Demand Curve and Profitable Pricing Strategy

Introduction to Microeconomics
Study case 1
The following is from the Washington Post, October 24, 1996:
"For whom the Booth tolls, Price Really Does Matter"
By Steven Pearlstein
"All business faces a similar question: What price for their product will generate the maximum profit? The answer is not always obvious: Raising the price of something often has the effect of reducing sales as price-sensitive consumers seek alternatives or simply do without. For every product, the extent of that sensitivity is different. The trick is to find the point for each where the ideal tradeoff between profit margin and sales volume is achieved. Right now, the developers of a new private toll road between Leesburg and Washington-Dulles International Airport are trying to discern the magic point. The group originally projected that it could charge nearly $2 for the 14-mile one-way trip, while attracting 34,000 trips on an average day from overcrowded public roads such as nearby Rout 7. But after spending $350 million to build their much heralded “Greenway”, they discovered to their dismay that only about a third that number of commuters were willing to pay that much to shave 20 minutes off their daily commute…It was only when the company, in desperation, lowered the toll to $1 that it came quite close to attracting the expected traffic flows."
Please answer the following questions.
* Based on the data given in the article above, write down (a linear approximation of) the (daily) demand curve that the firm faces.


Revenue

Price

Quantity

(Price *Quantity)

2

34,000/3

22666.67

1

34000

34000.00

P = -(Q/ 22667) + 2.5
OR
Q = -22667P + 56667
* Assuming that marginal cost is nearly zero, what is the price that maximizes the firm’s daily profit? (Hint: use the demand curve you estimated in part (a) above).
Marginal Revenue (MR) ($34,000.00 - $22,666.67) / (34,000.00 - 11,333.33) = $ 0.5
At the profit maximization point marginal revenue (MR) is equal to the marginal cost (MC or MC=MR.
c.Can you suggest a more profitable pricing strategy for the firm (there is no need for any calculations here, just give the general idea)?
Increasing the price is associated with lower demand, especially among the price-sensitive road users (consumers), and determining the price elasticity of demand for different road users is helpful. The income elasticity of demand measures the responsiveness of the quantity demanded changes as consumer income changes (Mankiw, 2020). One way to apply the principle of elasticity of demand is by considering differential pricing. Differential pricing is...