Finding Total Cost Curves
For each of the following production functions and prices find TC, VC, FC, ATC, AVC,
AFC, and MC, when K is fixed at 3. Where do MC and AVC cross? Where do MC and
ATC cross. Repeat for K fixed at 8, 20. Now assume that K can vary but that L is fixed
by the union at 5, 10, 14.
f(L,K)
w=5, v=5
.5 .5
L K
L1K.5
L.5K2
L.25K.25
L.25K.5
min(6L,4K)
min(5L,2K)
min(L2,K)
3L+9K
4L+3K
6L+K
w=2, v=7
w=4, v=6
w=2, v=2
w=6, v=3
Find LRATC and LRMC for each production function and set of factor prices given
above.
Competitive Model
Assume that the firms described above are in a competitive market.
Find the firms’ optimal quantities and associated profits in the short run if the market
price is 5, 20, 66, and 100. What is the shutdown price for the firm? What is the
breakeven price for the firm?
What quantity will each firm produce in the long run? What would be the long run
equilibrium price faced by each firm (assuming the firm is representative of others in the
industry).
If demand is given by P=1000-Q and there are 10 firms in the industry, what are the
profits to an individual firm? Will there be entry or exit? How many firms will be in the
market in the long run? Repeat for 5 firms and 25 firms. Repeat for demand given by
P=500-Q, P=2000-2Q, demand arising from 20 people who each have utility expressed
by u(x,y)=x2y where these firms are producing x and each person has income of 300 and
Py=7.
For a Demand Curve in column 1 and a Supply Curve in column 2 find Pe, Qe, CS and
PS.
Demand Equations
Supply Equations
P=100-Q
P=200-2Q
P=75-3Q
P=57-2Q
P=40
P=2Q
P=Q+20
Q=20
P=Q-25
P=15+3Q
Application of Competitive Model
For any Supply and Demand Curve given above what would be the impact of
1) a price floor of 10, 35, 50, 80?
2) a price ceiling of 10, 35, 50, 80?
3) a price support program with a target price of 15, 20, 45, 60?
4) a price guarantee program with a target price of 15, 20, 45, 60?
5) opening the market to the world economy when the world price is 10, 25, 55, 70?
6) placing a quota of 10, 20, 35 units when the world price is 10, 25, 55, 70?
7) placing a tariff of 3, 5, 10 per unit when the world price is 10, 25, 55, 70?
8) a per unit tax of 2, 5, 10, 20 per unit imposed on sellers in the market?