The government of Harlow plans a budget. Equilibrium output Y (millions of crowns per year) satisfies
with a fixed tax T (the same whatever the income), planned investment I, government purchases G and a marginal propensity to consume c1 with 0 < c1 < 1. The tax multiplier is the change in equilibrium output per one-crown rise in T, all else fixed (so it is negative). The budget balance is T - G: positive for a surplus, negative for a deficit.
A budget proposal changes purchases by dG and taxes by dT (either may be negative or zero). Write budget_plan(c0, c1, I, G, T, dG, dT) that returns a tuple (tax_multiplier, dY, balance): the tax multiplier, the change in equilibrium output caused by the whole proposal, and the budget balance after it.
Examples
Input: c0 = 60, c1 = 0.8, I = 150, G = 200, T = 200, dG = 50, dT = 50
Output: (-4.0, 50.0, 0.0)
Explanation: the extra purchases alone would add 50 * 5 = 250, the extra taxes alone
take away 50 * 4 = 200. Output rises by 50 although the budget stays balanced.
Input: c0 = 60, c1 = 0.8, I = 150, G = 200, T = 200, dG = 0, dT = -25
Output: (-4.0, 100.0, -25.0)
Constraints
- answers are compared with a tolerance of
1e-6; do not round
Goals
- Derive the tax multiplier and explain why it is smaller than the spending multiplier
- Combine a change in purchases and a change in taxes into one change of output
- See that a tax-financed rise in purchases still raises output in this model