AAEC 3315Agricultural Price Theory

Chapter 13

Price and Output Under Monopoly

Objectives

To learn: How the prices & quantities of goods & services

produced & consumed are determined under a monopoly market structure.

Characteristics of a Monopoly

Characteristics of monopolies are: Single seller but a large number of buyers Unique Product, i.e., there are no close substitutes Ability to Set Prices (monopolist is a price maker;

discriminating monopolists charge different prices to different classes of consumers)

Barriers to Entry (a monopoly generally has an economic, legal or technical barrier to entry to other firms)

Characteristics of a Monopoly

These characteristics of monopolies, clearly, make a monopolist a price-maker. However, a monopolist’s control over price is not absolute.

What causes Monopoly? Barriers to entry is the single most important factor that

contributes the existence of monopolies. A strong barrier for entry may exist because:

Control of the supply of key raw materials Patents on the product or on the production process A market franchise awarded by the government

The Monopolist’s TR, AR, and MR Curves

Since the monopolist is the only firm producing a product, the monopolist’s demand curve is precisely the same as the market demand curve. So, AR is the monopolist’s

demand curve And it is negatively sloped

Since AR is negatively sloped, AR & MR are not the same. MR is also negatively

sloped, and is twice as steep as the AR.

The Total Revenue curve is concave downward because the monopolist’s demand curve is downward sloping.

Q

P

MR AR

TR

The Monopolist’s Cost Curves

If the monopolist in the product market faces a perfectly competitive input market, then it can not affect input prices.

In that case, the concept of cost curves do not change.

The TC, TVC, TFC, ATC, AVC, AFC, and MC curves, therefore, are as discussed before for perfect competition.

Co

sts

Output

TOTAL COSTS

TC

TVC

TFC

ATC

AVCCosts/unit

Output

AFC

MC

Profit Maximizing Output Decisionunder Monopoly in the Short-run

The Total Curves Approach

Profit maximization output decision rule for a monopolist depends on two considerations.

One, whether there is any output level at which TR exceeds the TVC. If not, the profit maximizing strategy is to shut down.

If there are output levels at which TR > TVC, the monopolist will produce where the vertical distance between TR and TC is at its maximum.

$TR

TC

TVC

Q

Profit Maximizing Output Decisionunder Monopoly in the Short-run

The Total Curves Approach

In this case, the vertical distance between TR and TC is at maximum at the Q* level of output.

Note that at Q* units of output, TR and TC curves have the same slope, i.e., MR = MC. (This is called the Necessary Condition of profit maximization)

Further, the slope of MC exceeds that of the MR (MC has a positive slope and MR has a negative slope). (This is called the Sufficient Condition of profit maximization)

$TR

TC

TVC

QQ*

Profit Maximizing Output Decisionunder Monopoly in the Short-run

The Average & Marginal Curves Approach

Again, the same decision rules should be considered.

Does the AR lie above the AVC in some output range? If not, the best strategy in the short-run is to shut down.If yes, the profit maximizing output is where MR=MC and the slope of the MC is greater than the slope of the MR.This is the Q* level of output.

$/unit

Q

MR

AR

Q*

MC

AC

AVC

Price Determination under Monopoly

After deciding that Q* is the profit maximizing level of output, the monopolist must decide the price at which the output is to be sold.

The monopolist will sell the output at the maximum price at which he can sell the output.That maximum price is the price that the consumers are willing to pay (derived from the demand/AR Curve) – that is P*

At that price of P*, note that profit per unit is BA dollars and the total economic profit received by the monopolist is P*ABC.

$/unit

Q

MR

AR

Q*

MC

AC

AVCP*

A

BC

A Mathematical Example

Suppose that the Monopolist’s TR and TC curves are given by:

TR = 50 Q – 4 Q2

TC = 10 Q What is the Profit Maximizing level of output?

Note that at the profit max level of output, MR must equal to MC (the Necessary Condition of profit maximization)MR = ∂TR/∂Q = 50 – 8QMC = ∂TC/∂Q = 10At MR = MC, 50 – 8Q = 108Q = 40 or Q = 5

Also note that at the profit max level of output, the slope of MC must exceed the slope of the MR (the Sufficient Condition of profit maximization)Slope of MR = ∂MR/∂Q = – 8Slope of MC = ∂MC/∂Q = 0Thus the Slope of MC > the slope of MR

A Mathematical Example

The Monopolist’s TR and TC curves are given by:

TR = 50 Q – 4 Q2

TC = 10 Q What is Equilibrium Price?

Note that TR = P*Q = 50Q - 4Q2

So, P = 50 – 4Q

Since Q = 5, then P = 50 – 20 = $30

What is the Profit? Note that Profit = TR – TC

TR = 50 (5) – 4 (5)2 = $150

TC = 10 (5) = $50

So, Profit = $150 - $50 = $100

Multiplant Monopolist

This section extends the analysis to cover the case where the monopolist operates more than one plant.

How does a monopolist determine the profit maximizing allocation of production between multiple plants when it has multiple plants to produce the output that he sells in a single market?

The profit maximizing multiplant monopolist allocates the production of output between two plants by equalizing the MC in each plant.

Multiplant Monopolist

Let’s assume that the monopolist operates two plants. MCA and MCB show the MCs of two plants A & B, and MCt represents the firm’s MC.

Note that MCt is the horizontal summation of MCA and MCB and shows the firm’s MC when it uses either plant A or B, whichever has a lower MC.

AR and MR represent the monopolist’s Average Revenue and Marginal Revenue curves.

Plant A

Plant B

Firm

$/unit $/unit $/unit

Q Q Q

MCA MCB MCt

AR

MR

Multiplant Monopolist

By equating its MR and MCt, the monopolist determines the profit maximizing output of q t and price of Pt.

To produce qt at the least cost, the monopolist allocates production between the two plants such that the MC of production in each plant is the same.

That is, plant A produces qA and plant B produces qB, where qA + qB = qt.

Plant A

Plant B

Firm

$/unit $/unit $/unit

Q Q Q

MCA MCB MCt

qA qB qt

AR

MR

Pt

A Mathematical Example of Multiplant Monopolist

Suppose that the Monopolist’s TR and TC curves for two plants are given by:

TR = 136 Q – 4 Q2, TC1 = 20 Q1 + Q12, and TC2 = 10Q2 + 2.5 Q2

2

Now then MR = 136 – 8 Q = 136 – 8 (Q1 + Q2)

AR = 136 – 4 (Q1 + Q2)

MC1 = 20 + 2Q1

MC2 = 10 + 5Q2

To maximize profit, the multiplant monopolist will equate MC1 with MR and MC2 with MR.

That is 20 + 2Q1 = 136 – 8 (Q1 + Q2) ------ (1)

and 10 + 5Q2 = 136 – 8 (Q1 + Q2) ------ (2)

A Mathematical Example of Multiplant Monopolist

Taking equation (1), we have 20 + 2Q1 = 136 – 8Q1 - 8Q2

Or, 2Q1 + 8Q1 = 136 – 20 - 8Q2

Or, 10Q1 = 116 - 8Q2

Or, Q1 = 11.6 – 0.8Q2 -------- (3)

Note that equation (2) is 10 + 5Q2 = 136 – 8 (Q1 + Q2)

Or, 10 + 5Q2 = 136 – 8Q1 - 8Q2

Now substituting (3) in equation (2), we have10 + 5Q2 = 136 – 8(11.6 – 0.8Q2) - 8Q2

Or, 10 + 5Q2 = 136 – 92.8 + 6.4Q2 - 8Q2

Or, 5Q2 - 6.4Q2 + 8Q2 = 136 – 10 - 92.8

Or, 6.6 Q2 = 33.2

Or, Q2 = 5.03 units

Now substituting Q2 = 5.03 into equation (3), we calculate Q1 = 7.576

A Mathematical Example of Multiplant Monopolist

The profit maximizing production levels in plant 1 and plant 2 are then 7.576 and 5.03 units, respectively.

Now we can calculate the Price that the multiplant monopolist will charge in the market.

Note that:

AR = P = 136 – 4 (Q1 + Q2)

Or, AR = P =136 – 4(7.576+5.03)

Or, P = 136 – 50.424 = $85.576 Thus, we have this multiplant monopolist who produces 7.576 units of

the output in Plant 1 and 5.03 units of the output in Plant 2 at the least cost of production and sells the product in the marketplace for $85.576 per unit.

Can you calculate the amount of profit for this multiplant monopolist?

Price Discrimination

Price Discrimination is said to exist when an identical good is sold at different prices or when two similar goods are sold at prices that are in different ratios to marginal costs.

Prerequisites of Discriminatory Pricing The seller must have a monopoly or market power The market can be separated (i.e., product can’t be transferred from

one market to another) The elasticities of demand in different markets must be different

First Degree orPerfect Price Discrimination

The discriminatory pricing that attempts to take away the entire Consumers Surplus is called first degree price discrimination.

It assumes that the monopolist knows the demand of each customer and attempts to extract the maximum amount possible from each customer.

The monopolist charges different prices to each of the customers and takes away the entire consumer surplus.

This is a limiting case unless customers are few in numbers and can be well separated.

$/unit

Q

MR

AR

Q*

MC

Second Degree orPerfect Price Discrimination

The discriminatory pricing that attempts to siphon off a part of the CS is called the second degree price discrimination.

It charges different prices for different size purchases, as in the case of electric or gas utilities.

The monopolist charges P1 for up to Q1 units, P2 for between Q1 and Q2, and P3 for purchases exceeding Q2.

Note that the shaded triangles represent CS retained by the consumers.

$/unit

Q

MR

AR

Q3

MC

Q2Q1

P3

P2

P1

Third Degree orPerfect Price Discrimination

Third degree price discrimination refers to a discriminatory pricing by which a monopolist sells his good at different prices in different markets, but keeps the price uniform within each separate market.

In the figure below, the two markets are identified separately. The MRt is the MR for the firm and is obtained by summing the MR1 and MR2 horizontally.

$/unit $/unit $/unit

Q Q Q

MR1

D1MR2 D2 MRt

Market 1 Market 2 Firm

Third Degree orPerfect Price Discrimination

The MRt (MR for the firm) shows the additional revenue the firm can secure by selling an additional unit of the output either in Market 1 or Market 2, whichever has a higher MR.

To maximize profit, the monopolist must produce Qt – the level of output at which MRt = MC.

$/unit $/unit $/unit

Q Q Q

MR1

D1MR2 D2 MRt

MC

Qt

Market 1Market 2 Firm

Third Degree orPerfect Price Discrimination

The monopolist must now allocate this output between Markets 1 and 2 in such a way as to equalize the MR in the two markets.

This is the case at Q1 level of output in Market 1 and Q2 level of output in Market 2.

Note that Q1+Q2 = Qt (This is necessarily true because MRt curve is obtained as the summation of MR1 and MR2)

$/unit $/unit $/unit

Q Q Q

MR1

D1MR2 D2 MRt

MC

QtQ2Q1

Market 2Market 1 Firm

Third Degree orPerfect Price Discrimination

The prices charged in the two markets are P1 in Market 1 and P2 Market 2 as determined from their respective AR curves.

Note that the monopolist is charging a higher price in Market 1 than in Market 2.

That is because demand in Market 1 is relatively inelastic and demand in Market 2 is relatively elastic.

$/unit $/unit $/unit

Q Q Q

MR1

D1MR2 D2 MRt

MC

QtQ2Q1

Market 2Market 1 FirmP1

P2

Relatively Inelastic Relatively Elastic