International economics keynesian goods market

Consider the following model for the macroeconomy.

Consumption Function: C = a + b∙Y

Import Function: IM = k + m∙Y

Export Function: EX = k* + m*∙Y*

where a, b, k, m, k*, and m* ≥ 0, and G, I, G*, I*, Y* are exogenous variables.

(a) Derive the goods-market equilibrium expression for GDP ( Y ) if the economy is closed (EX = IM = 0). What is the fiscal multiplier, ΔY/ ΔG?

(b) Derive the equilibrium equation for Y if the economy is open. What is the multiplier now?

(c) Derive the equilibrium equation for the trade balance (TB = EX – IM). What is the effect of fiscal policy on TB, ΔTB/ ΔG?

Now consider the following data (in constant, 2005 prices) for Brazil:

billions of real

Year   GDP        C     EX   IM

2001   1,896 1,180   ?    232

2010   2,660 1,702 365 488

(d) Calculate the marginal propensities to consume (b) and import (m) over the 2001-2010 period.

Suppose Brazilian consumers want to reduce their debts, so there is a drop in exogenous consumption, a, by 1% of (2010) GDP. (e) Suppose Brazil is a closed economy. How would this drop in consumer confidence affect output? What fiscal policy (change in G) would prevent this output effect?

(f) Now suppose Brazil is open. How would the drop in consumer confidence affect output and the trade balance? What fiscal policy is needed now to neutralize the output effect?