When the price of a cruise rises from $19,500 to 20,500, the quantity demanded d

Question

When the price of a cruise rises from $19,500 to 20,500, the quantity demanded decreases from $2,100 to 1,900 travelers.

1. Use this information to calculate the chan in the total revenue of cruise providers is? ( how many?)

2. Base on that, the concepte of price elasticity of demand is useful beacuse if cruise providers know the price elasticity of demand for cruises, they can predict how total revenue will change when the price of a cruise changes. Is that Ture?

3. If the demand curve for cruises is a straight line, the price at which the demand is unit elastic is above or below $20000 a cruise?

Explanation / Answer

(1) Total revenue, TR = Price (P) x Quantity (Q)

When P = $19,500, Q = 2,100 & TR = $19,500 x 2,100 = $40,950,000

When P = $20,500, Q = 1,900 & TR = $20,500 x 1,900 = $38,950,000

Change in TR = $(38,950,000 - 40,950,000) = - $2,000,000 (Decrease)

(2) True.

Price elasticity = % Change in quantity demanded / % Change in price

So, if Elasticity & change in price is known, change in quantity can be computed and change in total revenue can be computed.

(3) Equation of linear demand curve: P = a - bQ

Using data,

19,500 = a - 2,100b ....(1)

20,500 = a - 1,900b ....(2)

(2) - (1) gives: 1,000 = 200b

b = 5

a = 19,500 + (2,100 x 5) = 19,500 + 10,500 = 30,000

So, equation of demand curve is:

P = 30,000 - 5Q

When Q = 0, P = 30,000. This is the vertical intercept of demand curve. Demand is unit elastic at the midpoint of demand curve, i.e. when P = 30,000 / 2 = 15,000 which is below $20,000.

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