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Consider an IS/LM model of an economy with the following equations :

C = 220 + 0.75Yd
I= 165 - 10i
G= 490
TR = 300
T = 0.15Y
L = 0.2Y - 3i
M/P= 550
(a) Using the above data, derive the equation for the IS curve.
(b) What is the equation for the LM curve?
(c) Calculate the equilibrium level of income and interest rates.Sketch the relevant diagram.
(d) What are the monetary values of the monetary policy multipler with respect to income and interest rates? If the money supplied is reduced by 50, what are the new market-clearing income and interest rate levels?

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Final answer:

To determine the equilibrium level of income in this Keynesian model, we sum the components of aggregate expenditure (AE) and set AE equal to Y. We then solve for Y. To reach a potential GDP of 3,500, we can either solve for the required level of G directly or use the multiplier to find the necessary change in G.

Step-by-step explanation:

To find the equilibrium for the economy given the parameters, we use the Keynesian cross model where equilibrium is when aggregate expenditure (AE) equals national income (Y). The aggregate expenditure is the sum of consumption (C), investment (I), government spending (G), exports (X), and minus imports (M). The consumption function is C = 400 + 0.85(Y - T), and taxes (T) are T = 0.25Y.

First, we calculate the equilibrium by setting Y equal to AE and solving for Y. We find that AE = C + I + G + X - M. Substituting the expressions for each component into the AE formula and then solving for Y provides the equilibrium level of income.

Next, to achieve a potential GDP of 3,500, we adjust government spending (G). We can do this directly by plugging 3,500 into the equilibrium equation and solving for G. Alternatively, we use the multiplier approach to find out by how much government spending should be adjusted. The multiplier is calculated as 1/(1-MPC(1-T)), where MPC is the marginal propensity to consume, and T is the tax rate.

User Scott Heath
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