Q3 consider a market with inverse demand p100 2q where q is...

Q3): Consider a market with (inverse) demand p=100-2Q (Where Q is total quantities produced by the two firms). There are two firms producing q1 and q2 respectively in the market with constant marginal and average costs of $10. One correctly predicts he is the leader. a. Determine the Cournot equilibrium quantities and price. b. What would be the collusive (joint-profit maximizing) price and quantity? c. What is the Stackelberg solution (P, q).

Transcript

00:01 Two parts at part a we need to find out nash equilibrium quantity nash equilibrium quantity.

00:08 So how we can find out for form 1 this is equals to phi 1 is equals to 16 minus q 1 minus q 2 multiply by q 1 minus c q 1.

00:23 So here after solving it we got 16 minus 2 q 1 minus q 2 multiply by q 1 taking derivative.

00:32 So we got d q 1 divided by d pi 1 divided by d q 1 is equals to 16 minus 4 q 1 minus q 2 is equals to 0 from here we got q 1 is equals to 16 minus q 2 divided by 4 similarly we can calculate proper form 2 so here pi 2 is equals to 16 minus q 1 minus q 2 is equals to multiply by q 2 minus c q 2 from here.

01:06 We got 16 minus q 1 minus 7 q 2 multiply by q 2 now again taking a derivative.

01:14 We got d pi 2 divided by d q 2 so here 16 minus q 1 minus 14 q 2 is equals to 0 and we find q 2 is equals to 16 minus q 1 divided by 4.

01:30 So these are the quantities we got now substituting we can substitute here substitute the expression for q 1 for form 1 into equation q 2 so here we got q 2 is equals to 16 minus 16 minus q 2 divided by 14.

01:55 So here we got 14 14 q 2 is equals to q 2 where q 2 is equals to 0 now substituting q 2 0 is equals to expression 1 for q 1 so here q 1 is equals to 16 minus 0 divided by 4 so q 1 will be 4 now therefore the equilibrium quantities we got q 1 is 4 and q 2 is 0 now solve it for b to find the value of x we could cause form 2 will not produce anything in equilibrium.

02:29 Okay, so form 2's profit is pi 2 is equals to 16 minus q 1 minus q 2 multiply by q 2 minus c q 2 from here...

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