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Analyzing the effect of price change on profitability

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.

-How do I find the Pub's profit before the price change?
-How would I get the percent change of the price of beer using the midpoint formula?
-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?
-how would I find the profit of the pub after the price change?

Solution Preview

-How do I find the Pub's profit before the price change?
Current price of beer=Pb1=$4.50
Current level of Beer sales=Qb1=250
Current price of wine=Pw1=$8
Current level of wine sales=Qw1=40
Current price of appetizer=Pa1=$6
Current level of appetizer sales=Qa1=70
Current price of entree=Pe1=$12
Current level of entrees=Qe1=25

Total Revenue=TR1=Pb1*Qb1+Pw1*Qw1+Pa1*Qa1+Pe1*Qe1

Marginal cost of beer=MCb=$2
Marginal cost of wine=MCw=$5
Marginal cost of ...

Solution Summary

Solution studies the effect of price change of beer on the sales of wine, appetizers and entrees in the given case. It also studies its effect on profit.