Question

The own-price elasticities of contingent input demand for labor and capital are defined as alway - Jw4 , a Calculate es, and ex, for each of the cost functions shown in Example 102. b. Show that, in general, 9... + = 0. c Show that the cross-price derivatives of contingent demand functions are equal that is show that afiəv = kraw. Use this fact to show that = SECR, where si Skare, respectively, the share of labor in total cost (wl/C) and of capital in total cost (wk/C). d. Use the results from parts (b) and (c) to show that +s4 =0. e Interpret these various elasticity relationships in words and discuss their overall relevance to a general theory of input demand.

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Answer 1

Ansuless The contingent infect neece to demand poodice of input is cost minimization a given leval of output. The contingent demand function of labor fixed propostions is given below. Go, w = acl Ei ose o dw : نما عع O l function of labor fixed poopotion s us diven below Te & KS eer. sk CkEuro demand function The contingent of labor too co-bb-Douglas is given below. TOTAL

13 1/wu8 ) : 118 KE S . ਕੇt B a + 3 dre ਹS dB , ਕੱਚ ਦਾ ਚ) ਕਮਲ (ਕੰਨ ' ' ਸੰਸਕ ਕੀ ਕਿ ਕੰਜ ਕ ਚ ਕੱ ਮ ਦੇ ( ਘ , ( 3 . 8 2 - d a 1 demand function of capital of cabb. Dauga * The contingent I Jasus given below Fਚ ਕੇਜਰ ਸ. ਸਰ - B ਕt 3 |cky : 0 ਜਲ . ਚੰਦ ਯੋs * * Elto . . rose .

The contingent demand funetion of labor for CES function is given below. 5C,w?). Set (via mwishes, wo vedere cat was to foia + wtajiet Wia + ${ute twitter for worry Csüsse er 14.women talvita is the sco 12 (1-0)2 with.. where, o tp * The contingent demand function of capital of foo cobbb- Douglas is given by below. K[v, w8, 9) = 2+ [vto + witho) Po.ro dre ter

har vieno = Gov ole 1.it [inner).(210+ 443 46+ sl em + e^] 01. Of on the jp dw 1

(b) The The contingent demand degree Dero se, apply given below. function is homogenous of the Eulers theodem as het wate r v= les wete wor). le s pour est to e de . so OV (c) The esen tele v 70. CDOSS Paice dositives of contingent demand can be cala ulated as shown below. de los com use young's theorem as shown below. dr bow le ss

o] The closs paile clasticites are given below min estava gre v 을 쁜 S쁜 The calculations for steic:r and Skekco SICEVE beste o SickE.WV pode ser Seefiv Siecie w is given below de

(d? Gr. wt ecc.v=o (exc. W + ekar js, zo Clc.W si + CK US, = 0 ekov si = ecc. ws, et Se + eccwsic=0 sel. These equation of elasticity demonstrate how cross factor elasticity is related to each other and how the share of each factor acts as a mederating Varuable. In some cases of cech shade of each factors even directly determine the elasticity relasticnship between facters ** Please please like this answer so that I can get small benifit. Please ** * Thank you x