Question

Consumer buys 10 units of Good A when the price of Good B is $5. When the price of Good B rises to $6 (the price of Good A remaining unchanged) the consumer buys 14 units of Good A.

Part A                                                                                              

Using an appropriate formula, calculate this Consumer’s cross Elasticity of demand for Good A. Show your working.

Answer 1

Cross price elasticity$=[\frac{Change\space in\space QD \space of\space good A}{Change\space in\space the\space price \space of\space good \space B}]\times[\frac{Price \space of\space good\space B}{Quantity\space demanded \space of \space good \space A}]$

$QD^A1=10 \space units\\ P^B1=\$5\\ P^B2=\$6\\ QD^A2=14 \space units$

Change on QD of good $A=QD^A2-QD^A1=14-10=4 \space units$

Change in price of good $B=P^B2-P^B1=6-5=\$1$

Price of good B=$5

QD of good A=10

Putting the value of these in the formulae:

$XED=[\frac{4}{1}]\times[\frac{5}{10}]\\ XED=2$

Cross price elasticity is positive. It means good A and good B are substitutes. When the price of one good increases, the quantity demanded of the other good increases.