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Demand and Supply Curve, Consumer Surplus and Producer Surplus, Deadweight Loss (DWL) and Tax

Suppose that the market demand for bus rides is given by Q=420-30P and the market supply of bus rides is given by Q=30P, where Q is bus rides per week in thousands and P is the price per bus ride in dollars.

a. Find the equilibrium price/quantity combination for bus rides.
b. How much is spent on bus rides? What is consumer surplus in dollars at this equilibrium? How much is the total benefit in dollars from bus rides?
c. How much does it cost to provide these bus rides? What is producer surplus in dollars at this equilibrium? How much is the bus companies' total revenue?
d. Graph your results (please be explicit).

Suppose that the state government decides to tax bus rides in an attempt to reduce its budget deficit. The tax is $2 per bus ride. The tax will be collected by the bus companies and remitted to the state government.

a. Find the new equilibrium prices to bus riders and to bus companies, the new equilibrium quantity and total tax payments in dollars to the state government (Remember: Ps=Pb-T).
b. What is the deadweight loss in dollars due to the tax?

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Solution Preview

Demand curve is: Q=420-30P (1)
Supply curve is: Q=30P (2)
a) at the equilibrium, both curves meet each other. So we should find Q and P which satisfy equation (1)& (2)
Use basic calculation, substitute (1) into (2): 420-30P = 30P
You can find P* = 7, then substitute P* into (2), you can get: Q* = 210 thousand

b) The total spending on bus is: P* Q* = 7*210 = 1,470 thousand$
Please refer to the attached graph, consumer surplus ...

Solution Summary

The solution answers the question(s) below with graphs in an attached Word document.