Calculate marginal products and technical rates of substitution for several frequently encountered production functions. Consider the production function f(x₁, x₂) = 2x₁ + √x₂. The marginal product of x₁ is the derivative of f(x₁, x₂) with respect to x₁, holding x₂ fixed. This is just 2. The marginal product of x₂ is the derivative of f(x₁, x₂) with respect to x₂, holding x₁ fixed, which in this case is 1/2√x₂. The TRS is −MP₁/MP₂ = −4√x₂. Those of you who do not know calculus should fill in this table from the answers in the back. The table will be a useful reference for later problems.

Transcribed Image Text:

Marginal Products and Technical Rates of Substitution M P2(x1, x2) TRS(x1,x2) f(x1, x2) MP; (x1, X2) Xi + 2x2 ari + br2 50х122 3„1/4 ,-1/4 1/4 „3/4 .-3/43/4 З7, ,b–1 Cba,x ax2 bx1 Cxta Сал1а a-1 X2+1 X1+2 |(T1 + 2)(x2 + 1) X2 +1 X2+b Ti+a Xị + a x2 + b (т1 + a)(т2 + b) 2а ут b. 2 T2 ax1 +b/T2 a- a-1 аг'? ‚a–1 axi xf + x5 12 a- (x4 + x5)° bax↑-1 (x† + x5)*-1 bax;-1 (x† + x5)°- 12