uppose that, within the simple Keynesian model used in S ection 1 8.4, the level

Question

uppose that, within the simple Keynesian model used in S ection 1 8.4, the level of government spending ( G ) was 100, the level of investment spending ( I ) was 75, and consumption ( C ) was given by C = 25 + 0.8YD

Net taxes ( T ) are initially given by the tax function T =-50 + 0.30Y

Calculate equilibrium income (Y). Now suppose that the tax rate is decreased from 0.30 to 0.25. Find the new level of equilibrium income. Compute the values of the autonomous expenditure multiplier before and after the tax cut.

Explanation / Answer

The components of aggregate demand (AD) are as follows: AD= C+I+G+NX where C: Consumption, I: Investment, G: Government Spending and NX: Net Exports. This example is that of a closed economy which means that there is no ‘net exports’ involved.

From the given information, we know that the aggregate consumption function is given by C = 25 + 0.8YD where YD is disposable income (income left after payment of taxes) given by (Y-T). The intended investment is 75 and the level of government spending ( G ) was 100. Net taxes ( T ) are initially given by the tax function T = -50 + 0.30Y

Here Y is the income and output where Y=C+I+G+NX.

Thus, Y = 25 + 0.8YD + 75 + 100

Or Y = 25 + 0.8(Y+50-0.30Y) + 175

Or Y = 200 + 0.8Y + 40 – 0.24Y

Or Y- 0.56Y = 240

Or Y = 545.45

Thus the equilibrium income when tax rate = 0.30 is Y = 545.45 units.

When the tax rate changes from 0.30 to 0.25, the tax equation becomes T = -50 + 0.25Y

Thus,

Y = 25 + 0.8YD + 75 + 100

Or Y = 25 + 0.8(Y+50-0.25Y) + 175

Or Y = 200 + 0.8Y + 40 – 0.2Y

Or Y- 0.6Y = 240

Or Y = 600

Thus the equilibrium income when tax rate = 0.30 is Y = 600 units. The income/output Y rises because a fall in tax rate raises the disposable income and in turn raises consumption thereby stimulating Y.

The formula of autonomous expenditure multiplier is given by:

1/{1- MPC* (1-t)} where MPC is the marginal propensity to consume and t is the tax rate.

The MPC is given by the value 0.8 which is the slope of the consumption function

Therefore autonomous expenditure multiplier before tax cut when tax rate is 0.30 = 1/ {1- 0.8* (1-0.3)} = 2.273

Similarly, autonomous expenditure multiplier after tax cut when tax rate is 0.25 = 1/ {1- 0.8* (1-0.25)} = 2.50.

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