More Economics Help

[COntr]

Hi, I was working on a couple economics problems in my textbook, and I came across one that I wasn't quite sure how to handle. I was hoping anyone here could help. By the way, this is a problem (Ch. 12 Ex. 6) taken from Pindyck/Rubinfeld's Microeconomics: Sixth Edition

Suppose that two identical firms produce widgets and that they are teh only firms in the market. Their costs are given by C1 = 60Q1 and C2 = 60Q2, where Q1 is output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve:

P = 300 - Q

where Q = Q1 + Q2

a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equlilibrium. (I actually got this part)

b. Suppose the two firms form a cartel to maximize join profits. How many widgets will be produced? Calculate each firm's profit.

c. Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1's profit differ from that found in part (b) above?

d. Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm's profits?

Thanks!

 

[Mo0o]

If you want help you gotta put some effort into it, show how far you've gotten

 

[COntr]

Well for (a), this is what I did.

I took the derivative of my profit function:
Profit1 = (300-Q1-Q2)Q1 - 60Q1 = 240Q1 - Q1^2 - Q1Q2
Derivative: 0 = 240 - 2Q1 - Q2 --> Q1 = 120 - 0.5Q2
(Firm 2 is the same with the Q's switched places)

Then substituted to solve for Q
Q1 = 120 - 0.5(120 - 0.5Q1)
Q1 = Q2 = 80

Plugged in 80 to the demand function:
P = 300 - 80 - 80 = 140

Plugged in to solve for profit:
Profit = (140 - 60)80 = 6,400

 

[DaWhim]

for part c, output is the same as part b, but firm 1 will make all the profit. already forgot how to do the math part, but use the monopoly function

 

[COntr]

Thanks, I think I got it.