Answer to Question #161210 in Microeconomics for Udit

Question

Rising peanut prices have forced peanut butter makers to raise the price of peanut butter from $2 to $3 per jar, causing quantity demanded to fall. In addition, sales of jelly also dropped by 15%. Soon thereafter, makers of chocolate spread dropped its price from $4 to $3 per jar. This resulted in a further decline in peanut butter sales by 20%. a) What is the cross elasticity of demand between peanut butter and jelly (use the midpoint method)? Are these two products complements or substitutes? b) What is the cross elasticity of demand between peanut butter and chocolate spread (use the midpoint method)? Are these two products complements or substitutes?

Answer 1

ANSWER

a) Let's denote the peanut butter by A (quantity demanded denoted by QAd, price denoted by PA), and jelly by B (quantity demanded denoted by QBd, price denoted by PB).

The cross-price elasticity of demand measures the responsiveness of the quantity demanded for a good to a change in the price of another good.

Hence, the formula for cross-price elasticity regarding A and B can be written as follows:

$E(B,A)=\frac{PC(QBd)}{PC(PA)}$ ,

where PC(x) can be calculated as follows:

$PC(x)= \frac{x(i)-x(i-1)}{(x(i-1)+x(i))\times0.5}$

PC is a peccent change in variable denoted by x (accordind to midpoint method).

$PC(QBd) =\frac{ -0.15QB}{0.5\times1.85QB} =-0.162$ according to the question

$PC(PA)= \frac{3-2}{(2+3)\times0.5} =0.4$

Hence,

$E(B,A)=\frac{-0.162}{0.4}=-0.405$

Hence, peanut butter and jelly are complements (Elasticity is not greater than zero).

b) Let's denote the chocolate spread by C. (quantity demanded denoted by QCd, price denoted by PC)

Hence, the formula for cross-price elasticity regarding A and C can be written as follows:

$E(A,C)=\frac{PC(QAd)}{PC(PC)}$

$PC(PC)=\frac{3-4}{(3+4)\times0.5}=-0.2857$

$PC(AQd)=\frac{-0.2QA}{1.8QA\times0.5}=-0.222$

$E(A,C)=\frac{-0.222}{-0.2857}=0.77$

The elasticity of demand between peanut butter and chocolate spread is greater than zero. Hence, peanut butter and chocolate spread are substututes