Human Psychology and Economic Fluctuation

Our analysis in the previous chapters has assumed: (1) that pure investment undertaken by firms during a given period of time has no impact on utility attrition rates or labor productivity parameters for the same period; and (2) that the household’s (or Robinson Crusoe’s) utility attrition function for each consumption good is linear (i.e. the utility attrition rate is a constant). Based on these assumptions—which were required in order to ensure stability—we derived our “basic equation of labor”, which describes the relationship between a household’s (or Crusoe’s) utility attrition rates and the time that it (or he) spends working. Short-run analysis based on a non-linear production technology satisfying the principle of diminishing marginal productivity yields the following equation for a two-good model: (4.28) $$\matrix{{T_L^* = {{{{({\beta _1}/{b_1})}^{2/3}} + {{({\beta _2}/{b_2})}^{2/3}}} \over {{{({\beta _1}/{b_1})}^{2/3}} + {{({\beta _2}/{b_2})}^{2/3}} + {{(a\varepsilon )}^{2/3}}}}(T - l)}\cr}$$