For each of the following cases, calculate the arc price elasticity of demand, and state whether demand is elastic, inelastic, or unit elastic. a. When the price of milk increases from $2.25 to $2.50 per gallon, the quantity demanded falls from 100 gallons to 90 gallons.
b. When the price of paperback books falls from $7.00 to $6.50, the quantity demanded rises from 100 to 150.
c. When the rent on apartments rises from $500 to $550, the quantity demanded decreases from 1,000 to 950.

a. Arc price elasticity of demand = - 1. The demand is unit elastic.

b. Arc price elasticity of demand = - 5.40. The demand is elastic.

b. Arc price elasticity of demand = - 0.54. The demand is inelastic.

Explanation:

The formula for calculating arc price elasticity of demand is as follows:

Arc price elasticity of demand = Percentage change in quantity demanded / Percentage change in price (1)

Where, based on the arc price elasticity of demand, we have:

Percentage change in quantity demanded = {(New quantity demanded - Old quantity demanded) / [(New quantity demanded + Old quantity demanded) / 2]} * 100

Percentage change in price = {(New price - Old price) / [(New price + Old price) / 2]} * 100

Therefore, we have:

a. When the price of milk increases from $2.25 to $2.50 per gallon, the quantity demanded falls from 100 gallons to 90 gallons.

Percentage change in quantity demanded = {(90 - 100) / [(90 + 100) / 2]} * 100 = -10.5263157894737%

Percentage change in price = {(2.50 - 2.25) / [(2.50 + 2.25) / 2]} * 100 = 10.5263157894737%

Substituting the values into equation (1), we have:

Arc price elasticity of demand = -10.5263157894737% / 10.5263157894737% = - 1

Since the absolute value of the arc price elasticity of demand is equal to 1, it implies that the demand is unit elastic.

b. When the price of paperback books falls from $7.00 to $6.50, the quantity demanded rises from 100 to 150.

Percentage change in quantity demanded = {(150 - 100) / [(150 + 100) / 2]} * 100 = 40%

Percentage change in price = {(6.50 - 7.00) / [(6.50 + 7.00) / 2]} * 100 = -7.40740740740741%

Substituting the values into equation (1), we have:

Arc price elasticity of demand = 40% / -7.40740740740741 = - 5.40

Since the absolute value of the arc price elasticity of demand is equal to 5.40 which is greater than 1, it implies that the demand is elastic.

c. When the rent on apartments rises from $500 to $550, the quantity demanded decreases from 1,000 to 950.

Percentage change in quantity demanded = {(950 - 1000) / [(950 + 1000) / 2]} * 100 = -5.12820512820513%

Percentage change in price = {(550 - 500) / [(550 + 500) / 2]} * 100 = 9.52380952380952%

Substituting the values into equation (1), we have:

Arc price elasticity of demand = -5.12820512820513% / 9.52380952380952% = - 0.54

Since the absolute value of the arc price elasticity of demand is equal to 0.54 which is less than 1, it implies that the demand is inelastic.