Question

Given that IS is Y = 2500-50i, and the interest rate reaction function is ip = 2 + 0.5(P-P*), where ip is the central bank policy rate. Assume that i (interest rate) is 0.5 + ip (interest rate is a wedge over the policy rate). Determine the AD function. If AS function was Y = 0.25(P-P*) + 2000 determine Y* and P* and inflation rate. Assume P* = 105.

Answer 1

AD function is

$AD = Y = C + I + G + NX = 2500 - 50(0.5 + 2 + 0.5(P-P*))$

where C is consumption, I is investment, G is government purchases, and NX is net exports.

If AS function was $Y = 0.25(P - P*) + 2000$ then:

$0.25(P - P*) + 2000 = 2500 - 50(0.5 + 2 + 0.5(P-P*))$

$25.25(P - 105) = 375$

$25.25P = 3026.25$

$P = 119.85$

$Y * = 0.25(119.85 - 105) + 2000 = 2003.71$