# 8.8: Problem Sets

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Problem Set 1. Bundle pricing (approximates first-degree price discrimination).

##### Exercise $$\PageIndex{1}$$

Given the following:

The individual inverse demand is P = 10-2Q.

Marginal cost is 4.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 3 units.

The bundle price is 21 dollars.

Profits per bundle are 9 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{2}$$

Given the following:

The individual inverse demand is P = 9-3Q.

Marginal cost is 3.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 2 units.

The bundle price is 12 dollars.

Profits per bundle are 6 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{3}$$

Given the following:

The individual inverse demand is P = 6-1.5Q.

Marginal cost is 3.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 2 units.

The bundle price is 9 dollars.

Profits per bundle are 3 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{4}$$

Given the following:

The individual inverse demand is P = 12-2Q.

Marginal cost is 6.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 3 units.

The bundle price is 27 dollars.

Profits per bundle are 9 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{5}$$

Given the following:

The individual inverse demand is P = 24-3Q.

Marginal cost is 6.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 6 units.

The bundle price is 90 dollars.

Profits per bundle are 54 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{6}$$

Given the following:

The individual inverse demand is P = 32-4Q.

Marginal cost is 16.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

Add texts here. Do not delete this text first.

##### Exercise $$\PageIndex{7}$$

Given the following:

The individual inverse demand is P = 20-2Q.

Marginal cost is 10.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 5 units.

The bundle price is 75 dollars.

Profits per bundle are 25 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{8}$$

Given the following:

The individual inverse demand is P = 12-3Q.

Marginal cost is 6.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 2 units.

The bundle price is 18 dollars.

Profits per bundle are 6 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{9}$$

Given the following:

The individual inverse demand is P = 15-3Q.

Marginal cost is 3.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 4 units.

The bundle price is 36 dollars.

Profits per bundle are 24 dollars.

Consumer surplus is 0 dollars.

##### Exercise $$\PageIndex{10}$$

Given the following:

The individual inverse demand is P = 8-2Q.

Marginal cost is 4.

Assume all individuals in the market have this inverse demand.

What is the bundle size, bundle price, and profits per bundle?

What is consumer surplus after purchasing the bundle?

The bundle size is 2 units.

The bundle price is 12 dollars.

Profits per bundle are 4 dollars.

Consumer surplus is 0 dollars.

Problem Set 2. Access fee (approximates first-degree price discrimination).

##### Exercise $$\PageIndex{1}$$

Given the following:

The individual inverse demand is P = 10-2Q.

Marginal cost is 4.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 9 dollars.

The per-unit price is 4 dollars.

Profits per customer are 9 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{2}$$

Given the following:

The individual inverse demand is P = 9-3Q.

Marginal cost is 3.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 6 dollars.

The per-unit price is 3 dollars.

Profits per customer are 6 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{3}$$

Given the following:

The individual inverse demand is P = 6-1.5Q.

Marginal cost is 3.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 3 dollars.

The per-unit price is 3 dollars.

Profits per customer are 3 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{4}$$

Given the following:

The individual inverse demand is P = 12-2Q.

Marginal cost is 6.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 9 dollars.

The per-unit price is 6 dollars.

Profits per customer are 9 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{5}$$

Given the following:

The individual inverse demand is P = 24-3Q.

Marginal cost is 6.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 54 dollars.

The per-unit price is 6 dollars.

Profits per customer are 54 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{6}$$

Given the following:

The individual inverse demand is P = 32-4Q.

Marginal cost is 16.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 32 dollars.

The per-unit price is 16 dollars.

Profits per customer are 32 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{7}$$

Given the following:

The individual inverse demand is P = 20-2Q.

Marginal cost is 10.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 25 dollars.

The per-unit price is 10 dollars.

Profits per customer are 25 dollars.

Each customer's surplus is 0 dollars

##### Exercise $$\PageIndex{8}$$

Given the following:

The individual inverse demand is P = 12-3Q.

Marginal cost is 6.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 6 dollars.

The per-unit price is 6 dollars.

Profits per customer are 6 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{9}$$

Given the following:

The individual inverse demand is P = 15-3Q.

Marginal cost is 3.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 24 dollars.

The per-unit price is 3 dollars.

Profits per customer are 24 dollars.

Each customer's surplus is 0 dollars.

##### Exercise $$\PageIndex{10}$$

Given the following:

The individual inverse demand is P = 8-2Q.

Marginal cost is 4.

Assume all individuals in the market have this inverse demand.

What is the access fee and per-unit price?

How many units will each customer purchase after paying the access fee?

What are the firm's profits per customer?

How much consumer surplus does each customer get?

The access fee is 4 dollars.

The per-unit price is 4 dollars.

Profits per customer are 4 dollars.

Each customer's surplus is 0 dollars.

Problem Set 3. Prices charged to each segment (third-degree price discrimination).

##### Exercise $$\PageIndex{1}$$

Given the following:

Sement 1's elasticity is -2.

Sement 2's elasticity is -3.

Marginal cost is 2.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 4 dollars.

Segment 2 is charged 3 dollars.

##### Exercise $$\PageIndex{2}$$

Given the following:

Sement 1's elasticity is -4.

Sement 2's elasticity is -1.5.

Marginal cost is 3.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 4 dollars.

Segment 2 is charged 9 dollars.

##### Exercise $$\PageIndex{3}$$

Given the following:

Sement 1's elasticity is -3.

Sement 2's elasticity is -2.

Marginal cost is 4.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 6 dollars.

Segment 2 is charged 8 dollars.

##### Exercise $$\PageIndex{4}$$

Given the following:

Sement 1's elasticity is -2.

Sement 2's elasticity is -1.5.

Marginal cost is 5.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 10 dollars.

Segment 2 is charged 15 dollars.

##### Exercise $$\PageIndex{5}$$

Given the following:

Sement 1's elasticity is -2.

Sement 2's elasticity is -3.

Marginal cost is 4.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 8 dollars.

Segment 2 is charged 6 dollars.

##### Exercise $$\PageIndex{6}$$

Given the following:

Sement 1's elasticity is -4.

Sement 2's elasticity is -2.

Marginal cost is 3.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 4 dollars.

Segment 2 is charged 6 dollars.

##### Exercise $$\PageIndex{7}$$

Given the following:

Sement 1's elasticity is -2.

Sement 2's elasticity is -3.

Marginal cost is 2.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 4 dollars.

Segment 2 is charged 3 dollars.

##### Exercise $$\PageIndex{8}$$

Given the following:

Sement 1's elasticity is -4.

Sement 2's elasticity is -2.

Marginal cost is 3.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 4 dollars.

Segment 2 is charged 6 dollars.

##### Exercise $$\PageIndex{9}$$

Given the following:

Sement 1's elasticity is -4.

Sement 2's elasticity is -2.

Marginal cost is 6.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 8 dollars.

Segment 2 is charged 12 dollars.

##### Exercise $$\PageIndex{10}$$

Given the following:

Sement 1's elasticity is -6.

Sement 2's elasticity is -2.

Marginal cost is 5.

Assume third-degree price discrimination is feasible.

What price is charged to Segment 1?

What price is charged to Segment 2?

Segment 1 is charged 6 dollars.

Segment 2 is charged 10 dollars.

Problem Set 4. Multiple Choice

##### Exercise $$\PageIndex{1}$$
1. Which best explains price discrimination?

a) Charging different prices based on quality differences

b) Charging higher prices to reflect higher costs of service

c) Charging different prices for the same product based on willingness to pay

d) All of the above

c

##### Exercise $$\PageIndex{2}$$
1. Which practice is most consistent with second-degree price discrimination?

a) Charging access fees that are equal to consumer surplus

b) Volume discounts

c) Special offers for groups of consumers (e.g., student discounts)

d) All of the above

b

##### Exercise $$\PageIndex{3}$$
1. Which practice could approximate first-degree price discrimination?

a) Charging access fees that are equal to consumer surplus

b) Volume discounts

c) Special offers for groups of consumers (e.g., student discounts)

d) All of the above

a

##### Exercise $$\PageIndex{4}$$
1. Under third-degree price discrimination

a) The firm takes the consumer’s entire surplus

b) The firm sets the monopoly or monopolistically competitive price (MR = MC) in each of the market segments it faces

c) The firm must worry about self-selection constraints and so must leave some surplus for high demand customers

d) The firm charges the competitive price (P = MC)

b

##### Exercise $$\PageIndex{5}$$
1. If individual demands are homogeneous, bundle pricing can approximate

a) First-degree price discrimination

b) Second-degree price discrimination

c) Third-degree price discrimination

d) Fourth-degree price discrimination

a

##### Exercise $$\PageIndex{6}$$
1. If individual demands are homogeneous, an access fee plus fixed price per unit can approximate

a) First-degree price discrimination

b) Second-degree price discrimination

c) Third-degree price discrimination

d) Fourth-degree price discrimination

a

##### Exercise $$\PageIndex{7}$$
1. In which case does the seller set price to take the consumer’s entire surplus?

a) First-degree price discrimination

b) Second-degree price discrimination

c) Third-degree price discrimination

d) Fourth-degree price discrimination

a

##### Exercise $$\PageIndex{8}$$
1. When would third-degree price discrimination not work?

a) When the market can be divided into segments with very different elasticities of demand

b) When all market segments have very similar elasticities of demand

c) When resale between segments is easy

d) Both (b) and (c)