ISI 2005 - IS LM Query

[MohitG]

5. Consider an IS–LM model. In the commodity market let the consumption function be given by C = a + b Y, a>0, 0< b <1. Investment and government spending are exogenous and given by I0  and G0 respectively. In the money market, the real demand for money is given by L = kY – gr, k> 0, g >0. The nominal money supply and price level are exogenously given at M0 and P0 respectively. In these relations C, Y and r denote consumption, real GDP and interest rate respectively.
(i) Set up the IS – LM equations.
(ii) Determine  how an  increase  in  the  price  level   P1, where P1  > P0,  would affect real GDP and the interest rate.
Please explain the second part, I am kinda stuck.

[Akshay Jain]

after setting up the IS-LM equations...substitute the value of int rate from LM equation into the IS equation and u will get the aggregate demand curve for the economy......now the effect of change in price on output will be
change in Y = dY/dP *(P1-P0)
now u have the equation of AD curve Y=function(...)
put this value of Y in LM equation and get an equation in the form of int rate = function(...)
change in int rate = di/dP *(P1-P0)

[MohitG]

Thanks a lot Akshay.....man you're a savior. Keep up the good work. Thanks again

[Dheeraj]

But I think there is no interest rate in IS equation i.e. IS equation is independent of interest rate because INvestment is exogenous at Io.
  Here IS equation is:  Y= (a + Io + Go)/(1-b) i.e. IS curve is vertical implying that at every interest rate Y is constant.

    and LM equation is an upward sloping curve. With increase in price level, real money supply decreases, which shifts LM curve upward. With this interest rate increases and real GDP remains same.