Profit maximizing

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.

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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