If you assume that deadweight loss from taxes is zero (and that it cannot be negative, which I admit being uncomfortable with as a concept but suspect is generally considered a condition), then the only way to have dP/dG be positive is for (r^d - g) to be more negative than employment hysterisis.
That seems to eliminate the possibility of the market being efficient by making investors (who demand r^d) believe the opposite of workers (g^[exp] < g). If you are requiring "premature capital optimism" as a condition for growth, the role of government should be to sustain lower rates for longer than necessary (the Powell Doctrine?).
Given that, the Second Run (which I doubt more than the third, while the first is obvious) doesn't require a surplus, but just a reduction in deficit, assuming that fiscal policy is run rationally; that is, that the power to tax that is required for sovereignty is available and used. (G spends an extra $1B in a recession; over the next five years, it spends less than that/taxes back some of the capital gains made due to sustained lower rates. No requirement to balance the budget so long as debt service is maintained and pay downs are possible.)
If you assume that deadweight loss from taxes is zero (and that it cannot be negative, which I admit being uncomfortable with as a concept but suspect is generally considered a condition), then the only way to have dP/dG be positive is for (r^d - g) to be more negative than employment hysterisis.
That seems to eliminate the possibility of the market being efficient by making investors (who demand r^d) believe the opposite of workers (g^[exp] < g). If you are requiring "premature capital optimism" as a condition for growth, the role of government should be to sustain lower rates for longer than necessary (the Powell Doctrine?).
Given that, the Second Run (which I doubt more than the third, while the first is obvious) doesn't require a surplus, but just a reduction in deficit, assuming that fiscal policy is run rationally; that is, that the power to tax that is required for sovereignty is available and used. (G spends an extra $1B in a recession; over the next five years, it spends less than that/taxes back some of the capital gains made due to sustained lower rates. No requirement to balance the budget so long as debt service is maintained and pay downs are possible.)