Question

In: Economics

Consider a goods market in the following situation. (1) Aggregate demand: Z=C+I+G (2) Aggregate supply: Y=Z...

Consider a goods market in the following situation.

(1) Aggregate demand: Z=C+I+G

(2) Aggregate supply: Y=Z

(3) C(Consumption)=c0+c1(Y-T),

(4) I(investment)=a0/i, i=policy interest rate

(5) (Exogenously given) G=government spending, T=government tax revenue

(a) Represent Y∗ as a function of exogenous variables, parameters, policy interest

(b) Suppose that the central bank of this country announces the policy rate cut. Assess

the effects of the lowered policy rate on the aggregate product by taking derivative.

(c) How will your answer in (b) change if the investment function is changed to

I=a0/i+a1C ? What is a rationale for assuming an investment function like this?

Solutions

Expert Solution

(a) The the aggregate demand would be as or . The equilibrium would be where or or or . Deducing it further, we have .

(b) We have , meaning that there is a negative association between Y* and i. If the interest rate decreases, then the equilibrium output would increase, by about or . Note that the basic assumption here is .

(c) For this new investment function, the equilibrium would be as where or or or or or .

In this case, we have , and the change dependes on the value of a1. That means, if , then for a decrease in i, the equilibrium output would increase by about .

If , which is not likely to happen, then the opposite would occur.

Rahul Sunny answered 7 months ago
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