Question

Consider the following CES production function: Q= AlaL +1-a)K-]%, capital, respectively where Q is output and L and K are inputs labour and i) Interpret the parameters A,a,t and V ii) Show that if f-0, the two input Labour and capital are imperfect substitutes in production

Answer 1

+(-a)k ATechnology parameter For A2o, mpuies impxouament in technolog and any improuament m technology 9efeited oy A uil lrad to invraaue in autput for a giuen lauel ot Land k A inuraare to A and AkA Then (1-a)K ie Rtimas inureae im A loody to B Himas imureaue im output

eelatiue t apreuends thekana ot A Labon Capteet in tha tatal output I is also bnousn as distaibution parameten 9t shous ho muth Labor intensiue iu the pYacluction loxa1) the Subshtuhon parameter ohich determinu the 'elashuly f Subshtuhon 1+l LOhere elashicily d Substitution 9t dletermines wether the U production funchia Or DRS IRS, CRS Fos eg Suppase L and k ineruaue by tactur Then RL,K) ALatL) ((-a) (Ak) QUL,AK) ALaf1- ta) elALAK) At- aL+-a)k ltL,tk)

Nous preduuren forchos them exhibits CRS It r than produchon fumuhon exhibits IRS Ihen preduchon funchon exhibits DRS IRSInuuasing 9taterns to scale CRS Constant 9retuns to scale DRS Decruating 9toturn to scale

A [aLCajk -/ Pake og both &icle loglauttia)k COhon Logt - ula can nous apply L-hospite eule Te, X arl tli-ak alogl tli-a)log k) - V at1-a 1-9 logia k-a log kta) (LK1-4)

A LaKA) perfect L and Kare not Subsh'tute Land Kare Subshitute imperfect Incae at perfect Subsh'tuta predluehdn unchen lorpk ik L+K