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Assume that you have the following open economy where C = 10 + 0.8(Y-T); I = 10; G = 10; T = 10 and imports and exports are given by IM = 0.3Y and X = 0.3Y* respectively where Y* is foreign output.
Then solve for the equilibrium output in the domestic economy given Y*. What is the multiplier effect for this open economy? What happens to Y and the trade balance over time if Y*'s economy grows faster than Y's economy. Assume the domestic government has a target level of output of 125 and the foreign country does not change G*, what increase in G is necessary to achieve the target output in the domestic economy? What would be the increase in G and T needed if the government wanted to keep a balanced
budget?

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Total output is given by

Y = C + I + G + X - M

Plugging in the values from above we get

Y = 10 + 0.8(Y - 10) + 10 + 10 + 0.3Y* - 0.3Y
or Y = 10 + 0.8Y - 8 + 20 + 0.3Y* - 0.3Y
or Y = 0.5Y + 22 + 0.3Y* (1)
or Y - 0.5Y = 22 + 0.3Y*
or 0.5Y = 22 + 0.3Y*
or Y = 44 + 0.6Y*

Depending on what Y* is the value of Y can be determined using the above formula. Say for example Y* is 100, then Y = 44 + 0.6*100 = 104.

If we assume that in equilibrium Y = Y* then the equation can be solved as

Y = 44 + 0.6Y
or 0.4Y = 44
or Y = 110

The multiplier is given by

Multiplier = 1 / (1 - Slope of AE)

For a given Y* the slope of AE curve is the coefficient of Y on the right hand ...

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