A restaurant/bar is analyzing its pricing of beer. It has determined that the pr

Question

A restaurant/bar is analyzing its pricing of beer. It has determined that the price elasticity of demand for beer is ?0.8; the cross-price elasticity for wine with respect to the price of beer is 0.9; the cross-price elasticity for appetizers is -1.4; and the cross-price elasticity for entrees is -2.2. The current average price of a beer at this bar is $4.50, and the restaurant sells 250 pints of beer a night. The price of wine averages $8 a glass, and on a typical night 40 glasses of wine are purchased. An appetizer is priced at an average price of $6, and an entree costs $12 on average. The average number of appetizers and entrees sold per night is $70 and $25, respectively. The marginal cost of a pint of beer is $2; an additional glass of wine sold increases costs by $5; an appetizer increases costs by $4; and an entree has a marginal cost of $7. The restaurant is considering lowering the price of beer to $4.

Explanation / Answer

(a)

Before price change,

Total revenue = $ (4.5 x 250 + 8 x 40 + 6 x 70 + 12 x 25) = $ 2165

Total cost = $ (2 x 250 + 5 x 40 + 4 x 70 + 7 x 25) = $ 1155

Profit = $(2165 - 1155) = $ 1010

(b) Beer price decreased to $4 (Change by $0.50, or 11.11%)

So quantity of beer sold will increase by 8.89%

New quantity of beer sold = 250 x 1.0889 = 272 glasses

(i) cross-price elasticity for wine with respect to the price of beer is 0.9

This means for 1% increase (decrease) in beer price, quantity of Wine sold increases (decreases) by 0.9%

So for 11.11% decrease in beer price, wine sales will decrease by 9.999%

So, New Wine Sales = 40 x 1.09999 = 44 glasses

(ii) cross-price elasticity for appetizers is -1.4

This means for 1% increase (decrease) in beer price, quantity of Appetizer sold decreases (increases) by 1.4%

So for 11.11% decrease in beer price, Appetizer sales will increase by 15.55%

So, New Apetizer Sales = 70 x 1.1555 = 81

(iii) cross-price elasticity for entrees is -2.2

This means for 1% increase (decrease) in beer price, quantity of Entree sold decreases (increases) by 2.2%

So for 11.11% decrease in beer price, Entree sales will increase by 24.44%

So, New Entree Sales = 25 x 1.2444 = 31

(c) New Profit

= Sum of [New Quantity x (Price - Cost)] for all 4 items

= 272 x (4 - 2) + 44 x (8 - 5) + 81 x (6 - 4) + 31 x (12 - 7)

= 544 + 132 + 162 + 155 = $ 993

(d) Compared to profit calculated in part (a), total profit decreased after beer price reduction. So price of beer should not be reduced.

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