Suppose the marginal propensity to consume is 0.75. If businesses become more optimistic about the future and raise their investment by $10, the short-run equilibrium output will _____________________ and consumption will _________________.

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First, identify the given values and the relationships involved. The marginal propensity to consume (MPC) is 0.75, so the consumption response to income changes is MPC × ΔY. The investment increase is ΔI = +$10. The simple Keynesian multiplier is 1 / (1 − MPC) = 1 / (1 − 0.75) = 1 / 0.25 = 4. This multiplier tells us how much the equilibrium output (Y) changes in response to a new autonomous spending, in this case the rise in investment.

Option A: 'increase by 40; increase by 7.5.' Here, the output change of +$40 is correct for ΔY = multiplier × ΔI (4 × 10 = 40). However, the implied change in consumption is +$7.5, which would correspond to MPC × ΔY = 0.75 × 40 = 30, not 7.5. Therefore, this option misstates the consumption effect.

Option B: 'increase by 10; stay the same.' An increase in output of only +$10 ignores the multiplier effect entirely; with a 4× multiplier, we should see a much larger ΔY. Additionally, stating that consumption stays the same contradicts the positive income rise, which would raise consumption via MPC.

Option C: 'increase by 40; stay the same.' The output change of +$40 is consistent with the multiplier calculation, but saying consumption stays the same ignores the induced consumption from higher income (MPC × ΔY). Since income increases, consumption should rise by 0.75 × 40 = 30.

Option D: 'increase by 40; increase by 30.' This aligns with the multiplier result ΔY = 4 × 10 = 40, and then the induced consumption change is MPC × ΔY = 0.75 × 40 = 30, matching the stated increase in consumption. The two figures are internally consistent under the model assumptions.

Option E: 'increase by 10; increase by 7.5.' Again, the output change is incorrect given the multiplier, and the consumption change 7.5 would require a ΔY of 10, which is not compatible with the baseline multiplier analysis. Moreover, 0.75 × 10 would be 7.5, but that contradicts the proper ΔY derived from the investment shock.

In summary, the internally consistent pair of changes—output rising by 40 and consumption rising by 30—follows from applying the multiplier to the investment shock and then applying the MPC to the resulting income change. The remaining options fail to match either the multiplier-driven output response or the induced consumption given the MPC.

ECO102H1 S LEC0101 Week 6 Quiz - Business Cycles and Aggregate Expenditure

Suppose the marginal propensity to consume is 0.75. If businesses become more optimistic about the future and raise their investment by $10, the short-run equilibrium output will _____ and consumption will _.

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