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QUESTION 5 (25 Marks) Rosebud Private Limited produces cooking oil and has many competitors producing close substitutes products
QUESTION 5 (25 Marks) Rosebud Private Limited produces cooking oil and has many competitors producing close substitutes products. The firm has the following revenue and cost functions. TR= 15Q-0.3Q2 TC = 8Q+0.02Q2 Where Q is output and price is in S: a. Identify the market structure the firm is operating in. Explain your choice. b. Determine the output that maximizes total revenue. c. Using marginal approach, determine the output and price that maximizes profit. (Hint: TR=P.2) d. Determine the profit loss of the firm. e. Based on approach in (c), illustrate using completely label diagram for situation that you obtain in (d). f. Is the firm operating in the short run or long run? Give your reason.
Expert Solution
TR = 15Q - 0.3*Q^2
TC = 8Q + 0.02Q^2
MR = 15 - 0.6Q
MC = 8 + 0.04Q
a) As MR is dependent on output level, firm must be operating in monopoly because perfectly competitive have constant MR.
b) To maximize total revenue, MR = 0
15 - 0.6Q = 0
Q = 25
At Q = 25, total revenue is maximized.
c) To maximize profit level, MR = MC
15 - 0.6Q = 8 + 0.04Q
7 = 0.64Q
Q = 10.93
At Q = 10.93, total profit is maximized.
P must be 15 - 0.3Q because TR = P * Q
At this Q level, P will be 15 - 0.3 * 10.93 = 11.721
d) At this output level, TR = 15 * 10.93 - 0.3 * 10.93^2 = 128.17
TC = 8 * 10.93 + 0.02 * 10.93^2 = 89.82
Profit = TR - TC = 38.34
e)
| Q | TR | MR | TC | MC | Profit |
| 2 | 28.8 | - | 16.1 | - | 12.7 |
| 4 | 55.2 | 26.4 | 32.3 | 16.2 | 22.9 |
| 6 | 79.2 | 24.0 | 48.7 | 16.4 | 30.5 |
| 8 | 100.8 | 21.6 | 65.3 | 16.6 | 35.5 |
| 10 | 120.0 | 19.2 | 82.0 | 16.7 | 38.0 |
| 12 | 136.8 | 16.8 | 98.9 | 16.9 | 37.9 |
| 14 | 151.2 | 14.4 | 115.9 | 17.0 | 35.3 |
f) This firm is operating in long run as TC is dependent on Q which changes as Q changes while some portion of TC must be fixed cost or independent of Q.
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