Final answer:
To increase GDP by $160, we can use the multiplier concept. By calculating the multiplier and change in government spending, we can determine how much taxes should be decreased. From the given information, we find that the change in government spending should be approximately $153.6 to achieve the desired increase in GDP.
Step-by-step explanation:
To increase GDP by $160, we need to determine the multiplier and use it to calculate the change in government spending. The multiplier represents the effect that a change in spending has on GDP. From the given information, we know that the tax rate is 0.4 of national income, and the MPC out of the after-tax income is 0.8. To find the multiplier, we can use the formula: 1 / (1 - MPC * (1 - tax rate)). Substituting the values, we get 1 / (1 - 0.8 * (1 - 0.4)) = 1 / 0.96 = 1.0417.
Now, to find the change in government spending necessary to increase GDP by $160, we can use the formula: change in GDP = multiplier * change in government spending. Rearranging the formula, we have: change in government spending = change in GDP / multiplier. Substituting the values, we get a change in government spending = $160 / 1.0417 = $153.6 (rounded to the nearest tenth). Therefore, to increase GDP by $160, we should decrease taxes by approximately $153.6.