isi me 2 2006

[Mauli]

please someone help me with this question.
q1 a . b.
http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/msqe2006.pdf

 guess answers a) max profit when w1=w2  .
L1 =L2 =50.
                     B)
the short run output
 the isoprofit line is y = pie(ie:profit)/p + w/p*x
                when p and w double, y = pie /2p + 2w/2p *x
 clearly the intercept term has become smaller, so the  output will fall  when the price of output and of variable factor doubles.



the short run  profit :
it will double coz earlier the  profit was  = py -wx  ( where x is the variable factor  
                                                                                                w the price of x ,
                                                                                                 p the price of the product and y is

                                                                                                                              the output.)
 now when the price of output  doubles and  w doubles
we have profit = 2py - 2wx = 2(py-wx) =2 * earlier profit.
please confirm these solutions.
thankyou.

[Sumit]

a). Let the cost function for a sector,
C(Li) = Wi*Li
As we Know profit is Maximum for a competitive firm
Where,  MC=P
For Sector-1
MC1=W1   =>  MC1=P----------(1)
Similarly, For Sector-2
MC2=W2   =>  MC2=P----------(2)
From 1 & 2
We get,
MC1=MC2  =>  W1=W2----------(3)
Now, f(Li)=15(Li)^1/2
For Sector-1
MPL=15/2*1/(L1)^1/2 --------------------------(4)
Similarly, For Sector-2
MPL=15/2*1/(L2)^1/2-------------------(5)
We Know that Competitive Firm will hire labor until
MPL=W/P-----(6)
So, From 3, 4 ,5 & 6
We get,
L1=L2=50

[Sumit]

b). profit(π)=Py-wx------(1)
y = π/p + w/p*x
After Doubling the price in of input as well as output we have,
Π’=2Py-2wx
Π’=2(Py-wx)------(2)
From 1 & 2
Π’=2 Π----(3)
Now,
y = π’/2p + 2w/2p*x  => y = 2π/2p +2 w/2p*x --from(3)

=> y = π/p + w/p*x

Which means the demand of input  and production of output by firm will remain same only profit will get double.

P.S: you made a small mistake-output  will not change..

[Mauli]

oh yes!
thanks a lot sumit:)
had i found the profit first, i could have avoided doing this stupid mistake:p
thanks a lot for pointing it out:)

[Sumit]

Hey Mauli,
 from where u're practicing questions on functions,relations and probability distribution??????

[Mauli]

i am doing the maths from sydsaeter and hammonds and probability distributions , i refer john freund.
for relations and functions high school ncert books are also good.

[Sumit]

thanks for prompt reply mauli....