Income & Cross Elasticities of Demand (AQA A Level Economics): Revision Note

A consumer's income rises from £100 to £125 a week. They originally consumed 12 bagels at the local bakery, but this increased to 15 bagels a week.

Calculate the YED of the bagels

Step 1:  Calculate the % change in QD

  $$\begin{gathered} \%△\mathrm{QD}=\frac{15-12}{12}\times 100 \\ \%△\mathrm{QD}=25\% \end{gathered}$$ 

Step 2: Calculate the % change in Y

$$\begin{gathered} \%△\mathrm{Y}=\frac{125-100}{100}\mathrm{x}100 \\ \%△\mathrm{Y}=25\% \end{gathered}$$

Step 3: Insert the above values in the YED formula

$$\begin{gathered} \mathrm{PED}=\frac{\%△\mathrm{in}\hspace{0.17em}\mathrm{QD}}{\%△\mathrm{in}\mathrm{Y}} \\ Y\mathrm{ED}=\frac{25}{25} \\ Y\mathrm{ED}=1 \end{gathered}$$

Leading into the release of FIFA 22 Ultimate, EA Sports discounted the price of FIFA 21 from £90 to £60. A game store in Winchester saw an increase in sales of their PlayStation 5 consoles. Prior to the discount, they were selling 50 units a week, and after the discount this increased to 80 units.

Calculate the XED and explain the relationship between the two products

Step 1:  Calculate the % change in QD_A

  $$\begin{gathered} \%△{\mathrm{QD}}_A=\frac{80-50}{50}\times 100 \\ \%△Q{D}_A=60\% \end{gathered}$$ 

Step 2: Calculate the % change in P_B

$$\begin{gathered} \%△P_B=\frac{60-90}{90}\mathrm{x}100 \\ \%△P_B=-33.3\% \end{gathered}$$

Step 3: Insert the above values in the XED formula

$$\begin{gathered} X\mathrm{ED}=\frac{\%△\mathrm{in}\hspace{0.17em}{\mathrm{QD}}_A}{\%△\mathrm{in}{P}_B} \\ X\mathrm{ED}=\frac{60\%}{-33.3\%} \\ X\mathrm{ED}=-1.8 \end{gathered}$$

Step 4: Explain the relationship between the two products

The negative sign indicates that these two products are complements and the high value suggests they are strong complements

The price of good Y, a substitute for X, rises from £50 to £60. As a result, the quantity demanded of good X rises from 2 units to 3 units per month. 

What is the value of the cross elasticity of demand for good X with respect to Y?

A: +0.4

B: -0.4

C: +2.5

D:-2.5

Step 1: Calculate % change in QD_A using formula

   $$\begin{gathered} \%△{\mathrm{QD}}_A=\frac{3-2}{2}\times 100 \\ \%△{\mathrm{QD}}_{\mathrm{A}}=50\% \end{gathered}$$

Step 2: Calculate % change in P_B using formula

   $$\begin{gathered} \%△{\mathrm{P}}_{\mathrm{B}}=\frac{60-50}{50}\mathrm{x}100 \\ \%△{\mathrm{P}}_{\mathrm{B}}=20\% \end{gathered}$$

Step 3: Insert the above values in the XED formula

   $$\begin{gathered} \mathrm{XED}=\frac{\%△\mathrm{in}\hspace{0.17em}{\mathrm{QD}}_{\mathrm{A}}}{\%△\mathrm{in}{\mathrm{P}}_{\mathrm{B}}} \\ \mathrm{XED}=\frac{+50\%}{+20\%} \\ \mathrm{XED}=+2.5 \end{gathered}$$

The positive sign indicates that these two products are substitutes and the high value suggests they are strong substitutes