Question

Given production function: y=f(x1,x2)=(α⋅x(σ−1)/σ1+(1−α)⋅x(σ−1)/σ2)σ/(σ−1)

consider,   α = 0.2 and σ = 0.7.

The first factor is currently used in the amount x₁ = 9, and the second factor is used in the amount x₂ = 3.  

a) When (x₁,x₂) = (9,3), how much output is being produced?

Output:    

b) When (x₁,x₂) = (9,3), what is the marginal product of factor 1?

Marginal product:   

c) When (x₁,x₂) = (9,3), what is the average product of factor 1?

Average product:    

d) When (x₁,x₂) = (9,3), what is the rate of technical substitution (a positive number)?

Rate of technical substitution:    

e) When (x₁,x₂) = (9,3), what is the elasticity of substitution (a positive number)?

Elasticity of substitution:   

Answer 1

a) y = f(x,x) = ax + (vw) x .7°44 2:02, 0.7 then a) y = f (9, 3) = [.29 + (1213. Jor 0-1 = -03. OER --3/ 7 4 -73. 8o y = $19,3) = [-2 9.3 + .8(35377-8/3. ! =.3.6. Ang Ang 102 b) Now Mpt = oy - (0) for ott (tax] A. a la (41)x)=='). (6) [axi (4, 5). (31) - (-29317+18 (31-34). "(-2) (9) + 1054 Arg (6 ) (-) AP, = 2 = 9 (9,3 ) = 3.6= of Ang d) MR15 = 3Aloxala xtrawski . (0x8+ (ver a Thai ((99) xo! -o = ()(3)# # (4)%+ e elasticity of substition = .0520 Ang afax "Let It T-(0-1) - Hoy