3. Y=C+I+G C = 120 + .6(Y – T) I=100-10r G = 50 T =...

3. Y=C+I+G C = 120 + .6(Y – T) I=100-10r G = 50 T = 40 $\left(\frac{M}{P}\right)^d$ = Y - 20r, M$^s$ = 600 P = 2 a) Identify each of the variables and briefly explain their meaning. b) Derive the equation for the IS curve, showing Y as a function of r alone. c) Derive the equation for the LM curve, showing Y as a function of r alone. d) Graph both the IS and the LM curves. e) What are the equilibrium level of income and equilibrium interest rate?

Transcript

00:01 In this problem they said that assume that an economy is characterized by as the following.

00:07 So as a first condition here y is equal to c plus i plus g if we put the values into this we will get the equation as y is equal to 100 plus 2 by 3 into y minus 100 y minus 600 plus 800 minus 50 by 3 r plus 500 so by solving this we will get the equation as 100 plus 2 by 3 into y minus 600 400 plus 800 minus 50 by 3 or 50 r by 3 plus 500 so simplifying further we'll get it as y is equal to 2 by 3 y equals to thousand plus 50 r by 3 so you'll get y by 3 x5 by 3 equals to 1 ,000 plus 50 r by 3 which will results into y equals to 3 ,000 plus 50 r so 50r let's consider this as a first equation and coming to the part b where lm is lm curve is so lm curve will be m p equals to 0 .5i minus 50r so by solving this we will get m by p equals to 0 .5i which will get which will take us as 50 plus 50 r equals to 0 .5 so let's consider this as a second equation so here the 50 r equals to 0 .5 will be, sorry, 0 .5i minus m by p.

03:13 So here by swapping the size, we will get the r equals to 0 .54 by 5y by 50, 5 y by 50 minus m by p by 50.

03:38 So by solving this we will get r s 0 .01y minus m by 50.

03:53 So this is the second equation.

03:57 Now coming to the part c where the condition c put value of r from the equation 2 in the equation 1.

04:09 So if we keep the equation 2 value of r value of r of from the equation 2 to from the equation 2 to equation 1 we will get the equation as y equals to 3 ,000 plus 50 into r is 0 .01y minus m by 50 so by solving this we will get the y as 3000 plus 0 .5 minus m by p.

05:05 So where p is equal to here here, p is equal to 1.

05:16 So p is equal to 1.

05:20 Now so we get y as 0 .5i is equal to 3 000 .0 .0 is equal to 3 000...

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