During the Enlightenment, the City of Calgary had a more-or-less free market in
taxi services. Any respectable �rm could provide taxi service as long as the drivers and cabs
satis�ed certain safety standards. Let us suppose that the constant marginal cost per trip of
a taxi ride is $5 and that the average taxi has a capacity of 20 trips per day. Let the demand
function for taxi rides be given by D(p) = 110020p, where demand is measured in rides per
day, and price is measured in dollars. Assume that the industry is perfectly competitive.
a. What is the competitive equilibrium price per ride? What is the equilibrium
number of rides per day? What is the minimum number of taxi cabs in equilibrium?
b. During the Calgary Stampede (big outdoor show), the in
ux of tourists raises
the demand for taxi rides to D(p) = 1500 20p. Find the following magnitudes, based
on the assumption that for these 10 days in July, the number of taxicabs is �xed and
equal to the minimum number found in part (a): equilibrium price; equilibrium number
of rides per day; pro�t per cab.
c. Now suppose that the change in demand for taxicabs in part (b) is permanent.
Find the equilibrium price, equilibrium number of rides per day, and pro�t per cab per
day, How many taxi cabs will be operated in equilibrium? Compare and contrast this
equilibrium with that of part (b). Explain any di�erences.
d. With care and precision on one diagram, graph the three di�erent competitive
equilibria found in part (a) through (c). In each case identify the supply curve, the
demand curve, and the equilibrium price and quantity.
a. To find the competitive equilibrium price per ride, we need to set the quantity demanded equal to the quantity supplied. In a perfectly competitive market, the quantity supplied equals the quantity demanded at equilibrium.
Given the demand function D(p) = 1100 - 20p and assuming constant marginal cost per trip of $5, we can find the equilibrium price by setting demand equal to supply:
Demand = Supply
1100 - 20p = 5 * Q
where Q represents the number of rides per day.
To find the equilibrium quantity of rides per day, we need to solve for Q. Rearranging the equation:
1100 - 20p = 5Q
Now, we know that the average taxi has a capacity of 20 trips per day. So the number of taxis required to meet the equilibrium quantity (Q) is:
Minimum number of taxis = Q / 20
b. During the Calgary Stampede, the demand for taxi rides changes to D(p) = 1500 - 20p, while the number of taxis remains fixed at the minimum number found in part (a). We can follow the same steps as before to find the equilibrium price and quantity:
1500 - 20p = 5Q
The equilibrium price and quantity can be calculated by solving this equation, and we can use the minimum number of taxis found in part (a) to determine the profit per cab.
c. If the change in demand from part (b) becomes permanent, we can determine the new equilibrium by using the updated demand function. We follow the same steps as before:
Demand = Supply
1500 - 20p = 5Q
Once again, we solve for equilibrium price and quantity and use the minimum number of taxis to calculate the profit per cab per day.
d. To graph the three different competitive equilibria, we can use a supply-demand diagram. In each case, we plot the demand curve and the supply curve and find the intersection point, which represents the equilibrium price and quantity.
- In Part (a), the demand curve is D(p) = 1100 - 20p, the supply curve is a horizontal line at $5 per trip, and the equilibrium is the intersection point.
- In Part (b), the demand curve is D(p) = 1500 - 20p, the supply curve is the same as before (horizontal line at $5 per trip), and the equilibrium is the intersection point.
- In Part (c), the demand curve remains D(p) = 1500 - 20p, but the supply curve may change based on the number of taxis operating in equilibrium. So, the vertical position of the supply curve may shift, and the equilibrium is the new intersection point between the updated supply curve and the demand curve.
On the graph, we label each equilibrium point with the corresponding equilibrium price and quantity.