After a scare about the future, the households of Lindhaven decide to save more: at every income they now consume thrift less than before, so autonomous consumption falls from c0 to c0 - thrift. All amounts are millions of crowns per year, and the model is
- consumption: C = c_0 + c_1 \, (Y - T), with a fixed tax
T - planned investment: I = I_0 + d \, Y (firms invest more when output is high;
d >= 0) - government purchases
Gare fixed - equilibrium: Y = C + I + G
with c1 + d < 1. Household saving is disposable income not consumed: S = (Y - T) - C.
Write belt_tightening(c0, c1, I0, d, G, T, thrift) that returns a tuple (Y_before, Y_after, S_before, S_after): equilibrium output and household saving at equilibrium, before and after the change.
Examples
Input: c0 = 100, c1 = 0.75, I0 = 150, d = 0, G = 200, T = 160, thrift = 20
Output: (1320.0, 1240.0, 190.0, 190.0)
Explanation: households try to save 20 more, output falls by 80, and at the lower income
they end up saving exactly as much as before.
Input: c0 = 100, c1 = 0.75, I0 = 150, d = 0.05, G = 200, T = 160, thrift = 20
Output: (1650.0, 1550.0, 272.5, 267.5)
Explanation: now investment falls with output too, and saving ends up lower than before.
Constraints
- answers are compared with a tolerance of
1e-6; do not round
Goals
- Compute equilibrium output and household saving before and after a shift towards thrift
- Show that in this model total saving cannot rise when investment is fixed
- See saving fall when investment rises with income