## Info

the elasticity ol xuKtitutmn >\% the ratio of the marginal ami average functions. Simplifying find by letting h

The marginal function t%

dtttlh h /ftv and the average function is kit. h(p,ipky"'» ./P,

By dividing the marginal function in (6 97) by the average function in (6.fl?0. the elasticity of substitution h

Pi'Pi

Since fi is a given parumetcr. o !•( 1 • ß) »v a constant, b) If 1<0<O. a>\. Ufi (). a 1. If0<ß- <*< 1.

6.60. Prove that the CES production function ls homogeneous of degree I and Ihiis has constant returns to scale.

Multiplying inputs A and I. by k. as in SccUon 6.7.

f(kK.kL) A|o<AA> * + (l - «><*/.) " * A[k *(«* o)L 'I) »*

6.61. Find the elasticity of substitution for the CES production function. q - 75(OJA 04 + 0.7/.-»') J\ given in Example 12.

I • fi where fi - 04. Thux <r • I/(I + 0.4) - 0.71.

6.62. Use the optimal KU. ratio in (6.V5) lo chcck the answer in Example 12 where q - 75(03* + 0.7/. "'j11 *as optimized under the constraint 4* ♦ 3L - 120. giving *- 11.25 and/.-25.