3. (a) Suppose that when the price of peanut butter rises from $2.10 to S3.20 pe
ID: 1149684 • Letter: 3
Question
3. (a) Suppose that when the price of peanut butter rises from $2.10 to S3.20 per jar, the quantity of jelly purchased falls from 30 million jars to 22 million jars. What is the cross-price elasticity of demand between peanut butter and jelly? Are they complements or substitutes? (b) Suppose that when the price of peanut butter experiences the same rise, the quantity of jelly purchased rises from 20 million jars to 26 million jars. What is the cross-price elasticity of demand between peanut butter and jelly? Are they complements or substitutes? NOTE: Round all intermediate calculations to 6 decimal places, and state both cross-price elasticities to 4 decimal places. Hint: Review Lecture 4, Slides 2-5. Let A -jelly and B-peanut butter in the cross-price elasticity formula. 4. When consumers' income is $180, they buy 200 units of a good. When consumers income increase to S300, they buy 320 units. Find the income elasticity of demand using the midpoint formula. Is the good inferior or normal? Is it a luxury good? NOTE: Round all intermediate calculations to 6 decimal places, and state both cross-price elasticities to 4 decimal places. Hint: Review Lecture 4, Slides 6-8.Explanation / Answer
3a.
Cross elasticity (Exy) tells us the relationship between two products. it measures the sensitivity of quantity demand change of product X to a change in the price of product Y.
Price elasticity formula: Exy = percentage change in Quantity demanded of X / percentage change in Price of Y.
In our case cross price elasticity is given as
Exy = Percentage change in quantity demanded of jelly / percentage change in price of peanut butter
Percentage change in quantity demanded of jelly = (22-30)/30 X 100 = -26.666667%
percentage change in price of peanut butter = (3.20-2.10)/2.10 X 100 = 52.380953 %
Therefore the cross price elasticity is -26.667/52.381 = -0.5091
As the value of cross elasticity is less than 0,the quantity of jelly and price of peanut butter are inversely proportional and hence are complements.
3b) In this case
Percentage change in quantity demanded of jelly = (26-20)/20 X 100 = 30.00%
percentage change in price of peanut butter = (3.20-2.10)/2.10 X 100 = 52.380953 %
Therefore the cross price elasticity is Percentage change in quantity demanded of jelly / percentage change in price of peanut butter
Cross price elasticity = 30/52.380953 = 0.5727 which is greater than Zero hence qty of jelly and price of peanut butter are directly related and hence peanut butter and Jelly are substitutes.
4.Income elasticity of demand is the ratio of percentage change in quantity demanded of a product to percentage change in the income level of consumer. It is a measure of responsiveness of quantity demanded to changes in consumers' income.
Percentages are calculated using the mid-point formula, i.e. by dividing the change in quantity by average of initial and final quantities, and change in income by the average of initial and final values of income. Therefore:
Where,
Qf and Qi are the final and initial quantities demanded of product A, respectively; and
If and Ii are the final and initial incomes of consumer, respectively.
Income elasticity of demand = [(320-200) / (320+200)/2 ] / [ (300-180)/ (300+180)/2]
= 0.461538 / 0.500000 = 0.9231
As the income elasticity is positive ( there is an increase in demand for goods) the goods are normal.As the value is less than 1 it is a necessity good and not a luxury good
Income Elasticity of Demand = Qf Qi ÷ If Ii (Qf + Qi) ÷ 2 (If + Ii) ÷ 2Related Questions
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