Suppose the Parameters of the IS Curve Are $\bar { a } _ { i } = 0 , \bar { b } = 0.5 , \bar { r } = 3 \%$

Suppose the parameters of the IS curve are $\bar { a } _ { i } = 0 , \bar { b } = 0.5 , \bar { r } = 3 \%$
and the real interest rate is initially $R = 3 \%$ .
(a) Is the economy in its long-term equilibrium? Explain.
(b) Suppose the real interest rate falls to 2 percent; what happens to the short-run equilibrium, holding everything else constant?
(c) What happens to the short-run equilibrium if $\bar { a } _ { \boldsymbol { g } }$
falls 3 percent, holding everything else constant?
(d) What occurs if the marginal product of capital rises to 5%? What would cause this to happen?