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###### Lessons
1. Cross & Income Elasticity of Demand Overview:
2. Cross Elasticity of Demand
• Formula for Cross Elasticity of Demand
• Do not take the absolute value
• Positive  →  goods are substitutes
• Demand curve for good shifts rightward
• Negative  →  goods are complements
• Demand curve for good shifts leftward
3. Cross Elasticity of Demand
• Formula for Income Elasticity of Demand
• Do not take the absolute value
• Positive  →  goods are normal
• Negative  →  goods are inferior
##### Examples
###### Lessons
1. Calculating Cross Elasticity of Demand
Suppose that a company decides to increase the price of juice by 20%. By doing this, they see a 15% increase in the quantity of coffee.
1. Find the cross elasticity of demand for coffee in respect to apple juice
2. State whether juice is a substitute or a complement.
3. What happens to the demand curve for coffee?
2. A company decides to increase their price of candy from $5 to$10. By doing so, the quantity of water decreases from 80 to 50, and decreases the quantity of candy from 100 to 50.
1. Calculate the price elasticity of demand for candy using arc elasticity of demand. Is it elastic, inelastic, or unit elastic?
2. Calculate the cross elasticity of demand for water in respect to candy. Are candies a substitute or a complement?
3. Calculating Income Elasticity of Demand
If Kevin's income increases from $100 to$150 a day, he increases his demand for ice cream by 10%, and decreases his demand for coffee by 20%. Calculate Kevin's income elasticity of demand for
1. Ice cream
2. Coffee
4. If Patsy's income increases from $50 to$100 a week., she increases her demand for chocolate from 2 kg to 5 kg.
1. Calculate the income elasticity demand for chocolate.
2. Is chocolate a normal good or inferior good? Why?
3. Is the income elastic or inelastic? Why?
###### Topic Notes

Cross Elasticity of Demand

To measure the responsiveness of substitutes and complements of goods, we use the cross elasticity of demand.

The cross elasticity of demand measures the change of demand from one good to a change in price of a substitute or complement. In other words,

Cross - price elasticity = $\frac{\% \;change \;in \;quantity \;demanded}{\% \;change \;in \;price \;of \;substitute \;or \;complement}$

The formula for cross elasticity of demand is

Cross - price elasticity = $\frac{(Q_{x_2}-Q_{x_1})/Q_{x_{avg}}}{(P_{y_2}-P_{y_1})/P_{y_{avg}}}$

If the cross elasticity of demand is positive, then the it is a substitute. This means when the price of the substitute increases, then the demand for the good increases.

If the cross elasticity of demand is negative, then the it is a complement. This means when the price of the complement increases, then the demand for the good decreases.

Income Elasticity of Demand

The income elasticity of demand is the responsiveness of the demand for a good to a change in income. In other words,

Income - price elasticity = $\frac{\% \;change \;in \;quantity \;demanded}{\% \;change \;in \;income}$

The formula for income elasticity of demand is

Income - price elasticity = $\frac{(Q_{2}-Q_{1})/Q_{_{avg}}}{(I_{2}-I_{1})/I_{_{avg}}}$

If the income elasticity of demand is greater than 1, then the good is normal and income elastic. In addition, the percentage of income spent on the good increases as income increases.

If the income elasticity of demand is less than 1 and positive, then the good is normal and income inelastic. In addition, the percentage of income spent on the good decreases as income increases.

If the income elasticity of demand is negative, then the good is inferior. This means when income increases, the demand for the good decreases.