In the valley of Tarrow, workshops borrow to buy new machines, and they buy fewer when borrowing costs more. All amounts are millions of crowns per year, and the interest rate r is a fraction (5 % is 0.05). Planned investment is
but firms never plan negative investment: if i_0 - i_1 r is below zero, I = 0. Households pay a fixed tax T and consume C = c_0 + c_1 \, (Y - T), where c1 is the marginal propensity to consume; government purchases are G. For a given interest rate, the goods market is in equilibrium when output equals planned spending:
The pairs (interest rate, equilibrium output) form the IS curve: the output that clears the goods market at each rate.
Write is_curve(c0, c1, T, i0, i1, G, rates) that returns one pair (I, Y) for each rate in rates, in the same order: planned investment at that rate and the equilibrium output.
To draw the IS curve the way economists do (output across, the rate up), collect the outputs in a list outputs and press Run with plot(outputs, rates).
Examples
Input: c0 = 100, c1 = 0.75, T = 100, i0 = 300, i1 = 2000, G = 200, rates = [0.02, 0.05, 0.1]
Output: [(260.0, 1940.0), (200.0, 1700.0), (100.0, 1300.0)]
Explanation: at r = 0.05 investment is 300 - 2000 * 0.05 = 200, and
Y = 100 + 0.75 * (1700 - 100) + 200 + 200 = 1700.
Input: c0 = 100, c1 = 0.75, T = 100, i0 = 300, i1 = 2000, G = 200, rates = [0.15, 0.2]
Output: [(0.0, 900.0), (0.0, 900.0)]
Explanation: at r = 0.2 the formula gives -100, so firms invest nothing.
Constraints
- answers are compared with a tolerance of
1e-6; do not round
Goals
- Compute planned investment that falls as the interest rate rises, with a floor at zero
- Solve the goods market for output at each given interest rate
- Read the list of (rate, output) pairs as the IS curve