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.

1. What is the restaurant's profit (prior to the price change)?

2.Using the midpoint formula (described at the top of page 73--use the midpoint instead of the initial point in calculating the percent change), by what percent would the price of beer change? Using the price elasticity of demand, the approximation for the percent change in the price of beer you just calculated, and the equation at the start of section 6.5, how many pints of beer would the restaurant sell after the price change?

Midpoint formula :

3. Using the price change of beer and the cross-price elasticities, how many glasses of wine, appetizers, and entrees would the restaurant sell after the price change of beer?

4. What would the profit of the restaurant be after the price change?

5. Should the restaurant lower the price of beer to $4 based on your analysis?

**Please show work and answer all questions

Explanation / Answer

1) Before price change:

Marginal profit for each product = price - marginal cost

Total profit = Sum of all marginal profits multiplied by respective quantity sold now.

So

Profit = 250 x (4.5 - 2) + 40 x (8 - 5) + 70 x (6 - 4) + 25 x (12 - 7)

= 625 + 120 + 140 + 125 = 1,010

(2)

NOTE: The midpoint formula your provided, is for calculating price-elasticity of demand. But here, we have only 3 data points: Original price, proposed new price & original quantity. How can elasticity be calculated, unless revised quantity is provided? On the other hand, if I assume that elasticity value should remain at - 0.80, then this midpoint formula will give us the new quantity demanded (and not the % change in price). So your question is unclear and confusing. I'm calculating the % change in price based on an average (midpoint) of prices as the base price, as follows:

% change in price = (New price - original price) / [(New price + original price) / 2] / x 100

= (4 - 4.50) / [(4 + 4.5) / 2] / x 100

= - 11.76%

that is, 11.76% decrease in price.

(2 - b)

Price elasticity of demand for beer = - 0.8, meaning for ever 1% decrease in beer price, quantity demanded will increase by 0.8%.

So, when price decreases by 11.76%, quantity demanded will increase by (11.76% x 0.8) = 9.41%

Revised quantity = 250 x (100 - 9.41)% = 226 (rounded off to whole number)

NOTE: Please double check the question requirement that requires use of midpoint formula. With the given information, and the given midpoint formula, the question does not make sense.

There are total 5 questions & I've answered the 1st two as per Chegg protocol.

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