#3.)
a) Compute the marginal cost curve for Ajax

Solution:

The marginal cost is the first derivative of the total cost curve w.r.t. Q

MC=dTC/dQ

= -5000 + 2*100Q

= 200Q-5000

b) Given Ajax's pricing strategy, what is the marginal revenue function for Ajax

Solution:

The price charged by the Ajax is taken from the market and not decided based on its supply curve so we have

MR=P=$20,000

c) Compute the profit-maximizing level of output for Ajax

Solution:

The profit maximizing output is the output when MC=MR

So we have

200Q-5000=20000

Q=125

d) Compute Ajax's total dollar profits

Solution:

Total Profits = Total revenue – Total cost

Total revenue = P*Q = 20000*125=2,500,000

Total cost = 800000-5000*125+100*125*125 = 1,737,500

Total Profits = 762,500

#5.)

a)

The demand function can be written as

P = 12 – Q/10000 ………………………………………………. (1)

TR = P*Q = 12Q – Q2/10000

b)

MR = dTR/dQ = 12 – Q/5000

c)

TC = 12000 + 1.50Q

d)

MC = dTR/dQ = 1.50

e)

TR = 12Q – Q2/10000 - 12000 - 1.50Q

First order condition for maximization: dTR/dQ = 0 implies

12 – Q/5000 -1.50 = 0, solving this, we get profit maximizing output i.e.

Q*= 52500

Profit maximizing price i.e. P* = 12 – 52500/10000 = 12-5.25 = 6.75

And the profit = 6.75*52500 - 12000 - 1.50*52500 = 263625

f)

We equate MR with MC

12 – Q/5000 = 1.50, solving this we get Q* = 52500

This output level is exactly same to the output level obtained by maximizing Profit in part e)

g)

The model of marketing pricing behavior assumed here is monopoly as monopoly always tries to maximize its profit.

#11.)

A.)

Total assets= $500,000

Profit = (250-.15Q)*Q-(25000+10Q)

1st order condition of profit maximization:

d(profit)/dQ=0

or, 250-.3Q=10

or, Q=240/.3=800

P=250-(.15*800)=130

Profit