Final answer:
The change in real GDP resulting from an increase in taxes can be calculated using the MPC and the multiplier effect. In this case, with an MPC of 0.67 and an increase in taxes of $1,286, real GDP will change by approximately $2,611.40.
Step-by-step explanation:
The MPC (Marginal Propensity to Consume) determines how much of an increase in income is spent. In this case, the MPC is given as 0.67. When taxes increase by $1,286, this reduces disposable income and therefore reduces consumption. The change in consumption would be equal to the change in taxes multiplied by the MPC. So, the change in consumption would be: $1,286 * 0.67 = $861.62.
According to the multiplier effect, a change in consumption affects overall GDP. The multiplier effect shows how changes in injections or withdrawals from the circular flow of income can result in a larger change in GDP. The multiplier is calculated as 1 divided by (1 - MPC). In this case, the multiplier would be: 1 / (1 - 0.67) = 3.03.
Therefore, to find the change in real GDP, we multiply the change in consumption by the multiplier: $861.62 * 3.03 ≈ $2,611.40. So, holding all else constant, real GDP will change by approximately $2,611.40.