The Fishing Fleet, Year by Year

The fishing town of Corrow measures its capital in boats per fisher, k. Each year every fisher lands

crates of fish (output per worker, with 0 < \alpha < 1). The town follows the Solow model of capital accumulation:

• a fixed share s of each year's output is saved and turned into new boats (investment per worker s\,y_t);
• a share delta of the boats wears out during the year (depreciation);
• the number of fishers grows by a share n a year, so the existing boats are spread over more people.

Capital per worker therefore moves from year t to year t+1 by

where both y_t and the last term use year t's capital. All three rates are fractions: 5 % is 0.05.

Write fleet_path(A, alpha, s, delta, n, k0, T) that returns the list [k_0, k_1, \ldots, k_T] (so T + 1 numbers, starting with k0). Press Run with plot(path) to watch it level off.

Examples

Input:  A = 1, alpha = 0.5, s = 0.2, delta = 0.05, n = 0.05, k0 = 1, T = 3
Output: [1, 1.1, 1.19976177, 1.29885287]
Explanation: in year 0, y = 1, so k1 = 1 + 0.2 * 1 - 0.1 * 1 = 1.1.
In year 1, y = sqrt(1.1) = 1.0488, so k2 = 1.1 + 0.20976 - 0.11 = 1.19976.

Input:  A = 2, alpha = 0.3, s = 0.25, delta = 0.06, n = 0.01, k0 = 20, T = 2
Output: [20, 19.82822803, 19.66530590]
Explanation: the town starts with more boats than its saving can keep up,
so wear and newcomers outrun new boats and capital per worker falls.

Constraints

• answers are compared with a tolerance of 1e-6; do not round

Goals

• Simulate capital per worker with the Solow accumulation rule
• Use this year's output for this year's investment (state timing exactly)
• See capital rise from below its long-run level and fall from above it