is the average total cost at the profit maximizing quantity?

Given, TC = 5Q2 +10,500Q + 25,625,125
Average total cost ATC = TC/Q = 5Q +10,500 + 25,625,125/Q
At the profit maximizing quantity Q = 1287,
ATC = [5*1287 +10,500 + 25,625,125/1287] = 6435+ 10500 + 19910.74 = 36845.74

E What is the average variable cost at the profit maximizing quantity?
Given, TC = 5Q2 +10,500Q + 25,625,125
Here, the fixed cost is 25,625,125.
The total variable cost TVC = 5Q2 +10,500Q
Hence, the average variable cost is TVC/Q = AVC = 5Q +10,500
At the profit maximizing quantity Q = 1287,
AVC = 5Q +10,500 = 6435+ 10500 = 16935



F. If costs and revenues are given by the equations above, what is the profit which will be earned at the profit maximizing level of output?
Profit = TR – TC
Given, TC = 5Q2 +10,500Q + 25,625,125
And TR = 43,324Q - 7.75Q2
The profit maximizing quantity Q = 1287
Now, TC = 5Q2 +10,500Q + 25,625,125 = 5(1287)2 +10,500(1287) + 25,625,125 = 8281845 + 13513500 +25,625,125 = 47420470
And TR = 43,324Q - 7.75Q2 = 43,324(1287) - 7.75(1287)2 = 55757988 – 12836860
= 42921128
Now, Profits = TR – TC = 42921128 – 47420470 = - 4499342
This shows that the firm is making losses and the losses are minimum at Q = 1287 units.
Loss incurred = - 4499342


G. What is the quantity of automobiles at which this firm will minimize its average total cost? What will be that total cost
Given, TC = 5Q2 +10,500Q + 25,625,125
Average total cost ATC = TC/Q = 5Q +10,500 + 25,625,125/Q
To find minimum ATC, differentiate ATC with respect to Q.
dATC/dQ = 5 - 25,625,125/Q2
Setting dATC/dQ = 5 - 25,625,125/Q2 = 0,
Or, 5Q2 = 25,625,125
Or, Q2 = 5125025
Or, Q = 2263.852
Thus, ATC is minimized at Q = 2263.852 units.
Minimum ATC = 5Q +10,500 + 25,625,125/Q
Substituting Q = 2263.852,
Minimum ATC = 5(2263.852) +10,500 + 25,625,125/2263.852
= 11319.26 + 10500 + 11319.26
=33138.52
Total cost (at Q = 2263.852) = 33138.52 * 2263.852 = 75020705



H. At what price would this company shut down rather than produce?

At P = minimum AC, the company will shut down rather than produce.
Thus, at P = min AC = 33138.52, the company will shut down.

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