# Price elasticity

1:

The demand for personal computers can be characterized by the following elasticities:

Price elasticity = -5

Cross-price elasticity with software* = -4

Income elasticity =2.5

*relates a change in computer prices to changes in the quantity demanded of software

Indicate whether each of the following statements is true, false, or uncertain and explain your answer.

(a) A price reduction for personal computers will increase both the number of unites demanded and the total revenue of sellers

(b) The cross price elasticity indicates that a 5% reduction in the price of personal computers will cause a 20% increase in the quantity of software demanded.

(c) Demand for personal computers is price elastic and computers are normal goods

(d) Falling software prices will increase revenues by sellers of both computers and software

(e) A 2% price reduction would be necessary to overcome the effects of a 1% decline in income.

2:

FORMULA: Qd=130-9P+8Pc-.001I+2A

QUESTION: Suppose the demand function given above is the demand for Maine lobster in Prtsmouth, New Hampshire. Qd is the quantity demanded per day, p is the price of lobster, Pc is the price of Alaskan King Crab, I is average consumer income and A is the average amount of advertising be the industry per day. Assume that Pc=$12.00 I=$20,000 and A=$15.00.

(a) Calculate the point price elasticity of demand if p=$14.00. Explain what your result means in words

(b) Calculate the arc price elasticity of demand if p falls between $10.00 and $16.00. Explain what your results mean in words.

(c) Calculate the point cross-price elasticity of demand between Alaskan King Crab and lobsters if the price of lobsters is $14.00 and the price of crabs is $10.00

(d) Calculate the arc cross price elasticity of demand between Alaskan King Crab and lobsters if the price of lobsters is $14.00 and the price of crabs range from $10.00 to $16.00

3:

Kitty Russell's Longbranch café in Sausalito recently reduced Nachos Supreme appetizer from $5 to $3 for afternoon "early bird" customers and enjoyed a resulting increase in sales from 60 to 180 orders per day. Beverage sales also increase from 30 to 150 units per day

a. Calculate the arc price elasticity of demand for Nachos Supreme appetizers.

b. Calculate the arc cross price elasticity of demand between beverage sales and appetizer prices.

#### Solution Preview

Please refer to the attachment.

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<br>(a) A price reduction for personal computers will increase both the number of unites demanded and the total revenue of sellers

<br>

<br>True.

<br>Price elasticity = -5, which means deduction in price will raise the number of unites demanded.

<br>It's absolute value is |-5|=5, so personal computer is price elastic good.

<br>Then the proportional change (increase) in number of unites demanded is greater than the proportional change (decrease) in price. Thus, the total revenue of sellers will also increase.

<br>

<br>(b) The cross price elasticity indicates that a 5% reduction in the price of personal computers will cause a 20% increase in the quantity of software demanded.

<br>

<br>True.

<br>Cross-price elasticity with software = -4, which means deduction in price of personal computers will raise the quantity of software demanded.

<br>And the proportional increase in the quantity of software demanded is 4 times the the proportional change (decrease) in price. Thus, increase in the quantity of software demanded will be 5%*4=20%

<br>

<br>(c) Demand for personal computers is price elastic and computers are normal goods

<br>

<br>True.

<br>As stated in part a, the absolute value is |-5|=5 >1, so personal computer is price elastic good.

<br>Normal good is defined that an increase in income will cause increase in consumption of the good. Since Income elasticity =2.5 >0, PCs are Normal ...

#### Solution Summary

Calculate the point cross-price elasticity of demand between Alaskan King Crab and lobsters and other facets of this problem.