a. The price elasticity of demand measures the responsiveness of the quantity demanded to a change in price. If the price elasticity is less than 1, it is inelastic; if it is equal to 1, it is unitary elastic; and if it is greater than 1, it is elastic.
b. The same concept applies here. If the price elasticity is -3.25, it is elastic because the absolute value of the elasticity is greater than 1.
2a. If the demand curve is downward sloping, it means that as prices increase, quantity demanded decreases. If the consumer is elastic, it means that small changes in price lead to larger changes in quantity demanded. If the consumer is inelastic, it means that changes in price have a smaller impact on quantity demanded. If the consumer is unitary elastic, it means that changes in price have a proportional impact on quantity demanded.
2b. The same reasoning applies here, but in this case, we are looking at the behavior of consumers at lower prices on the demand curve.
3a. If the good takes up a large portion of the consumer's budget, it is likely to be elastic because consumers will be more responsive to changes in price.
3b. If there are no substitutes for the good, it is likely to be inelastic because consumers have limited options and will be less responsive to price changes.
4a. If the demand curve is a horizontal line, it means that quantity demanded remains constant regardless of price changes. In this case, the demand curve is perfectly elastic.
4b. If the demand curve is a vertical line, it means that quantity demanded is fixed regardless of price changes. In this case, the demand curve is perfectly inelastic.
5. To calculate the price elasticity of demand, we use the formula: (Q2 - Q1) / Q1 divided by (P2 - P1) / P1. Given the values:
Q1 = 40, Q2 = 55, P1 = 8, and P2 = 7, we can plug them into the formula:
((55-40)/40) / ((7-8)/8) = (15/40) / (-1/8) = -0.375 / -0.125 = 3
Since the absolute value of the elasticity is greater than 1, the good is elastic.
6a. If the income elasticity is negative, like -2, it means the good is an inferior good. Inferior goods are those for which demand decreases as income increases.
6b. If the income elasticity is positive, like 10, it means the good is a luxury good. Luxury goods are those for which demand increases as income increases.
7. To calculate the cross elasticity of demand, we use the formula: % change in quantity demanded for X / % change in price of Y. Given the values: % change in quantity demanded = 6% and % change in price = 3%, we can plug them into the formula: 6 / 3 = 2
Since the cross elasticity is positive, the goods are substitutes.
8. To calculate the price elasticity of supply, we use the formula: % change in quantity supplied / % change in price. Given the values: % change in quantity supplied = (80-50)/50 = 60% and % change in price = (13-12)/12 = 8.3%, we can plug them into the formula: 60 / 8.3 = 7.23
Since the absolute value of the elasticity is greater than 1, the good is elastic.