Answer to Question #306162 in Microeconomics for atul

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

a)

let;

A -represents the peanut butter.

$QAd$ - quantity demanded denoted.

PA- price.

B- jelly.

$QBd$ - quantity demanded.

PB- price

Since the cross-price elasticity of demand measures the responsiveness of the quantity demanded a good to a change in the price of another good, the cross-price elasticity for A and B is given by;

$E(B,A)= \frac {{PC(PA)}} {{PC(QBd)}},$

where PC(x) can be calculated as follows:

$PC(x)= \frac {{x(i)-x(i-1)}} {{ x (i-1)+ x(i) \times 0.5}}$

PC is a percent change in variable denoted by x (according to midpoint method)

$PC(QBd)=\frac {-0.15 QB}{0.5\times 1.85QB}=-0.162$

$PC(PA)=\frac {3-2}{(2+3)\times 0.5}=0.4$

Therefore,

 $E(B,A)=\frac {-0.162}{0.4}=-0.405$

Hence, peanut butter and jelly are complements since the elasticty is less tha zero.

b)

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

$PC(PC)= \frac {3-4}{(3+4)\times 0.5}= -0.2857$

$PC(AQd)= \frac {-0.2QA}{1.8QA\times 0.5} =-0.222$

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

Hence, peanut butter and chocolate spread are substitutes since the elasticity between them is greater than zero.