The government of Halvard plans to change its purchases by dG (a bridge, or a cut). Output Y is in millions of base-year crowns per year, the interest rate r is a fraction (5 % is 0.05), T is a fixed tax, G government purchases, M the money supply and P the price level:
- goods market: output equals planned spending, Y = C + I + G, with consumption C = c_0 + c_1 \, (Y - T) and investment I = i_0 - i_1 \, r;
- money market: the real money supply equals real money demand, \dfrac{M}{P} = k \, Y - h \, r.
The economy is in its IS-LM equilibrium: the one pair (Y, r) that clears both markets.
Extra purchases raise output, so people want more money, so the rate rises, so firms invest less: private investment is crowded out. To see how much, compare with the Keynesian-cross change: the change in equilibrium output the same dG would cause if the interest rate stayed at its old value.
Write crowding_out(e, dG) that returns a tuple (dY, dr, dY_cross, lost), all as changes caused by adding dG to G with everything else fixed:
dY,dr: the change in IS-LM equilibrium output and interest rate;dY_cross: the Keynesian-cross change in output;lost: the investment lost, planned investment before minus planned investment after (negative if investment rises).
The tests build each economy with the helper economy(c0, c1, T, i0, i1, G, k, h, M, P), which returns the dict {"c0": c0, "c1": c1, "T": T, "i0": i0, "i1": i1, "G": G, "k": k, "h": h, "M": M, "P": P}; you may use it too.
Examples
Input: e = economy(100, 0.75, 100, 300, 2000, 200, 0.5, 4000, 1300, 2), dG = 100
Output: (200.0, 0.025, 400.0, 50.0)
Explanation: equilibrium moves from (1700, 0.05) to (1900, 0.075). At the old rate the
multiplier 1 / 0.25 = 4 would give 400 more. The rate rise cuts investment
from 200 to 150.
Input: e = economy(100, 0.75, 100, 300, 2000, 200, 0.5, 4000, 1300, 2), dG = -40
Output: (-80.0, -0.01, -160.0, -20.0)
Constraints
- answers are compared with a tolerance of
1e-6; do not round
Goals
- Find how an IS-LM equilibrium moves when government purchases change
- Compare the IS-LM effect with the Keynesian-cross multiplier at a fixed rate
- Measure crowding out as the private investment lost to a higher rate