9.6. Consider the model of investment in Sections 9.2–9.5. Describe the effects of each of the following changes on the K˙ = 0 and q˙ = 0 loci, on K and q at the time of the change, and on their behavior over time. In each case, assume that K and q are initially at their long-run equilibrium values.

(a) A war destroys half of the capital stock.

(b) The government taxes returns from owning firms at rate τ (so that a firm’s profits per unit of capital for a given aggregate capital stock are

(1 − τ)π(K(t)) rather than π(K(t))).

(c) The government taxes investment. Specifically, firms pay the government

γ for each unit of capital they acquire, and receive a subsidy of γ for each unit of disinvestment.