Question

Consider an economy with autonomous consumption of 700, marginal propensity to consume of 0.8 , net income taxes of 100 , investment spending of 300 , government spending of 250, and net export of 80 .

a) Derive and state the aggregate planned expenditure function for this economy.
b) What is the value of autonomous aggregate planned expenditure when real GDP of the country is $1000 ?
c) What is the value of induced aggregate planned expenditure when real GDP of the country is $1000 ?
d) What is the value of equilibrium aggregate expenditure?
e) What is the value of unplanned changes in the inventory investment when real GDP is $7000?
f) How would the graph of the aggregate planned expenditure change if net export increases by 20 ? What would be the value of the new equilibrium real GDP?
g) What is the multiplier for this economy?
h) Verify your answer to part f using the multiplier: solve for the value of new equilibrium real GDP in the same scenario using the multiplier this time.

Answer 1

The aggregate planned expenditure function for this economy is
`AE = C + I + G + X - M.` The autonomous aggregate planned expenditure when real GDP is $1000 is $1500. The induced aggregate planned expenditure when real GDP is $1000 is $3500.

Step-by-step explanation:

The aggregate planned expenditure function for this economy can be derived by summing up the components of aggregate expenditure: consumption, investment, government spending, and net exports. In this case, the aggregate planned expenditure function is:
`AE = C + I + G + X - M.`

The value of autonomous aggregate planned expenditure when real GDP is $1000 is $1500.

The value of induced aggregate planned expenditure when real GDP is $1000 is $3500.

The value of equilibrium aggregate expenditure can be found by setting aggregate planned expenditure equal to real GDP. In this case, the equilibrium aggregate expenditure is $5000.

The value of unplanned changes in the inventory investment when real GDP is $7000 is $0.

If net exports increase by 20, the graph of the aggregate planned expenditure will shift upwards, leading to a new equilibrium real GDP of $1500.

The multiplier for this economy can be calculated as
`1 / (1 - MPC)`, where MPC is the marginal propensity to consume. In this case, the multiplier is
`1 / (1 - 0.8) = 5.`

Using the multiplier, the new equilibrium real GDP can be calculated by multiplying the change in autonomous expenditure (in this case, the change in net exports) by the multiplier and adding it to the initial equilibrium real GDP. In this case, the change in net exports is 20, so the new equilibrium real GDP is
`$1000 + (20 * 5)`
`= $1100`