# Of the solow swan model to incorporate the romer

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of the Solow-Swan model. To incorporate the Romer model into the Solow-Swan model we recall that in the Solow-Swan model all persons were engaged in production and all "per-capita" terms such as Y / L and K / L were implicitly "per production worker". Thus, the substitution L ( t ) -→ ( 1 - γ ) L ( t ) ( 35 ) recasts the Solow-Swan model in Romer form. After this substitu- tion we have the same capital accumulation equation for κ shown in Eq. ( 10 ) and the same expression for κ * , but with κ now given by κ = K E ( 1 - γ ) L . ( 36 ) Carrying this substitution through to the expression for per-capita income results in income per production worker Y ( t ) ( 1 - γ ) L ( t ) = κ ( t ) α E ( t ) . ( 37 ) Multiplying both sides of this expression by ( 1 - γ ) yields Y ( t ) L ( t ) = ( 1 - γ ) κ ( t ) α E ( t ) ( 38 ) which is per-capita income including both those in production and R&D.
the solow - swan and romer models 9 E ndogenizing g E with the R omer model provides more eco- nomic variables whose shocks can change the evolution of the econ- omy. Let’s consider each in turn. If the efficiency of R&D, χ , increases there is an immediate in- crease in g E which causes κ * to drop but has no immediate effect on κ ( t ) : the economy is now above the new steady state. The right-hand side of the capital accumulation equation will now be negative and the associated dynamics will slow the growth of the economy ini- tially. The economic shock will dissipate faster since the half-life of the recovery will be smaller. Once steady-state as been reestablished the economy will grow at the new higher g E . If the fraction of the labor force engaged in R&D, γ , increases there will be an immediate drop in Y / L because of the associated decrease in the number of people working in production. With more capital than production labor (the capital used in production by those now in R&D is now not being used in production) the economy will be above steady state and the growth rate will slow until the economy is once again on the balanced-growth path. Mathematically, the ( 1 - γ ) pre-factor together with the same factor in the denominator of κ α will result in a factor of ( 1 - γ ) 1 - α which gets smaller. This shock will cause κ to increase because ( 1 - γ ) in the denominator will have decreased and cause κ * to decrease because g E has increased. By increasing κ and decreasing κ * this shock moves the economy above steady state. The right-hand side of the capital accumulation equation will now be negative and and contribute a growth drag to the new g E . As before the economic shock will dissipate faster since the half-life of the recovery will be smaller, and once steady-state as been reestablished the economy will grow at the new higher g E . If the labor force L increases there will be an immediate decrease in κ ( t ) and Y / L and an immediate increase in g E that will result in an associated decrease both of κ * and of the half-life t 1 / 2 . If the resulting sign of the capital accumulation equation is negative the economy will be above steady state and the associated negative g κ will slow economic growth during the transition phase. If, on the other hand, the sign is positive, then the economy will be below steady state and, like Germany following WWII, g κ will enhance