4. Consider the Q model of investment with adjustment costs. Equilibrium suggests that capital K(t) evolves as K (t) = C'1 (alt) 1) (normalizing the number of firms N = 1 and assuming no depreciation), while the marginal value of capital, q(t) evolves as (t) rq(t) 7(K(t)), where r is the real interest rate. Note that the capital adjustment cost function, C(I(t)) satisfies C(0) = 0, C'(0) = 0, and C"(-) > 0 and the real profit function, 7(K(t)), satisfies a'() 0 and the real profit function, 7(K(t)), satisfies a'()