# Suppose a movie monopolist sells to adults, seniors, and students. The adult demand is QA= 30 -...

## Question:

Suppose a movie monopolist sells to adults, seniors, and students. The adult demand is QA= 30 - P. The senior demand is QSR = 30 - 2P. The student demand is QST = 50 - 5P. The MC = $4 per ticket. The firm's fixed cost is $100.

Find the inverse demand curves for each group and graph them on a rough graph (find P and Q intercepts).

Assume the firm price discriminates

What prices will the monopolist set for each group and how many tickets will they purchase?

Mark these points on your graph.

How much profit will the firm earn?

Calculate the consumer surplus for each group.

What is the total consumer surplus?

Assume the firm does not discriminate

Find the combined demand (there will be 2 kinks)

On a new rough graph, draw this combined demand curve (find intercepts and kink points)

Find the MR for this combined demand curve (it will have 3 parts) and draw them on your graph.

Find the profit-maximizing Q and P for the combined demand (MC will cross MR 3 times, choose the Q that earns the highest profit). Indicate this point on your graph.

How much profit will the firm earn?

Calculate the consumer surplus for each group (it may be helpful to look at your first graph).

What is the total consumer surplus? Compare your results. How many movie tickets will the firm sell in each case?

Compare profit in each case Compare the total consumer surplus in each case.

Does price discrimination lead to an increase or a decrease in total surplus? Explain.

## Price Discrimination

Price Discrimination is a pricing strategy used by a monopolist in an attempt to increase profits. A monopolist discriminates the price by charging different prices to consumers based on their willingness to pay (first-degree discrimination), by offering a different version of the product (second-degree discrimination(), or by dividing the population into segments or clusters.

## Answer and Explanation:

Suppose a movie monopolist sells to adults, seniors, and students. The adult demand is QA= 30 - P. The senior demand is QSR = 30 - 2P. The student demand is QST = 50 - 5P. The MC = $4 per ticket. The firm's fixed cost is $100.

**1. Find the inverse demand curves for each group and graph them on a rough graph (find P and Q intercepts).
**

The inverse demand curve for adult is

P = 30 - Qa

The inverse demand curve for senior is

P = 15 - 0.5 Qsr

The inverse demand curve for student is

P = 10 - 0.2 Qst

**2. Assume the firm price discriminates What prices will the monopolist set for each group and how many tickets will they purchase? Mark these points on your graph. **

Computing the revenue and the MR from each market,

For adult market

Ra(Qa) = pa*qa = (30 - Qa) Qa = 30Qa - Qa^2 and MR = 30 - 2Qa

For senior market

Rsr (Qsr) = psr*qsr = (15 - 0.5Qsr) Qsr = 15Qsr - 0.5Qsr^2 and MR = 15 - Qsr

For student market

Rst (Qst) = pst*qst = (10 - 0.2 Qst) Qst = 10Qst - 0.2Qst^2 and MR = 10 - 0.4Qst

The monopolist sets MR = MC, Hence,

MRa = 30 - 2Qa = 4 = MC

MRsr = 15 - Qsr = 4 = MC

MRst = 10 - 0.4Qst = 4 = MC

Solving for the first equation,

MRa = 30 - 2Qa = 4 = MC

Qa = 13

Substituting Qa to get Pa,

P = 30 - Qa = 30 - 13 = 17

Solving for the second equation,

MRsr = 15 - Qsr = 4 = MC

Qsr = 11

Substituting Qsr to get Psr,

Psr = 15 - 0.5 Qsr = 15 - 0.5 (11) = 9.5

Solving for the third equation,

MRst = 10 - 0.4Qst = 4 = MC

Qst = 15

Substituting Qst to get Pst,

Pst = 10 - 0.2 Qst = 10 - 0.2 (15) = 7

**3. How much profit will the firm earn? **

Profita = (17 - 4) (13) = 169

Profitsr = (9.5 - 4) (11) = 60.5

Proiftst = (7 - 4) (15) = 45

Total profits = 274.5

**
**

**4. Calculate the consumer surplus for each group. What is the total consumer surplus? **

Adult: CS = (30 - 17) (13) (0.5) = 84.5

Senior: CS = (15 - 9.5) (11) (0.5) = 30.25

Student: CS = (10 - 7) (15) (0.5) = 22.5

Total CS = 137.25

**5. Assume the firm does not discriminate. Find the combined demand (there will be 2 kinks). On a new rough graph, draw this combined demand curve (find intercepts and kink points). Find the MR for this combined demand curve (it will have 3 parts) and draw them on your graph. **

30 - P + 30 - 2P + 50 - 5P = 110 - 8P

The firm's profit without price discrimination is:

Q = 110 - 8P

P = 55/4 - 1/8Q

Revenue = PQ

= (55/4 - 1/8Q) Q

= 55/4Q - 1/8Q^2

Hence,

MR = 55/4 - 1/4Q

**6. Find the profit-maximizing Q and P for the combined demand (MC will cross MR 3 times, choose the Q that earns the highest profit). Indicate this point on your graph. **

MR = MC

55/4 - 1/4Q = 4

Q = 39

Substituting Q for P,

P = 55/4 - 1/8Q = 55/4 - 1/8 (39) = 8.875

**7. How much profit will the firm earn? **

Profit = (P - MC) Q

= (8.875 - 4) (39)

= 190.125

**8. Calculate the consumer surplus for each group (it may be helpful to look at your first graph). What is the total consumer surplus? Compare your results. **

CS: (13.75 - 8.875) (39) (0.5) = 95.0625

**9. Does price discrimination lead to an increase or a decrease in total surplus? Explain. **

The total surplus is higher with third-degree price discrimination than a uniform price. This is because the monopolist produces more output and hence, more consumers are served.

#### Learn more about this topic:

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Chapter 3 / Lesson 53This lesson defines types of price discrimination. We'll use several scenarios to explore the use of price discrimination in the real world.