Re: ISI ME II 2014

Posted by Ridhika on May 04, 2014; 9:24am
URL: http://discussion-forum.276.s1.nabble.com/ISI-ME-II-2014-tp7587168p7588489.html

@Shahbaaz and Ron

Q4(a)

This firm wil always produce along L/2 = K/3 => L=(2/3)K

Now to derive the cost function..

To Produce q=1 the firm needs L=2 and K =3. w=r=1.
So C(1) = 2+3 = 5
Similarly C(2) = 4+6 = 10
and C(3) = 6+9 = 16 and so on..

So we see that C(Q) = 5Q

Now if I set up the profit maximization problem:

P = Q(20-Q) - 5Q
dP/dQ => 20 -2Q - 5=0
=> Q = 7.5

This is the unconstrained profit max. This requires k = 3(7.5) = 22.5

Now if K = 24, then the firm will NOT use the full K = 24, it will stick to the solution above.

(ii) if k= 18, Qmax = 6.

At all Q<7.5 MR>MC
so in this case Q = 6

Hope this makes sense..