Question

The number of taxicabs in Motorville and the taxicab fares are regulated. The fare currently charged is Rs.500 a ride. Motorville taxicab drivers want to obtain government's permission to raise the fare to increase their revenues and ask you to be their economic adviser. After studying the market, you come up with the following demand schedule for taxicab rides:
Price (Rupees per ride) Quantity demanded (rides per month)

300 160

400 120

500 80

600 40

700 0



(i) Calculate the price elasticity of demand for taxicab rides as the fare rises from Rs.500 to Rs.600. Is the demand price elastic or inelastic for this fare rise? (2 Marks)

(ii) What happens to the taxicab drivers' total revenue if the fare rises from Rs.500 to Rs.600? How can you use your answers in part “a” to answer this question? Should the drivers try to obtain permission to raise the fare? (2 Marks)

(iii) Calculate the price elasticity of demand for taxicab rides as the fare falls from Rs.500 to Rs.400. Is the demand price elastic or inelastic for this fare decrease?



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Answer 1

Answer:

The answer is below

Explanation:

i) The price elasticity of demand is given by the formula:

$Price \ elasticity\ of \ demand=\frac{\Delta Q}{\Delta P} =\frac{\frac{Q_2-Q_1}{(Q_2+Q_1)/2} }{\frac{P_2-P_1}{(P_2+P_1)/2} } \\\\Price \ elasticity\ of \ demand=\frac{\frac{40-80}{(40+80)/2} }{\frac{600-500}{(600+500)/2} }=\frac{-2/3}{2/11} =3.667 (ignore \ the\ sign)$

Since the price elasticity of demand is greater than 1 hence it is elastic

ii) Since the price elasticity of demand is elastic as a result of increase in fare, hence the total revenue would decrease.

iii)

$Price \ elasticity\ of \ demand=\frac{\Delta Q}{\Delta P} =\frac{\frac{Q_2-Q_1}{(Q_2+Q_1)/2} }{\frac{P_2-P_1}{(P_2+P_1)/2} } \\\\Price \ elasticity\ of \ demand=\frac{\frac{120-80}{(120+80)/2} }{\frac{400-500}{(400+500)/2} }=\frac{0.4}{-2/9} =1.8 (ignore \ the\ sign)$

Since the price elasticity of demand is greater than 1 hence it is elastic