Softco is a software company that sells a patented computer program to businesse

Question

Softco is a software company that sells a patented computer program to businesses. It operates

with TVC = Q2

a. The firm faces a market demand represented by P = 100 %u2013 5Q.a. Suppose the firm sets the uniform price that maximizes profit. What would that price

be?

b. Suppose the firm were able to act as a perfect first degree price-discriminating

monopolist. Draw out the graph including the following: MR curve, D curve, MC curve,

the lowest price they will sell at, and label producer surplus.

c. Using the same demand curve with MC = 20, graph what block tariff would look like if I

told you the firm maximizes their block by charging a second block of P2 = 40 , Q2 =4 .

Label P1, P2, Q1, Q2, and the profit earned by the company. What is the total profit?

d. Assume that there are 2 markets for your good and you are operating with the same

marginal cost curve as in part C, MC = 20.

Explanation / Answer

a. The firm faces a market demand represented by P = 100 %u2013 5Q.a. Suppose the firm sets the uniform price that maximizes profit. What would that price be?

TVC = Q^2 ;

MC = dTVC/dQ = 2*Q ;

TR = Q*(100-5*Q) = 100*Q - 5*Q^2

MR = 100 - 10*Q ;

MC = MR ;

2*Q = 100 - 10*Q

Q = 100/12 ;

P = 100 - 5*100/12 = $58.33

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