Final answer:
The change in permanent income, Δyp, is determined by the multiplier effect and is usually larger than the initial change in government spending, Δgl.
Step-by-step explanation:
The change in permanent income, Δyp, is likely to be different from the change in government spending, Δgl. In this case, the question assumes that there is a permanent increase in government expenditures equal to Δg1, which is then financed by an increase in lump sum taxes. The change in permanent income, Δyp, refers to the change in income level that occurs in response to the permanent increase in government spending. It is determined by the multiplier effect, which represents the magnification of the initial change in spending throughout the economy.
The multiplier effect is calculated by taking the reciprocal of the marginal propensity to save (MPS). In this case, the MPS is equal to 0.1, meaning that 10% of additional income is saved. Therefore, the multiplier is equal to 1/MPS = 1/0.1 = 10. This means that a $1 increase in government spending will lead to a $10 increase in permanent income. So, if Δg1 = $1, then Δyp = $10.
In summary, the change in permanent income, Δyp, is determined by the multiplier effect and is usually larger than the initial change in government spending, Δgl. In this case, if Δg1 = $1, then Δyp = $10.