# Determine optimal pricing policy

1. Using the data above, calculate the output the firm will provide.
2. Determine the price at this output level.
3. Complete the Microsoft Excel Template given below using the data in the problem.
4. Check whether your data is consistent with your calculations in question 1. Why or why not?
5. Now assume that the state decides to give as many contracts as it can for the same activity, so your firm is now operating in a perfectly competitive market. How will your price and output decisions change? Explain the differences and why these changes happened.
 Quantity Price MR MC TR TC Profit 0 1,00,000 1,50,000 2,00,000 2,50,000 3,00,000 3,50,000 4,00,000 4,50,000 5,00,000 5,50,000 6,00,000 6,50,000 7,00,000 7,50,000 8,00,000 8,50,000 9,00,000 9,50,000 10,00,000 10,50,000

Solution

The firm will provide output at a level where the profit-maximization happens. In a monopolistic situation, profit is maximized when marginal revenue (revenue generated from an additional unit of product sold) is equal to the marginal cost (cost of an additional unit of product manufactured).

Therefore, the output quantity for a monopoly firm is computed at the point where

MR=MC

Given that MR= 1400-0.0008Q

MC=derivative of TC wrt Q

TC = 1000Q since there is no fixed cost

MC = d (1000 Q)

dQ

= \$1000, is constant.

Now, since the output quantity for a monopoly firm is computed at the point where MR=MC

• 1400-0.0008Q = 1000
• 400 = 0.0008Q
• Q =500,000

Thus, the output that the firm will provide is 500,000 units.

The price at the output level of 500,000 units can be given by:

P = 1400 – 0.0004*Q  = 1400 – 0.0004 * 500000

= 1400 – 200 = 1200

Thus, the price at this output level is \$1200.

Table 1: Data from Excel Template

 Quantity Price MR MC TR TC Profit 0 1400 1400 1000 0 0 0 100,000 1360 1320 1000 136000000 100000000 36000000 150,000 1340 1280 1000 201000000 150000000 51000000 200,000 1320 1240 1000 264000000 200000000 64000000 250,000 1300 1200 1000 325000000 250000000 75000000 300,000 1280 1160 1000 384000000 300000000 84000000 350,000 1260 1120 1000 441000000 350000000 91000000 400,000 1240 1080 1000 496000000 400000000 96000000 450,000 1220 1040 1000 549000000 450000000 99000000 500,000 1200 1000 1000 600000000 500000000 100000000 550,000 1180 960 1000 649000000 550000000 99000000 600,000 1160 920 1000 696000000 600000000 96000000 650,000 1140 880 1000 741000000 650000000 91000000 700,000 1120 840 1000 784000000 700000000 84000000 750,000 1100 800 1000 825000000 750000000 75000000 800,000 1080 760 1000 864000000 800000000 64000000 850,000 1060 720 1000 901000000 850000000 51000000 900,000 1040 680 1000 936000000 900000000 36000000 950,000 1020 640 1000 969000000 950000000 19000000 1,000,000 1000 600 1000 1000000000 1000000000 0 1,050,000 980 560 1000 1029000000 1050000000 -21000000

From the calculations, we see that in monopolistic situation, the profit maximizing point s where MR = MC. That is, when the additional cost of producing a unit of product is equal to the additional revenue generated by the sale of a unit of product. The price point for MR=MC is \$1200 (refer Answer 2) and the output level is: 500,000 (refer Answer 1). The data in the above table (Answer 3) also shows that the profits of the company are highest (\$100,000,000) at the price point of \$1200 and at output level of 500,000. This is also the point where the MR=MC at \$1000 each.

Profit-maximization in monopoly happens at 500,000 level of output where Marginal revenue is equal to marginal cost and the price is 1200. Thus, the economic profit (yellow-shaded portion in graph) exists. But in perfectly competitive market, the equilibrium output is at the point where price is equal to marginal cost i.e. at \$1000 and thus, the equilibrium output is 1,000,000. And thus, the companies in perfectly competitive market do not enjoy super normal profits but only normal profits.

In monopoly, the price is higher than the average cost as seen in the graph. The price is \$1200 while the average cost is \$1000. However, in perfectly competitive market, price is equal to marginal cost and thus, both the price and average cost are at \$1000 as shown in the graph. In case of a perfectly competitive market, the price is determined by the industry with large number of firms operating in the industry. A firm has no control over the pricing and it has to accept that price. However, under monopoly, monopolist firm decides the price. In a perfectly competitive market, average revenue (AR) is equal to marginal revenue (MR), whereas under monopoly, average revenue(AR) can be higher than the marginal revenue (MR). This results in the change in Price and output decisions.

 Quantity Price MR MC TR TC Profit 0 1400 1400 1000 0 0 0 1,00,000 1360 1320 1000 136000000 100000000 36000000 1,50,000 1340 1280 1000 201000000 150000000 51000000 2,00,000 1320 1240 1000 264000000 200000000 64000000 2,50,000 1300 1200 1000 325000000 250000000 75000000 3,00,000 1280 1160 1000 384000000 300000000 84000000 3,50,000 1260 1120 1000 441000000 350000000 91000000 4,00,000 1240 1080 1000 496000000 400000000 96000000 4,50,000 1220 1040 1000 549000000 450000000 99000000 5,00,000 1200 1000 1000 600000000 500000000 100000000 5,50,000 1180 960 1000 649000000 550000000 99000000 6,00,000 1160 920 1000 696000000 600000000 96000000 6,50,000 1140 880 1000 741000000 650000000 91000000 7,00,000 1120 840 1000 784000000 700000000 84000000 7,50,000 1100 800 1000 825000000 750000000 75000000 8,00,000 1080 760 1000 864000000 800000000 64000000 8,50,000 1060 720 1000 901000000 850000000 51000000 9,00,000 1040 680 1000 936000000 900000000 36000000 9,50,000 1020 640 1000 969000000 950000000 19000000 10,00,000 1000 600 1000 1000000000 1000000000 0 10,50,000 980 560 1000 1029000000 1050000000 -21000000 