DOC 11 - California State University, Northridge



11.a. Profit-Maximization by a Monopolist

A monopoly is a firm that is the exclusive seller of a product with which there are no close substitutes. The monopoly retains this control because it is not possible for other firms to enter into that particular market; therefore, eliminating competition over the selling of that product. This concept is known as barriers to entry.

The fundamental difference between a competitive firm and a monopolistic firm is the monopoly’s influence over the price of its product or output. This arises because a competitive firm is too small in relation to its market in which it operates to have any control over the price of its output. However, a monopoly does not face this dilemma because it is the only producer in its market so it adjusts the price of its output by simply changing the quantity it supplies. This illustrates the characteristic of a monopolistic firm as a price maker. Since monopolies are the only producer in its market and are price makers they face a downward sloping market demand curve and thus must sell at a lower price in order to sell more output.

Like a competitive firm, a monopoly operates at maximum profit where its marginal revenue equals its marginal cost. However, its marginal revenue curve is no longer equal to its demand curve because the downward sloping quality of its demand curve causes the monopoly to lower its prices in order to increase the quantity, resulting in less revenue per extra unit of output. Therefore, in order to find the price a monopoly charges you must determine the profit-maximizing quantity where its marginal revenue equals its marginal cost and then go up to its demand curve at that quantity.

Below are two examples that provide first a conceptual understanding then second a numerical explanation of a monopoly’s profit-maximization.

Example #1:

Imagine there is some sort of monopoly over a product of software, like Microsoft. In columns 1 and 2 of Table 11.a.1 we can see the demand schedule for this particular monopoly. From this you can see that as the quantity increases the price decreases, representing the downward sloping demand curve characteristic of monopolies. The third column computes the firm’s total revenue which calculates the quantity sold (column 1) times the price (column 2). By looking solely at this column we would conclude this firm should produce at a quantity of 3 or 4. However, we can take it one step further by computing the firm’s profit by subtracting the firm’s total cost (column 4) from its total revenue (column 3) at each quantity. This column indicates that at 4 units the firm will experience a loss in profit even though it appeared the firm was earning its highest revenue at 4 units.

|Table 11.a.1 |

Quantity |Price |Total Revenue

(P x Q) |Total Cost |Profit

(TR - TC) |Average Total Cost

(TC / Q) |Marginal Cost |Marginal Revenue | |0 |$7 |$0 |$3 |$-3 |$∞ | | | |1 |6 |6 |5 |1 |5 | | | |2 |5 |10 |8 |2 |4 | | | |3 |4 |12 |12 |0 |4 | | | |4 |3 |12 |17 |-5 |4.25 | | | |5 |2 |10 |23 |-13 |4.6 | | | |6 |1 |6 |30 |-24 |5 | | | |As a result, you must use the firm’s marginal cost and marginal revenue to accurately calculate its profit maximization. Marginal cost can be computed by calculating the increase in the total cost (column 4) from an additional unit of output (column 1) produced. Similarly, marginal revenue can be computed by calculating the change in total revenue (column 3) from an additional unit of output (column 1) sold. Once those values have been computed you can compare the firm’s marginal cost and marginal revenue values to determine the actual profit maximization. From the table it is evident that the firm’s marginal cost is less than its marginal revenue up until the second unit is sold. However, if the firm were to produce the third unit it would cost the firm $4 while that third unit only brought in $2 of additional revenue. Therefore, from the table we can conclude that this monopolistic firm’s profit-maximizing quantity is about 2 units and its profit-maximizing price is about $5.

Once, you have a firm understanding of how the numbers in Table 11.a.1 are computed the next step is to transfer the numbers onto a graph in Figure 11.a.1. In this figure it is evident that this firm’s profit–maximizing quantity is about 2, while its profit-maximizing price is about $5 which is what consumers will be willing to pay for 2 units. In order to calculate the profit received by this firm we need to calculate the firm’s average total cost at every quantity by dividing the firm’s total cost by quantity. This is illustrated in the column 6 of Table 11.a.1. Since we already know the profit-maximizing quantity is about 2 we just look at the average total cost value at the quantity of 2 in the table which is $4. Now that we have all of these values we just need to plug it into the total profit equation (P –ATC) x Q which equals a total profit of $2 ((5-4) x 2). This total profit of $2 is illustrated by the purple rectangle in Figure 11.a.1.

Example #2:

Given the equations…

Demand (D): P=50-Q and

Total Cost (TC): P=80+20Q+[pic]

Find the profit-maximizing quantity and price as well as the total profit of this monopolistic firm. Illustrate in graphs…

(In order to calculate the profit maximizing quantity of a monopoly you need to find the quantity in which the firm’s marginal cost equals its marginal revenue. In order to calculate the firm’s marginal revenue equation you need to calculate the firm’s total revenue equation and then take the derivative of the firm’s total revenue to give you its marginal revenue. To find the marginal cost equation you just take the derivative of its total cost equation…

TR = P x Q = (50-Q)Q = 50Q - [pic] MR = 50 – 2Q

MC=dTC/dQ=20+Q

(Now we can set the firm’s marginal cost equal to its marginal revenue so that we can calculate its profit-maximizing quantity…

MC = MR

20 + Q = 50 – 2Q

3Q = 30

[pic]= 10

(Next, you need to plug Q = 10 into the Demand equation in order to calculate the profit-maximizing price of the monopoly…

D: P = 50 – 10

[pic] = 40

( Once you have calculated the profit maximizing quantity and price of the monopoly you need to calculate the equation for the average total cost curve in order to compute total profit of the monopolistic firm. The average total cost curve is computed by dividing the total cost equation by quantity. Once the firm’s average total cost curve is calculated you need to plug Q = 10 into this equation in order to calculate the firm’s price on the average total cost curve at the profit-maximizing quantity…

ATC: P = [pic] = [pic] + 20 + [pic]

P = [pic] + 20 + [pic] = 33

(Now that these values have all been calculated you can determine the total profit of this monopolistic firm one of two ways. First, you can compute the total profit by subtracting the firm’s total cost from its total revenue. Second, you can manipulate the total profit equation (TR – TC) in terms of price, quantity, and average total cost and then solve for total profit...

Total Profit = TR – TC Total Profit = TR – TC

= (50Q –[pic]) – (80 + 20Q +[pic]) = ([pic] – [pic]) x Q = ([pic] – ATC) x Q

= (50(10) – [pic]) – (80 + 20(10) +[pic]) = (P – ATC) x Q

= 400 – 330 = (40 – 33) x 10

= 70 = 70

(Look at Figure 11.a.2 and Figure 11.a.3 to see how all of the calculations above can be illustrated in graphs.

Study Questions:

1. Why is a monopoly’s demand curve downward sloping and what affect does this have on its profit-maximization price and quantity?

2. What should a monopoly do if its price equals its average total cost?

a. Increase output

b. Lower its price

c. Nothing, it is making zero profits

d. Decrease output

e. Raise its price

f. It is not a monopoly

3. What should a monopoly do if its price equals its marginal cost?

a. Increase output

b. Lower its price

c. It is making zero profits

d. Decrease output

e. Raise its price

f. It is not a monopoly

4. What is characteristic of a monopoly’s marginal revenue curve?

a. It is the same as its demand curve

b. It decreases as quantity sold increases

c. It is a horizontal line

d. It increases as quantity sold decreases

Answers:

1. Since monopolies are the only producer in its market they are able to adjust their own prices. However, given that they are the only firm in the market they face the market demand curve where they have to lower prices if they want to increase output. This decrease in price from an increase in quantity illustrates the characteristic of a downward sloping demand curve. Since monopolies face a downward sloping demand curve their marginal revenue no longer equals their demand because the price of the output is decreasing as more output is produced and therefore less revenue is made per extra unit of output. To find its profit-maximization you need to go where its marginal revenue curve equals its marginal cost curve to find the quantity and then up to its demand at that quantity to find the price. Since the marginal revenue curve no longer equals its demand curve the price always ends up being above the firm’s marginal cost curve in a monopoly, rather than equal to its marginal cost curve like a competitive firm.

2. C. Nothing, it is making zero profits

3. F. It is not a monopoly

4. A. It decreases as quantity sold increases

-----------------------

> $2

> 3

> 4

> 5

> 6

> 7

> $6

> 4

> 2

> 0

> -2

> -4

*Black numbers indicate given values, while red numbers indicate calculated values.

[pic]

In Figure 11.a.2 the purple triangle represents the total profit = 70 calculated above. From the graph we can see how the equation (P – ATC) x Q is used. The yellow area represents the total cost = 330 calculated above and the two areas put together equal the total revenue (330 + 70 = 400). If you compare the two figures you can see that the yellow rectangle in Figure 11.a.2 is represented in Figure 11.a.3 by the point on the total cost curve where it has a quantity of 10. Also, in Figure 11.a.3 you can see what total revenue equals by looking at the point on the total revenue curve where is has a quantity of 10. This value is represented by the purple and yellow areas combined. Therefore, the purple area (total profit = 70) in Figure 11.a.2 can also be represented by the red line between the total cost and total revenue curves in Figure 11.a.3. Another interesting piece of information we can take away from Figure 11.a.3 is a proof of why a firm maximizes profits where its marginal cost equals it marginal revenue. This figu)*+-56f w “

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ŠhßkhV5?CJOJQJaJhh&Ûre indicates that the slopes of the total cost and total revenue (the blue lines) curves are equal. Another name for these curves is the marginal cost and marginal revenue because the slope of the total cost is the marginal cost while the slope of the total revenue curve is the marginal revenue. Since these lines’ slopes equal at the profit-maximizing output we can conclude that a monopolistic firm operates at maximum profit where its marginal revenue equals its marginal cost, which we achieved in Figure 11.a.2.

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