Problem 1. Suppose the demand curve for a good is given by the equation P = 200 - .5Q, and the supply curve is given by the equation P = 50 + .25Q, where P = price and Q = quantity.
A. What are the equilibrium price and quantity?
B. Suppose a sales tax of $9/unit is levied. Find the new equation for demand, the new equilibrium Q, the post tax price received by suppliers, and the post tax price paid by demanders.
C. What portion of the tax falls on buyers? What portion falls on sellers?
Problem 2. A firm’s total cost schedule and the demand for its product are summarized in the table below.
Costs Revenues
Q $TC MC Q $P TR MR
0 0 0 155
1 70 1 150
2 142 2 145
3 217 3 140
4 297 4 135
5 385 5 130
6 485 6 125
7 603 7 120
A. Complete the table and use the equimarginal principle to determine the level of output that maximizes the firm’s profit. Also determine the price charged by the firm and its maximum profit level.
B. What would happen to your answers if the firm’s total costs rose by $ 40?
C. What would happen to your answers if the firm’s costs rose by $ 40 per unit?