Consider the Keynesian model at the Maple Application Center.
The equations of the model are:
(1) C = a + b(Y-T)
(2) I = e - fR
(3) Md/P = h + iY - jR
Parameters:
a = 1200, b = 0.8, e = 600, f = 10, h = 500, i = 1, j = 100
Exogenous variables:
G = 3000, T = 1000, M = 10000, P = 0.5
Questions
1. Use the equilibrium condition in the goods market to obtain the IS equation.
2. Use the equilibrium condition in the money market to obtain the LM equation.
3. Write the IS and LM equations in matrix form, AX = B, where X is the 2x1 matrix of unknowns (Y and R).
4. Use Cramer's Rule to solve for Y and R. [Check your results with those on the Maple website: Y = 19833.]
5. Plot the IS and LM equations. Note that the intersection point corresponds to the equilibrium values in Q. 4.
6. Increase G by 300. Using revised IS and LM equations, obtain the corresponding output and interest rate. Has the increase in government spending caused output to rise or fall? What about interest rates?
7. Continue with the problem in Q.6. Plot the new IS and LM curves. Has the IS curve has shifted to the right or left? How about the LM curve?
8. Go back to the original parameter values. Suppose money supply falls by 1000, ceteris paribus. Find Y and R. Has the decrease in money supply caused output to increase or decrease? How about the interest rate?
9. Problem 8 continued. Plot the new IS and LM curves. Has the IS curve shifted to the left or right? How about the LM curve?
10. Show that an increase in taxes, ceteris paribus, will cause the IS curve to shift to the [insert right or left] _____________. Further, this will lead to [insert higher or lower] _____________ GDP and [insert higher or lower] _____________ interest rates.