BEA325 Prices and Profits

Group problem solving session 6

1.* The table below shows the monthly demand for movies for three individuals: Sandy, Elle and Joy.

1. Use this data to draw the demand curve for each individuals and for the market.

1. Use this data to calculate the price the firm sets if it must charge the same linear price to all customers. Assume marginal cost is 5 and that there is a zero fixed cost.

1. Now suppose the firm identify each customer, so can set a different linear price for each of them. (That is, it conducts third degree price discrimination.) What price would the firm charge each customer?

1. Compare the profit under the pricing strategy in part b and part c.

2. The following advertisement for two restaurants, Matteo’s and No35, appeared in the Epicure (i.e. Food) section of The Age newspaper on Tuesday 27^th April 2010.

Matteo’s, North Fitzroy, 9481 1177.

       How much $70 for two courses; $85 for three courses.

       Why Matteo’s? No one puts combinations on a plate like Matteo’s. Think avocado chawan mushi served with a sweet dashi sauce topped with a yabby tail. If your mum’s idea of dining out is about eating things you can’t make at home, she’ll love this.

       No35, Sofitel, City, 9653 7744.

       How much $90 an adult for a buffet lunch. $5 a year of age for kids.

       Did somebody say buffet? Think what you like about buffets but if you’re going to do it, No35 is a fine destination. Perfect if lunch is to be an extended-family event — all tastes are accommodated. Think frittata, edamame salad with toasted sesame seeds, pumpkin gnocchi, roast beef. And the buffet means no wait for impatient children.

a             Identify two price discrimination strategies that Matteo’s and No35 are using. Explain your answer.

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b             Can you anticipate any difficulties arising from the price discrimination strategy adopted at No35? Explain your answer.

c              Using diagrams explain why third degree price discrimination generates more profit for a restaurant with constant marginal costs than a uniform or single price.

3. The Boston Globe releases an early edition of its Sunday paper with the Saturday edition. Individuals pay a premium for the Saturday delivery of the Sunday paper. Can you explain why the Boston Globe introduced an Early edition of the Sunday paper? Can you explain why the Mercury (Examiner/Local newspaper in Kuwait) does not produce an early edition of the Sunday paper?

4. Suppose a firm has two distinct markets; a high-demand group and a low-demand group, with inverse demand curves given by;

P₁ = 10 – Q₁

P₂ = 20 – Q₂

The firm has constant marginal costs.

a             Construct two graphs to show these demand functions and their associated marginal revenue functions – either side by side or back to back.

b             If the marginal cost of supplying the product is $2 what is the profit maximising quantity and price in each market. Note:

MR₁ = 10 –2Q₁

MR₂ = 20 – 2Q₂

c              Calculate the total profit the firm makes if they can prevent arbitrage.

5. The table below shows the monthly marginal benefit of movies for two individuals: Jill and Pauline.

Suppose the firm’s marginal cost is $1. If the firm can conduct direct price discrimination with linear pricing (third degree price discrimination) then to maximise profit:

2. a) The firm should charge Jill $15 and Pauline $12.
3. b) The firm should charge Jill $3 and Pauline $5.
4. c) The firm should charge Jill $9 and Pauline $12.
5. d) The firm should charge both customers $12
6. e) None of the above.

6. (a) Explain the conditions for profit maximisation by a monopolist when (i) the monopolist chooses only its level of output and (ii) when the monopolist chooses both its output level and its advertising level. (b) If the customer’s marginal benefit is given by:

P = (100-Q) + A^0.5

where Q is quantity and A is the advertising level. It can be shown that:

MR = 100-2Q + A^0.5

and

MR_A = 0.5QA^-0.5

Marginal cost is 10, so the firm’s total cost is:

C = 10Q +A.

(i) interpret the firm’s cost function (ii) It can be shown that the profit maximising output is 60.  (You don’t have to show this.) Find the profit maximising level of advertising. Show the determination of the profit maximising level of advertising on a graph. (iii) Calculate the firm’s maximum profit.

7. How does the sensitivity of a firms demand to advertising affect the advertising sales ratio? What is a product that you would expect to see a high advertising sales ratio, and what is a product you would expect to see a low advertising sales ratio?

8. Consider a firm that is currently selling 20 units. Suppose that if a firm’s advertising increases by $200 it could raise price by $8 without losing sales.

1. a) The firm should increase advertising to increase profit
2. b) The firm should not change adversting because it is already using the profit maximising level of advertising
3. c) The firm should decreas advertising to increase profit.
4. d) There is not enough information to tell whether the firm should increase or decrease advertising to increase price.

9. Suppose a popular product, the iFad, is sold in Australia and China. The marginal cost of the product is the same in both countries, being $20. Suppose the elasticity of demand in Australia is 5 and the elasticity of demand in China is 6. Then:

1. a) The profit maximising price in Australia is $100 and in China is $120.
2. b) The profit maximising price in Australia is $25 and in China is $24.
3. c) The profit maximising price in both countries is $20
4. d) The profit maximising price in Australia is $25 and in China is $26.
5. e) None of the above.

 * indicates the problem to be discussed by groups.

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