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 the area below demand curve (DD) AND above price level = the area (1)
On the demand curve, when P=0, Q=420, when Q=0, P=14.
So consumer surplus = 1/2*(14-7)*210 = 735 thousand$
The total benefit = consumer surplus + spending = 735+ 1470 = 2205 thousand$
c) However, the producer surplus is the area above supply curve (SS) AND below price level = the area (2) = 1/2*7*210 = 735 thousand$
Total revenue = total spending by consumers = ...