Posted: April 20th, 2015
BEA325 Prices and Profits
1.* The table below shows the monthly demand for movies for three individuals: Sandy, Elle and Joy.
Quantity(Movies/month) 

Marginal Benefit 
Sandy 
Elle 
Joy 
10.00 
0 
0 
0 
7.50 
1 
0 
0 
5.00 
2 
1 
0 
2.50 
3 
2 
1 
0.00 
4 
3 
2 
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 extendedfamily 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.
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.
P_{1} = 10 – Q_{1}
P_{2} = 20 – Q_{2}
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:
MR_{1} = 10 –2Q_{1}
MR_{2} = 20 – 2Q_{2}
c Calculate the total profit the firm makes if they can prevent arbitrage.
Jill 

MB ($ per unit) 
Sales (units a month) 

15.00 
1 

9.00 
2 

3.00 
3 

0.00 
4 
Pauline 

MB ($ per unit) 
Sales (units a month) 

12.00 
1 

5.00 
2 

0.00 
3 
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:
P = (100Q) + A^{0.5}
where Q is quantity and A is the advertising level. It can be shown that:
MR = 1002Q + 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.
* indicates the problem to be discussed by groups.
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