Monopolist Equilibrium With Zero Marginal Cost

A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity (this contrasts with a monopsony which relates to a single entity’s control of a market to purchase a good or service, and with oligopoly which consists of a few entities dominating an industry). Monopolies are thus characterized by a lack of economic competition to produce the good or service and a lack of viable substitute goods. The verb “monopolize” refers to the process by which a company gains the ability to raise prices or exclude competitors. In economics, a monopoly is a single seller. In law, a monopoly is business entity that has significant market power, that is, the power, to charge high prices. Although monopolies may be big businesses, size is not a characteristic of a monopoly. A small business may still have the power to raise prices in a small industry (or market).

CHARACTERISTICS OF MONOPOLY:

Profit Maximiser: Maximizes profits.

Price Maker: Decides the price of the good or product to be sold.

High Barriers to Entry: Other sellers are unable to enter the market of the monopoly.

Single seller: In a monopoly there is one seller of the good that produces all the output. Therefore, the whole market is being served by a single company, and for practical purposes, the company is the same as the industry.

Price Discrimination: A monopolist can change the price and quality of the product. He sells more quantities charging less price for the product in a very elastic market and sells less quantities charging high price in a less elastic market

NATURAL MONOPOLY

A natural monopoly is a company that experiences increasing returns to scale over the relevant range of output and relatively high fixed costs. A natural monopoly occurs where the average cost of production “declines throughout the relevant range of product demand”. The relevant range of product demand is where the average cost curve is below the demand curve. When this situation occurs, it is always cheaper for one large company to supply the market than multiple smaller companies; in fact, absent government intervention in such markets, will naturally evolve into a monopoly.

An early market entrant that takes advantage of the cost structure and can expand rapidly can exclude smaller companies from entering and can drive or buy out other companies. A natural monopoly suffers from the same inefficiencies as any other monopoly. Left to its own devices, a profit-seeking natural monopoly will produce where marginal revenue equals marginal costs. Regulation of natural monopolies is problematic. Fragmenting such monopolies is by definition inefficient. The most frequently used methods dealing with natural monopolies are government regulations and public ownership. Government regulation generally consists of regulatory commissions charged with the principal duty of setting prices. To reduce prices and increase output, regulators often use average cost pricing. By average cost pricing, the price and quantity are determined by the intersection of the average cost curve and the demand curve. This pricing scheme eliminates any positive economic profits since price equals average cost. Average-cost pricing is not perfect. Regulators must estimate average costs. Companies have a reduced incentive to lower costs. Regulation of this type has not been limited to natural monopolies. Average-cost pricing does also have some disadvantages. By setting price equal to the intersection of the demand curve and the average total cost curve, the firm’s output is allocatively inefficient as the price exceeds the marginal cost (which is the output quantity for a perfectly competitive and allocatively efficient market).

MARGINAL REVENUE

In microeconomics, marginal revenue (MR) is the additional revenue that will be generated by increasing product sales by 1 unit. It can also be described as the Unit Revenue the last item sold has generated for the firm. However, a Monopoly determines the entire industry’s sales. As a result, it will have to lower the price of all units sold to increase sales by 1 unit. Therefore the Marginal Revenue generated is always less (lower) than the price the firm is able to charge for the unit sold since each reduction in price causes unit revenue to decline on every good the firm sells. The Marginal Revenue (the increase in total revenue) is the price the firm gets on the additional unit sold, less the revenue lost by reducing the price on all other units that were sold prior to the decrease in price.

MR=TRn-TRn-1

File:Average and marginal revenue.svg

Typical marginal revenue MR and average revenue (price) curves for a firm that is not in perfect competition

TOTAL REVENUE:

Total revenue is the total receipts of a firm from the sale of any given quantity of a product.

It can be calculated as the selling price of the firm’s product times the quantity sold, i.e. total revenue = price Ã- quantity, or letting TR be the total revenue function:

TR(Q) = P(Q) times Q

Where, Q is the quantity of output sold, and P(Q) is the inverse demand function (the demand function solved out for price in terms of quantity demanded).

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A typical total revenue curve (linear, not perfectly elastic demand curve illustrated)

Relation between total revenue (TR), average revenue (AR) and marginal revenue(MR) is discussed with reference to different market situations.

Broadly, a producer may encounter either of the two situations:

(a) There is a large number of firms selling a product at a constant price. An individual firm is so small in the market that it cannot change price of the product. Or, it has no control over price of the product. Accordingly, to a firm, price is given of course, it can sell any amount of the product at a given price.

(b) A firm enjoys partial control over price through product differentiation or it has full control over price because it is a monopoly firm. Accordingly, a firm can plan to increase its sale by lowering its price.

The basic difference between the two situations is the following:

(a) When a firm has no control over price, it can sell any amount at a given price. Accordingly, firm’s demand curve (or AR curve) is a horizontal straight line as in Fig. 1.

(b) When a firm has partial or full control over price, it can sell more of a product only by lowering its price. Accordingly, its demand curve (or AR curve) slopes downward, showing a negative relationship between price and output as in Fig. 2.

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Fig. 1. shows that a firm (having no control over price) sells its product at the given price (= OP). It cannot change the price. Implying that it can sell whatever amount it wishes to sell at the given price.

Fig. 2. shows that a firm (having partial or full control over price) can sell more only if it lowers the price of the product.

Relationship between TR, AR and MR when firm’s demand curve slopes downward.

Note a fact:

When AR tends to decline corresponding to every next level of output, MR should be declining even faster. Reason: average value of a series (AR) will decline only when additional value (MR) declines faster than the average value. Take an illustration, as under:

Output

AR

TR

MR

1

10

10

10

2

9

18

8

3

8

24

6

4

7

28

4

5

6

30

2

6

5

30

0

7

4

28

-2

8

3

24

-4

We find that when AR is declining by 1 unit (corresponding to a unit increase in output), MR is declining by 2 units. Implying the fact that when AR declines, MR should be declining faster than AR. (Note: when AR curve is a straight line and slopes downward, the slope of MR curve should be twice the slope of AR curve. )

http://www.xamidea.in/concept_revenue/image012.gif

Fig.3 illustrates the relationship between TR, AR and MR when firm’s demand curve (AR curve) slopes downward.

OBSERVATIONS:

(i) When marginal revenue curve declines till point ‘M’ in part ‘B’, total revenue is increasing at diminishing rate as shown by the segment O to B in part ‘A’.

(ii) When marginal revenue becomes zero at point ‘M’ in part ‘B’, total revenue is at its maximum as shown by point ‘B’ in part ‘A’.

(iii) When marginal revenue falls, the average revenue also falls but lies above the marginal revenue curve. Implying that in a situation of falling price, MR falls even faster.

(iv) After point ‘M’, marginal revenue becomes negative. Now total revenue starts diminishing.

(v) A situation of zero AR obviously implies a situation of zero TR. (Zero price situation is not a general phenomenon, but, of course has examples as in government or charitable hospitals where medicines are given to the patients at zero price.)

WHEN ARE PROFITS MAXIMIZED?

Profit maximization normally occurs at the rate of output at which marginal revenue equals marginal cost.

In order to determine the profit maximizing level of output, the monopolist will need to supplement its information about market demand and prices with data on its costs of production for different levels of output. As an example of the costs that a monopolist might face, consider the data in Table 1 . The first two columns of Table1 represent the market demand schedule that the monopolist faces. As the price falls, the market’s demand for output increases. The third column reports the total revenue that the monopolist receives from each different level of output. The fourth column reports the monopolist’s marginal revenue that is just the change in total revenue per 1 unit change of output. The fifth column reports the monopolist’s total cost of providing 0 to 5 units of output. The sixth and seventh columns report the monopolist’s average total costs and marginal costs per unit of output. The eighth column reports the monopolist’s profits, which is the difference between total revenue and total cost at each level of output.

TABLE 1

Monopoly Output, Revenues, Costs, and Profits

Output

Price

Total revenue

Marginal revenue

Total cost

Average total cost

Marginal cost

Monopoly profits

0

$14

$0

–

$2

–

–

−2

1

12

12

$12

6

$6

$4

6

2

10

20

8

8

4

2

12

3

8

24

4

12

4

4

12

4

6

24

0

20

5

8

4

5

4

20

−4

35

7

15

−15

The monopolist will choose to produce 3 units of output because the marginal revenue that it receives from the third unit of output, $4, is equal to the marginal cost of producing the third unit of output, $4. The monopolist will earn $12 in profits from producing 3 units of output, the maximum possible.

Graphical illustration of monopoly profit maximization. Figure 1 illustrates the monopolist’s profit maximizing decision using the data given in Table 1 . Note that the market demand curve, which represents the price the monopolist can expect to receive at every level of output, lies above the marginal revenue curve.

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Figure 1

The monopolist’s profit-maximizing decision

The result of the monopolist’s price searching is a price of $8 per unit. This equilibrium price is determined by finding the profit maximizing level of output-where marginal revenue equals marginal cost (point c)-and then looking at the demand curve to find the price at which the profit maximizing level of output will be demanded.

MONOPOLIST EQUILIBRIUM WITH ZERO MARGINAL COST:

Under certain exceptional cases, the cost of additional units of output, i.e., marginal cost (MC) may be equal to zero. With constant value ‘zero’ of marginal cost, the value of average cost is also constant and is equal to zero. Its graph coincides with x- axis. With zero cost of production, the monopolist has only to decide at which output, the total revenue will be maximum. And total revenue is maximum at the output level at which marginal revenue is equal to zero. Further, with zero marginal cost, the condition of profit maximization, i.e., the equality of marginal cost (MC) and marginal revenue (MR) can be achieved, where the latter is also equal to zero.

Figure1 shows the equilibrium of the monopolist, where marginal cost is equal to zero. E is the point of monopolist equilibrium, where MC cuts MR from below. The equilibrium price and the equilibrium quantity at this equilibrium are OP and OE respectively. Here, total revenue and hence total profits (area OPBE) of the monopolist are maximum. Beyond OE level of output, MR becomes negative and total revenue starts declining. Elasticity of demand o the AR curve corresponding to zero marginal revenue is equal to one. Therefore zero cost of production, monopolist equilibrium will be established at a level, where elasticity of demand is unitary.

It is important to note that the monopolist will never produce the output at any level, where MR is negative. If he does so, his total revenue will fall as output increases. He can increase total revenue by reducing the output. In other words, monopolist can earn larger profits by restricting the output. Further since, MC cannot be negative, equality of MC and MR (equilibrium condition) cannot be achieved, where MR is negative.

We know from the relationship among AR, MR and elasticity of demand that when MR is negative, elasticity of demand is less than one. Therefore, no rational monopolist will produce on that portion of demand curve, where MR is negative, i.e., the elasticity of demand is less than one. That is why; no monopolist ever operates on the inelastic portion of the average revenue curve or the demand curve.

With the positive marginal costs, the monopolist fixes his level of output for which MR is also positive, i.e, TR rises with increase in the level of output.in other words, the equilibrium will always lie, where elasticity of demand is greater than one.

In figure 1, if the price is fixed at point B, where elasticity of demand is equal to one, the MC curve will pass through the MR curve at zero point. Here, both MC and MR are zero. It is rare possibility. Further, below the middle point B of the demand curve, elasticity of demand is less than one. If price is fixed in this inelastic portion of the demand curve, both the MC and the MR assume negative values, as the point of intersection between them is below point ‘E’ on the MR curve in figure 1. However MC can never be negative. Given positive costs, MC curve must cut the MR curve from below at a point, where both the MC and MR are positive. The equilibrium in this case will be established at a point above “E” on the MR curve in the figure and the price will be fixed in the elastic portion of the demand curve, i.e, above the point of the AR curve.

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Figure 1. Monopolist Equilibrium with Zero Cost of Production

When there is only one spring catering to the drinking water requirement of a village in a remote area, then this spring happens to be under control of one individual. We know that TR is maximized when MR is zero. So monopolist will supply his product (water) till MR=0 so that TR is maximized. Hence it’s the case of zero cost monopoly.