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Consumer spending initially rises by 5 billion for each 1% increase in household wealth. Investment spending initially increases $20 billion for each 1% decrease in real interest rate. The multiplier is 4.

If house household wealth decreases by 5% and real interest rate falls by 2%, (1) in what direction and by how much will aggregate demand shift at each price level. (2) In what direction and by how much will it eventually shift.

$$\quad -5\% \quad \text{in} \quad HH\quad { Y }_{ d }\text{ } \Longrightarrow \text{ } -$25\text{ }\text{billion in}\text{ } C$$

$$\quad -2\%\quad \text{in}\quad i\text{ } \Longrightarrow \text{ } +$40\text{ }\text{billion in}\text{ } { I }_{ g }$$

If I treat aggregate demand the same way as aggregate expenditure (is this right?), then with government spending and exports constant, the initial change is

$$-$25\quad billion\quad +\quad $40\quad billion\quad =\quad +$15\quad billion$$

and for the long term we use the multiplier,

$$\Delta C\quad =\quad -$25\quad billion\quad \times \quad 4\quad =\quad -$100\quad billion$$

and

$$\Delta I\quad =\quad $40\quad billion\quad \times \quad 4\quad =\quad $160\quad billion$$

So the long term change is +$60 billion? (i.e. curve shift out to the right)

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