Question

You are the manager of a small company that operates in a perfectly competitive market. You observe that the number of firms in the market has increased intensifying competition. You believe that this trend may continue until next year because several foreign companies have expressed interest entering the U.S. market. Concerned by the changing market conditions, you decided to examine the degree of profitability of your business next year. You hired an economist to estimate the market demand and supply functions for the product and he obtained the followings: ​​​​​​​​​

Where P is price, M is income, and is the price of a key input.

According to just released government data, forecasts for the next year are M = $10,000 and = PI = $20.

Furthermore, you estimate that your production cost next will be:

C (Q) = 6,000 + 14Q – 0.008Q2 + 0.000002Q3

a. What is the price forecast for next year?

b. What will be the profit-maximizing output choice for the company?

c.. What will the firm’s profit (loss) be?

d. Will the company stay in the industry (continue production) or exit in the long run? Explain.

Qd = 25,000 - 5,000P + 25M

Qs = 240,000 + 5,000P - 2,000PI

Answer 1

a) Price forcast for next year------

Where Qd=Qs

25000-5000p+25M. = 240000+5000P-2000pI

As,M=$10000& PI= $20,putting these values in equations----

25000-5000P +25(10000). = 240000+5000P-2000(20)

275000-200000=10000P

P= 7•5$

price forcast for next year=$7•5

b)profit maximising output for company is determined where marginal revenue( MR) equals marginsl cost ( MC)

Finding MC-----

TC(Q)=6000+14Q-0•008Q²+•000002Q³

MC=derivative of TC(Q)-----

MC=14-2(•008)Q+3(•000002)Q²

13•984+•000006Q²

Finding MR-------

Q=275000-5000P

(p after puttingM=10000)

Or

P= 55-(1/5000)Q

As ,TR=AR×Q---

PQ= 55Q-(1/5000)Q²

MR = derivative of TR-----

MR= 55-•0004Q

We know ,at profit maximising point of output ----

MR=MC

55-•0004Q= 14-•016Q+•000006Q²

•000006Q²-•0156Q-41=0

Using quadratic equations ,

-b±√b²-4ac/2a

We get Q= 4050 units

profit maximising output = 4050 units

C)firm' s profit/ loss will be ----: TR-TC

Putting value of Q in TR & TC equations-----

TC= 6000+14(4050)-•008(4050)²+•000003(4050)³

TC= 58340$

TR=

55Q-1/5000(Q)²

55(4050)-1/5000(4050)²

TR= 219470$

Profit= 219470-58340=$161130

profit=$161130

d) yes, the firm will stay in the industry in the long run.,as in the long run ,its prices will occur at minimum of AC.