Suppose all of the firms in a small sconomy satisfy the conditions for efficiency except for one firm, LuthorCorp, which is a monopolu producer of computer anti-virus programs. LuthorCorp is also the only hirer of anti-virus program engineers in this economy. Suppose the production function for anti-virus program is Q=F(L)=2L, where L is the number of anti-virus program engineers hired. Assume also that the demand for anti-virus programs is given by Q^D=100-P, and the labor supply curve for anti-virus program engineers is given by w=20/2L
a) How many anti-virus programs will LuthorCorp make in order to maximize profits? At this level of output, what will L, w re nd P be? What are LuthorCorp's profits, PI? What is the consumer surplus enjoyed by anti-virus program buyer, CS?
b) What would be the outcome if LuthorCorp behaves as a competitive firm in the market for anti-virus programs, but remained an oligopoly purchaser of labor? Once again, solve for Q, L, w, P, PI, and CS.
c) Finally, what would be the outcome if LuthorCorp behaves as a competitive firm in both the output and labor markets? Again, solve for Q, L, w, P, PI, and CS.
Please refer to the attachment.
Production: Q = F(L) = 2L
Demand: Qd = 100-P, or P = 100 - Q
Labour Supply: w = 20 + 2L
a) For the firm, the total revenue is P*Q = 100Q - Q^2
Substitute Q = 2L: TR =100*2L - (2L)^2 = 200L - 4L^2
Also, the firm's total cost is TC = wL = (20+2L)L = 20L + 2L^2
Then profit = TR - TC = 200L - 4L^2 - (20L + 2L^2) = 180L - ...
The total profit of the firm is discovered.