Question

You own and operate PC’s R Us, a firm that manufactures customized computers to meet the specifications of universities that offer online MBA programs. Nearly 70% of your customers are Webster University MBA students. Your firm is not the only business that makes the custom computers, but competes with other firms that sale via retail channels as well as by mail-order and online. You differentiate your product from that of your competitors by offering 2 years of free onsite repair for any system you sell. Because you wish to know more about the underlying market conditions that impact your business, you decide to trade a Webster Business 6120 student a free computer for a study on your firm’s demand and cost structure. The study results are:
Yearly cost of producing computers is: C(Q) = 20,000 + 2Q2 , where ‘Q’ represents the number of computer systems produced.
Marginal Cost (MC) = 4Q
Yearly demand for computers is: Q = 1,000 – P, where ‘P’ represents the selling price of a computer system.

a. How many PC’s should you produce to maximize profits?

b. If you charge the profit maximizing price, what is your firm’s profit or loss?

c. How much does the last unit you produce cost you to make?

d. How can you keep your profits from eroding over time as the market matures?

Answer 1

Ok well here is what I have so far:
a.
MC (Q) = MR (Q) P = MC
P = 1000 – Q & C (Q) = 20,000 + 2Q2
MR = a + 2bQ
MR = 1000 – 2Q
MC = 4
1000 – 2Q = 4
6Q = 1000
Q = 167 units
= 20,000 + 2(167) ^2
=$75,778
MC = 668
MR = 666
P = $833

b.
Profits are given by the difference between revenues and costs
= P*Q* - C (Q*)
= 833* 167 – 20,000 + 2(167) ^2
= 139,111 – 75,778
= $63,333 Profit

c.
The marginal cost curve intersects the average total cost curve and the average variable cost curve at their minimum points. The reason is that ATC and AVC are averages of the cost of the first unit of output, the second unit, and so on. If the average is falling, the last unit must have a cost below the average, in order to be bringing down the average. If the average is rising, the last unit must have a cost above the average, in order to be bringing up the average

d.
Due to the free entry of monopolistic markets, if we are earning a profit in the short run additional firms will probably enter the market too, in the long run to capture some of those profits. As new firms enter the market they will make different PC’s and offer other service plans, setting themselves apart from us. Some of our consumers will then use the newer firms PCs and substitute for our PC. As the demand curve decreases where it is just tangent to our average cost curve, we’ll be earning probably no profits and other firms won’t enter the market. So, for us to be successful over time we’ll have to charge a price that exceeds the MC of producing our PCs.

How close am I?

Answer 2

Take a shot. What do you think?
Hint: always always always, maximize profits where MC=MR.
Hint 2: Total revenue (TR) is P*Q