Price AverageMarginal Cost 225 200 175 150 ATC 100 MCAVC 75

($) Price, Average/Marginal Cost 225 200 175 150 ATC 100 MC-AVC 75 50 25 MR 0 20 40 60 80100 120 140 160 180 Quantity (units per month) SETTINGS Reset PROFIT CALCULATIONS Market Price (Pmks) $125.00 $50.00 $95.00 $7,500.00 $8,100.00 ($600.00) Cost Structure Low Cost High Cost Marginal Revenue (MR) Marginal Cost (MC) Quantity Revenue 120 Costs Quantity 60 Profit

Solution

The equation for demand curve is --> (Q/160) + (P/200) = 1, where Q denotes x-axis and P denotes y-axis.

Reducing it, we get --> 5Q + 4P = 800

Rearranging it, we get --> P = 200 - (5/4)Q

Now, the equation for MR is --> (Q/80) + (P/200) = 1

Reducing it, we get --> 5Q + 2P = 400

Rearranging it, we get --> P = 200 - (5/2)Q

Also, the equation for MC is --> P = 95

a) Now, for profit maximization in natural monopoly, MR = MC

Thus, we set MR = MC and solve for Q*

200 - (5/2)Q* = 95

Q* = 42

Thus, answer is 42 units

b) For maximum profit, we have to put the quantity found above in the demand equation

P* = 200 - (5/4)Q* = 200 - (5/4)(42)

P* = 147.5

Now, for the same Quantity of 42 units, we have to locate intercept on y-axis for ATC graph.

The intercept on y-axis for Q* = 42 units is P1 = 150

Therefore, now to calculate the profit made or minimum loss occurred, we have to subtract the area of graph under ATC with intercepts as x1 = 42 and y1 = 150 from area of graph under Demand curve with intercepts as x2 = 42 and y2 = 147.5

Therefore, profit or loss = (x2)(y2) - (x1)(y1) = (42)(147.5) - (42)(150) = - 105

Thus, negative sign indicates that loss is made and thus, it is minimum loss that can be obtained at that optimum quantity.

Thus, minimum loss i.e. answer is $ 105 (Note - if it doesn\'t accept answer then please try again by putting negative sign)

c) The demand equation is P = 200 - (5/4)Q

Multiplying it by Q on both side will yield Revenue, thus, --> Revenue = PQ = 200Q - (5/4)Q*Q

Now, differentiating this equation for getting marginal demand equation --> MR = 200 - (5/2)Q

This, is same as the earlier equation we calculated and we were only reverifying it.

For, Quantity = 42 units, MR = MC

Therefore, MR = 95

Thus, answer is $ 95

d) The marginal cost is same irrespective of change in quantity as clearly evident from graph.

Thus, MC = 95

Thus, answer is $ 95

e) For profit maximizing price, we have to put the Q = 42 units in the demand equation

P* = 200 - (5/4)Q* = 200 - (5/4)(42)

P* = 147.5

Thus, answer is $ 147.5