To determine the profit maximizing point the firm has to consider the demand. We assume a linear inverse demand function of the form
P = a – b. Q
where ‘a’ and ‘b’ are arbitrary positive constants (a > b).
Then Total Revenue
(TR) = P. Q = aQ – bQ2 (1)
Therefore,
Total Profit = Total Revenue – Total Cost = aQ – bQ2 – (285 + 7.
8Q)
Now, the profit maximizing point is characterized by the equality of marginal revenue and marginal cost (MR = MC). Since
TR = aQ – bQ2, MR = d(TR)/dQ = a – 2bQ
Again since
TC = 285 + 7. 8Q, MC = d(TC)/dQ = 7.8
Therefore, the profit maximizing condition becomes
a – 2bQ = 7.8
solving which we get the profit maximizing output as
Q = (7. 8 – a) / 2b
Putting this in the demand function we obtain the profit maximizing price as
P = a – b (7. 8 – a)/2b
Thus, the profit maximizing point
(P,Q) is {a – b (7. 8 – a)/2b, (7. 8 – a) / 2b}
The shape of the total profit curve is determined by the total revenue curve and the total cost curves since total profit is in essence the difference between these two.
Profits are zero or negative at zero output since there are no revenues while the firm may have to bear fixed costs ($285 per day in the present context). Then as output rises, revenue outstrips costs per unit and profit starts to rise and reaches a maximum. After this point the gap between revenue and costs declines and total profits begin to fall. In the present case, the total profit curve reaches its maximum for
Q = (7.8 – a) / 2b
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