Suppose that the consumption function is given by

C = 270 + 0.63×Y - 1,000×R

rather than by the traditional consumption function. Add this consumption function to the other four equations of the macro model:
Y = C + I + G + (X - IM)
M = (0.1583×Y - 1,000×R)×P
I = 1,000 - 2,000×R
X = 525 - 0.1×Y - 500×R.

Assume the price level is 1.0, government spending is $1,200 and the money supply is $900.

a. Derive an algebraic expression for the IS curve for this model and plot it to scale. Compare it with the IS curve with the traditional consumption function. Which is steeper, why?

b. Derive the aggregate demand curve and plot it to scale. How does it compare with the aggregate demand curve with the traditional consumption function?

c. find out the effect of an increase in government spending on GDP. Is the effect larger or smaller than in the case where consumption does not depend on the interest rate? Describe the process of crowding out in this case.

d. find out the effect of an increase in the money supply on GDP. Is the impact larger or smaller than in the case where consumption does not depend on the interest rate? describe