RDP 9512: Consumption, Investment and International Linkages Appendix A: Solution to the Neo-Classical Investment Framework

To solve the firm's investment problem, we set up the present value Hamiltonian:

The first order conditions for optimisation give:

which can be rewritten as

Rearranging the latter equation:

Integrating this forward from time t gives:

That is λ is the present discounted value of the future marginal product which is the marginal product of capital less the cost of installing that capital. This is essentially Tobin's q and is replaced by q in the text.