Macroeconomics: Aggregate Demand, Equilibrium Dynamics and Expenditure Multipliers

Question

I am having a hard time with the following economic questions (See attached). Here is my approach:

Note about the curves: The graph below depicts an economy where a decline in aggregate demand has caused a recession. Assume the government decides to increase government purchases as fiscal policy to reduce the burden of this recession.

1. How much does aggregate demand need to increase to reach long-run equilibrium?

   A: 100 billion Because that's the AD1-AS equilibrium to AD1-LRAS line

2. MPC =.75 (and thus MPS = .25)

   How much do government purchases need to increase to shift aggregate demand by the amount you found in part 1)?

   My logic: The expenditure multiplier = 1/MPS = 1/(.25) =4

   Delta Y from 1) is 100 billion

   Therefore, 4X= 100 (x = government purchases) leading to x = 25

3. Suppose the MPC is 0.6. To restore the economy to its long-run equilibrium, aggregate demand must be increased by i) ___________ and government purchases must be increased by ii) ________________

   Delta Y is the same as 1), so it's 100 billion for i)

   MPS changes to .6, so the multiplier is 1/.4 = 2.5, 100/2.5 = 40 billion in government purchases to restore long-run equilibrium.

So then, how are my answers wrong according to the program?

Answer 1

1. In shifting the$\ AD_1 \rightarrow AD$ curves to achieve long run equilibrium, Real GDP will have to increase by 200 billion. Refer to the diagram below, (in purple).

2. $\ MPC = 0.75 \rightarrow MPS = 0.25$

In this 3 sector closed-economy model, the multiplier can be calculated using :

$$\ K = \frac{1}{MPS+MPT} $$

Assuming MPT (Marginal Propensity to Tax) = 0, then $\ K = \frac{1}{MPS} = \frac{1}{0.25} = 4 $

$\ \Delta Y=K\Delta (AE) $, considering only government expenditure, then $\ \Delta Y=K\Delta G $

Substituting the values, $\ 200B = 4G \rightarrow G = 50 $

3. If currently, the $\ AD $ component is $\ AD = 400B $ at $\ MPC = 0.75 $, then we can calculate the original income, $\ Y = (0.75)^{-1} \times AD = (0.75)^{-1} \times 400Bil = 533.33Bil $

Now using this value of $\ Y $, we can calculate the new $\ AD $ component at $\ MPC = 0.6 $, which is $\ AD_{new} = 0.6 \times 533.33Bil = 320Bil $

Hence, using the same approach as in Part 1, the lime-green line is $\ AD_{new} $, the purple section represents $\Delta AD, $ which, as in Part 2, with a new multiplier of $\ K $ calculated using the new $\ MPS = 0.4 $, and substituting those values into $\ \Delta Y=K\Delta G $ will result in your new government expenditure.

Answer 2

1. 200 billion

Look at P = 80. If you shift the aggregate demand curve over by 100, the AD curve will intersect the LRAS at P = 80 instead of P = 100. You need to shift it by 200.

2. 50

Since the answer to 1 has changed so has 2.

3. 80 billion

Same as 2.