Question

The following equations describe an economy. (Think of C, I, G, etc., as being measured in billions and I as a percentage; a 5 percent interest rate implies I=5).

C = 0.8 (1 – t) Y

                              t = 0.30

                              I = 1000 – 50 i

G= 500

                              L = 0.25Y – 65 i

M/P = 700

                       

1. Derive the IS equation.

AD = C + I + G + NX

AD = 0.8 (1 – t) Y + 1000 – 50i + 500

AD = 0.8 (1 – 0.3) Y + 1500 – 50i

             At equilibrium AD = Y so

                        Y= 0.8 (1 – 0.3) Y + 1500-50i

                        Y- [0.8 (1 - .3) Y]=1500 – 50i

                        Y[1 – (0.8(1 - .3))] = 1500 – 50i

                        Y= [1/ (1- (0.8 (1- 0.3))] x (1500- 50i)

                        Y= 2.27(1500 – 50i)

                        Y= 3405 – 113.5i

2. Derive the LM equation.

M-bar/P-bar = L

700= .25Y – 65i

0.25Y = 700 +65i

Y= 4(700 + 65i)

Y= 2800 + 260i

3. What are the equilibrium levels of income and interest rate?

3405 – 113.5i = 2800 + 260i

3405 – 2800 = 113.5i + 260i

605= 373.5i

i= 1.62

Y= 2800 + 260(1.62)

Y= 3221.2

4. What is the value of a_G which corresponds to simple multiplier with taxes?
   1. AG= 2.27 (First question)
5. What would be the new equilibrium levels of income and interest rate if the congress passed a tax-cut and the new tax rate was 25%, and concurrently, people became less frugal and consequently marginal propensity to consume increases to 0.90.
6. If the increased spending overshoots and the economy starts to experience inflation, calculate the new levels of equilibrium income and interest rate if the new Federal Reserve decided to curb spending and by lowering the real money supply to 550?
7. For each step, graph the IS and LM curves and clearly show their movements for the problems above. Although the graph needs not to be precise, you must clearly show if IS or LM curves shifted or tilted and in which direction.

Answer 1