Question

Question 3. (a)(8 points) Find the elasticity of substitution for the following production functions: 1)F(KL) = AKL, ii)F(K, L) = R0.270.8,
If someome could answer this question and write out the steps/ explain the solution in words as well that would be great, as this concept really confuses me.

Answer 1

! solution Ans (i): Production function is given as F(x, L) IAK a b the elasticity of substitution measures the % change in the capital Labor ratio (W/L) for each 1 to change in marginal rates of technical substitution (MRTS) 2,K we move along the iso quant. Therefore, mpic MPL 2 MRTSLK = where, MP2= MPR = a b-/ a-1 b Aa K L n 2 marginal production of labor. marginal production of capital. In order to get mp, Differentiate eh wort(2) MP2 = Abkab- a similarly, Differentiale ec 0 wirtk for MPK. mpk = lak now, putting these in eq Abka bb MRTSLK = Aak" now, the formula for elasticity of substitution (0) is given by , A) do 4 () 1, AMRTSC,K b-1 bk 3 al where, " Xoo 4.4) k L AMRTS LK ma ol. Amris = Lire MRTS ,,K X100 1 cs Scanned with CamScanner

A (4) A) WIL AMRTSLK MRTS L,K AMRTSL,K Х - 사 MRT SLK MRISLIK A) AMRTSLIK 4 X r = L bk substitute this MRTS LIK AL from een e in eq" G Al) Х K - ☺ bk AL K AMOTSLK Maya 2 L b A) X a AMRTSLK Now, we have, be MRTSLK AL for (4) ( putting this int OMRTSL, K = L 5 c olo 4) AMRTS LK > Pulting in een 1 a xa = Thus, Elasticity of substitution (0) will be 1 equal to Ans (ii) :- we have already derived that, b b a Therefore, To=11 Cs Scanned with CamScanner