The number of taxicabs in Motorville and the taxicab fares are regulated. The fare currently charged is $5 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: a) Calculate the price elasticity of demand for taxicab rides as the fare rises from $5 to $6. (Use the midpoint method in your calculations.) Is the demand price elastic or inelastic for this fare rise? b) What happens to the taxicab drivers' total revenue if the fare rises from $5 to $6? How can you use your answers in part a to answer this question? Should the drivers try to obtain permission to raise the fare? c) Calculate the price elasticity of demand for taxicab rides as the fare falls from $5 to $4. (Use the midpoint method in your calculations.) Is the demand price elastic or inelastic for this fare decrease? d) What happens to the taxicab drivers' total revenue if the fare falls from $5 to $4? How can you use your answers in part c to answer this question? Should the drivers try to obtain permission to lower the fare? e) What fare will maximize the taxicab drivers' total revenue? Explain.

a) When the fare rises from $5 to $6, the number of rides decreases from 80 to 40. The percentage change in the quantity demanded is the change in the number of rides, 40, divided by the average number of rides, 60, multiplied by 100 or (40/60 ) × 100, which is 66.7 percent. The percentage change in the price is the change in the price, $1, divided by the average price, $5.50, multiplied by 100, or ($1/$5.50 ) × 100, which is 18.2 percent. So the price elasticity of demand is 66.7%/18.2%, which equals 3.67. The demand is elastic because the elasticity, 3.67, exceeds 1.
b) A direct calculation shows that the total revenue decreases from $400 ($5 × 80 ) to $240 ($6 × 40 ). In part a, we calculated that the demand is elastic. When the demand is elastic, the decrease in the number of rides decreases the total revenue by more than the rise in fare increases it and so, on net, total revenue falls. Therefore the drivers should not try to raise the fare.
c) When the fare falls from $5 to $4, the number of rides increases from 80 to 120. The percentage change in the quantity demanded is the change in the number of rides, 40, divided by the average number of rides, 100, multiplied by 100 or (40/100 ) × 100, which is 40.0 percent. The percentage change in the price is the change in the price, $1, divided by the average price, $4.50, multiplied by 100, or ($1/$4.50 ) × 100, which is 22.2 percent. So the price elasticity of demand is 40.0%/22.2%, which equals 1.80. The demand is elastic because the elasticity, 1.80, exceeds 1.

d) Once again a direct calculation show that in this case the total revenue increases from $400 ($5 × 80 ) to $480 ($4 × 120 ). In part c, we calculated that the demand is elastic. When the demand is elastic, the increase in the number of rides increases the total revenue by more than the fall in fare decreases it and so, on net, total revenue rises. Therefore the drivers should try to lower the fare.
e) Total revenue is maximized at the point where the price elasticity of demand is 1. On a straight-line demand curve, demand is unit elastic at the midpoint. The demand curve intersects the price axis at $7, so the midpoint on the demand curve is where the price is $3.50. This fare will maximize the taxicab drivers' total revenue.