Please can you give some ideas on how to solve the problem, even if you can't help with the final solution..Thank you!

The demand for bus transportation in a small city is P=100-Q, where P is the price of the bus fare, and Q are rides per month (units=10,000 rides).

(a) What is the revenue function for bus rides? Plot this function.

(b) How many rides per month will maximize revenue, i.e., what is the Q value from the revenue function in (a) which maximizes revenue?

(c) What is the demand elasticity at the revenue maximizing level of Q, to the left of this point (rides fewer than the revenue-maximizing level), and to the right of this point (rides greater than the maximizing revenue point?

(d) From your answer in (c) what is the relationship between dR/dQ and the demand elasticity? Note: R is revenue, and Q is rides, so dR/dQ is change in revenue with the number of rides.

(e) Suppose the operating costs of provisioning bus service is: C= 20Q, and the goal of the transportation authority is to maximize revenues less costs (net operating profit). What number of rides maximizes net-operating profit?

(f) Given your answer in (e), what is the bus fare the transportation authority should charge to maximize its net-operating profit

Solution Summary

Demand elasticity is found here. Revenue functions or bus rides are plotted.

... price elasticity Q1 = original quantity demanded Q2 = new quantity demanded P1 = Original ... value of elasticity is 1, arc price elasticity of demand is unit ...

... absolute value of elasticity is less than 1, income elasticity is inelastic. ... effect of each of the following on the quantity demanded or the demand for new ...

... (thetimes100, 2009) We can show this in a simple formula: Price elasticity demand = percentage change in quantity demanded divided by percentage change in the ...

... this in a simple formula: Price elasticity demand = percentage change in quantity demanded divided by percentage change in the price of the goods Hence PEoD ...

... the percentage change in quantity demanded is greater ... Based on this relative elastic demand, I would ... the different types of product elasticity demands that are ...

... It is calculated by using the formula: price elasticity of demand= percentage change in quantity demanded divided per percentage change in price. ...