Final answer:
The introduction of a lump-sum tax of $100 with an MPC of 0.5 will lead to a $200 decrease in equilibrium GDP due to the multiplier effect.
Step-by-step explanation:
When introduced in an economy, a lump-sum tax decreases disposable income, which in turn lowers consumption based on the marginal propensity to consume (MPC). If the MPC is 0.5, this indicates that for every dollar of increased income, consumption will increase by 50 cents. Conversely, if income falls by $100 due to a new tax, it is expected that consumption will decrease by $50 (0.5 * $100).
The decrease in consumption will have a subsequent multiplier effect on the equilibrium GDP. The size of the multiplier is determined by the formula 1/(1 - MPC). In this case, with an MPC of 0.5, the multiplier would be 2 (1/(1-0.5)). Therefore, the decrease in GDP would be the tax increase ($100) times the multiplier (2), resulting in a $200 decrease in equilibrium GDP.