Question

Answer All Questions. Show your Computation.

Using the midpoint method:

1. Compute the income elasticity of good Z. State what kind of good Z is (inferior, necessity, or luxury?)

Hint: To obtain the effect of Income only, you need to look for where income is changing, but prices of Y and Z are constant.

2. Compute cross-price elasticity of demand for good Z with respect to the price of good Y. State if goods Y and Z are complements or substitutes

Hint: you need to look for where the price of Y is changing, but the income and price of Z are constant.

3. What would happen to the quantity of Good Z if income increases, and the price of Y decreases? (increase, decrease, or ambiguous?) Explain

Hint: consider the two effects one by one. What happens to the Quantity of Z when income increases? Then what happens to the quantity of Z when Price of Y decreases? Then put the two effects together to suggest a net effect.

Income	Quantity of Good Y Purchased	Quantity of Good Z Purchased	Price of GoodY	Price of Good Z
$35,000	25	20	16	30
$35,000	35	15	10	30
$45,000	45	18	10	30

Answer 1

Income elasticity = % Change in quantity due to change in income / % Change in Income

Income elasticity of product Z

% Change in income = {($45000 - $35000) / $35000 } * 100 = 28.57%

% Change in Quantity = {( 15 - 18) / 15 } * 100 = 20%

= Income elasticity of Product Z = 20%/28.57% = 0.70 ( Less the unitary elastic)

Inferior Goods have negative income effect and Necessity or luxury goods has positive income effect. Which means with the increase in Income quantity demanded for inferior goods decreases and quantity demanded for necessity and luxury goods increases. If Income elasticity is more than 1 then it is a luxury goods and if it is less than 1 then it is a necessity goods.  Hence Product Z is a necessity product Since with the increase in income quantity demanded of product Z is Increases and the income elasticity is less then 1.

Cross Price elasticity :- It represent the responsiveness of change in quantity demanded of one product Due to change in the price of other goods.

Cross price elasticity of Product z is calculated where Price of product Z and Income is constant.

= % Change in quantity of product Z / % Change in Price of product Y

% Change in quantity of product Z = {(20 -15) / 20 } * 100 = 25%

% Change in Price of Product Y = {( 16 - 10) / 16 } * 100 = 37.5%

Cross price elasticity = 25% / 37.5% = 0.67 ( Less then Unitary elastic)

Substitute goods can be used as a second choice goods. They can use at the place of one another. There is positive effect of Change in quantity of one product and Change in price of other product.

Complementary goods are used together. There is negative effect of Change in quantity of one product and Change in price of other product.

Goods Y and Goods Z are Substitute goods. When price of Y decreases people move to consumption of product Y and quantity demanded of product Z will decreases.   

Effect of change in income and price of y on quantity demanded of product Z

Product P has less then 1 income elasticity which shows effect of increase in income on the quantity demanded of product Z is less. Hence Quantity demanded increases with the increase in income.

Product P and Product Y are substitute goods and if price of Y decreases then quantity demanded of product Z is also decreases.

Income elasticity is more then the cross price elasticity which means increase in income has more effect on quantity of product Z as compare to decrease in price of product Y.

Hence Quantity of product Z will increases.