The price-quantity combination that maximizes the firm’s total profit will be $210 and 30 units respectively.
The inverse market demand function = 300 - 3Q
The total revenue will be:
= (300 - 3Q) × Q
= 300Q - 3Q²
The marginal revenue will be:
= 300 - 6Q
The total cost is given as:
= 1500 + 2Q².
The marginal cost will be:
= 4Q
The equilibrium level of output will then be: MR = MC
300 - 6Q = 4Q
6Q + 4Q = 300
10Q = 300
Q = 300/10
Q = 30.
The quantity is 30 units.
The equilibrium price will then be:
P = 300 - 3Q
P = 300 - 3(30)
P = 300 - 90
P = 210
Therefore, the price is $210.
The maximum profit that the firm will earn will be:
Profit = Revenue - Cost
= (210 × 30) - [(1500 × (2 × 30²)]
= 6300 - (1500 + 1800)
= 6300 - 3300
= $3000
Therefore, the profit will be $3000.
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