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# Analyzing the effect of price change on profitability

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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
TR1=4.50*250+8*40+6*70+12*25=\$2165

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.

\$2.19