The table shows the average income of households and the quantity demanded of products M and N at different prices and levels of income. Year Average Income Price of M Quantity of M Price of N Quantity of N 1 $44,000 $2.40 105 $18 820 2 44,000 2.70 95 18 800 3 44,000 2.70 85 26 780 4 50,000 2.70 95 26 810 a) What is the price elasticity of demand for product M between years 1 and 2? Round your answers to 2 decimal places. b) What is the price elasticity of demand for product N between years 2 and 3? Round your answers to 2 decimal places. c) What is the income elasticity of demand for product M between years 3 and 4? Round your answers to 2 decimal places. d) What is the income elasticity of demand for product N between years 3 and 4? Round your answers to 2 decimal places. e) What is the cross-elasticity of demand of product M for a change in the price of product N between years 2 and 3? Round your answers to 2 decimal places and remember to enter a minus (−) sign to indicate negative values.

Answer:

Price and Income Elasticity of Demand

Elasticity of demand measures how much the quantity demanded of a product changes in response to a change in price or income. Price elasticity of demand measures the responsiveness of quantity demanded to a change in price. Income elasticity of demand measures the responsiveness of quantity demanded to a change in income. Cross-elasticity of demand measures the responsiveness of quantity demanded of one product to a change in the price of another product.

Price Elasticity of Demand for Product M between Years 1 and 2

To calculate the price elasticity of demand for Product M between Years 1 and 2, we can use the following formula:

Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

In this case, the quantity of Product M demanded decreased from 105 at a price of $2.40 in Year 1 to 95 at a price of $2.70 in Year 2, so the % Change in Quantity Demanded is -10%. The price of Product M increased from $2.40 in Year 1 to $2.70 in Year 2, so the % Change in Price is 12.5%. Using the formula above, we can calculate the Price Elasticity of Demand for Product M between Years 1 and 2 as follows:

Price Elasticity of Demand = (-10%) / (12.5%) = -0.80

Therefore, the Price Elasticity of Demand for Product M between Years 1 and 2 is -0.80.

Price Elasticity of Demand for Product N between Years 2 and 3

To calculate the price elasticity of demand for Product N between Years 2 and 3, we can use the following formula:

Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)

In this case, the quantity of Product N demanded decreased from 800 at a price of $18 in Year 2 to 780 at a price of $26 in Year 3, so the % Change in Quantity Demanded is -2.5%. The price of Product N increased from $18 in Year 2 to $26 in Year 3, so the % Change in Price is 44.4%. Using the formula above, we can calculate the Price Elasticity of Demand for Product N between Years 2 and 3 as follows:

Price Elasticity of Demand = (-2.5%) / (44.4%) = -0.06

Therefore, the Price Elasticity of Demand for Product N between Years 2 and 3 is -0.06.

Income Elasticity of Demand for Product M between Years 3 and 4

To calculate the income elasticity of demand for Product M between Years 3 and 4, we can use the following formula:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

In this case, the quantity of Product M demanded increased from 85 at an average income of $44,000 in Year 3 to 95 at an average income of $50,000 in Year 4, so the % Change in Quantity Demanded is 11.8%. The average income increased from $44,000 in Year 3 to $50,000 in Year 4, so the % Change in Income is 13.6%. Using the formula above, we can calculate the Income Elasticity of Demand for Product M between Years 3 and 4 as follows:

Income Elasticity of Demand = (11.8%) / (13.6%) = 0.87

Therefore, the Income Elasticity of Demand for Product M between Years 3 and 4 is 0.87.

Income Elasticity of Demand for Product N between Years 3 and 4

To calculate the income elasticity of demand for Product N between Years 3 and 4, we can use the following formula:

Income Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Income)

In this case, the quantity of Product N demanded increased from 780 at an average income of $44,000 in Year 3 to 810 at an average income of $50,000 in Year 4, so the % Change in Quantity Demanded is 3.8%. The average income increased from $44,000 in Year 3 to $50,000 in Year 4, so the % Change in Income is 13.6%. Using the formula above, we can calculate the Income Elasticity of Demand for Product N between Years 3 and 4 as follows:

Income Elasticity of Demand = (3.8%) / (13.6%) = 0.28

Therefore, the Income Elasticity of Demand for Product N between Years 3 and 4 is 0.28.

Cross-Elasticity of Demand of Product M for a Change in the Price of Product N between Years 2 and 3

To calculate the cross-elasticity of demand of Product M for a change in the price of Product N between Years 2 and 3, we can use the following formula:

Cross-Elasticity of Demand = (% Change in Quantity Demanded of Product M) / (% Change in Price of Product N)

In this case, the quantity of Product M demanded decreased from 95 at a price of $2.70 in Year 2 to 85 at a price of $26 in Year 3, so the % Change in Quantity Demanded of Product M is -10.5%. The price of Product N increased from $18 in Year 2 to $26 in Year 3, so the % Change in Price of Product N is 44.4%. Using the formula above, we can calculate the Cross-Elasticity of Demand of Product M for a change in the price of Product N between Years 2 and 3 as follows:

Cross-Elasticity of Demand = (-10.5%) / (44.4%) = -0.24

Therefore, the Cross-Elasticity of Demand of Product M for a change in the price of Product N between Years 2 and 3 is -0.24.