Problem:
A pub 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 pub is $4.50 and the pub sells 250 pints of beer a night. The price of wine averages $8 a glass and in 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 pub is considering lowering the price of beer to $4.
1) How do I find the Pub's profit before the price change?
2) How would I get the percent change of the price of beer using the midpoint formula?
3) If I used the price change of beer and the cross-price elasticities, how could I find how many glasses of wine, appetizers, and entrees the pub would sell after the price change of beer?
4) How would I find the profit of the pub after the price change?