Problem Set #6: Answer Key
1.
a) Qd = 100
–
2P, Qs = 10 + P
Thus equilibrium price and quantity is 100
–
2P = 10 + P
90 = 3P
P = 30, Q = 40.
Now, if a price floor is instituted at $35, Qd = 30, Qs = 35+10 = 45. Therefore, we have excess supply
in the market of 15 units.
b) Before Price Floor:
CS: (1/2) (40) (20) = 400
PS: (30) (10 + 40) (1/2) = 750 (Note in this case the Producer Surplus is a trapezoid!)
TS: CS + PS = 400 + 750 = 1150
After Price Floor:
CS: (1/2) (30) (15) = 225
The calculation of the producer surplus is a little more complicated. Referring to the graph, we first
calculate the area of A and then the area of B.
A: (15) (30) = 450
B: (20)(0.5)(10+30) = 400
So, P.S. = 850
TS: CS + PS = 1075
2.
a) Equilibrium Price and Quantity in the short run:
10000
–
200 P = 2000 + 800P
1000P = 8000
P = 8.
To determine quantity, we plug the price back into either the demand or supply equation. So, Q =
10000
–
200(8) = 10000
–
1000 = 9000 units.
b)
. Note here that variable costs are that portion of the cost function
which varies with the amount of output produced.
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c) In the short run, all firms will produce where P = MC, in a perfectly competitive industry. This leads
to
q = 150 units. Profits are equal to the difference between total revenue and total
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 Winter '09
 STEVENS
 Supply And Demand, producer, tax burden

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