ABSTRACT
Let us im agine a perfectly com p etitive eco n o m y operating under th e usual n eo-classica l a ssu m p tions o f decreasing returns, convexity o f preferences, etc. T o m ake our d iscu ssion sim ple w e further lim it ourselves to a on e-g o o d tw o-p eriod fram ew ork , in w h ich in itia l re sources can be a llocated to im m ediate co n su m p tio n or to investm ent, and in w hich investm ent produces the g o o d s availab le for future co n sum ption . W ith a perfect loan m arket con su m ers w ill equate their m arginal rates o f tim e preference to the rate o f in terest, w hile private firm s w ill carry investm ent to the p o in t w here the m arginal prod uc tiv ity o f private cap ita l is equal to the in terest rate. S u p p ose n ow thatfor reasons that w e shall take as g iven — part o f the to ta l investm ent o f the econ om y takes p lace in p u b lic ly -ow n ed “ firm s” . It is then ob vious that the op tim al am oun t o f pub lic in vestm en t is fo u n d b y equating the m arginal productiv ity o f public in vestm en t to the m arket rate o f inter est; the m arginal con d ition s for efficiency or P areto -op tim ality w ill then be satisfied all around.
