Final answer:
The government purchases multiplier, given an initial marginal propensity to consume of 0.90 and a tax rate of 0.20, is calculated to be 3.57. This means that each dollar of government spending results in a $3.57 increase in total economic output.
Step-by-step explanation:
The government purchases multiplier can be calculated given the marginal propensity to consume (MPC) and the tax rate. Since MPC is given as 0.90 and the tax rate is 0.20, first we need to adjust the MPC to account for the tax leakage, which would give us an after-tax MPC equal to MPC multiplied by (1 - tax rate), which is 0.90 * (1 - 0.20) = 0.72. Next, we'll use the formula for the government spending multiplier: multiplier = 1 / (1 - MPC), which becomes 1 / (1 - 0.72) after plugging in the adjusted MPC.
The calculation then is 1 / (1 - 0.72) = 1 / 0.28 = 3.57. Hence, the government purchases multiplier is 3.57. This multiplier signifies that for every dollar of government spending, total economic output increases by $3.57, assuming no other changes in the economy.