Notes on Current Account and Investment G6904

Current Account and Investment with Adjustment Costs Small open economy selecting consumption and investment path subject to adjustment costs. Households with inelastic labor supply wish to maximize value of firm by selecting a sequence of Is Subject to Note that value of firm plus human capital, wage income drops out and just want to maximize present value of net output (net of adjustment cost).

Current Account and Investment with Adjustment Costs Set up the Lagrangian First order condition for Is

Current Account and Investment with Adjustment Costs The Lagrangian First order condition for Ks+1

Dynamics Dynamics of the system evaluated at steady state Totally differentiate and use fact that square term drops out and that Fkk dK + Fkk dq term remains evaluated at steady state.

Model is Saddle Path Stable q 1 dk /dt = 0 dq /dt = 0 k

Current Account Implications With r equal to time preference, the a version of the Sachs equation holds What happens in response to permanent rise in productivity? We see that dq /dt = 0 must shift up and to the right

A Rise in Productivity q Q rises in anticipation of higher future MPK and adjustment costs. GDP, consumption, and investment boom 1 dk /dt = 0 dq /dt = 0 k

Dynamics Y C A I t0

Current Account in Deficit Along Adjustment Path With Y rising and I falling along adjustment path, CA must be in deficit until new steady state with CA balance. In new steady state, a trade surplus to finance the interest bill on debt incurred during adjustment. Y A CA

Derivation Totally differentiate at dq/dt = 0 and use fact that square term drops out at q = 1.