Question

1. Suppose that output is generated by the production function Y = F(K, L, M = AK1-0-BL M. where M is the quantity of raw materials used in production. What condition is necessary for the production function to exhibit constant returns to scale? 2. Suppose instead that output is generated by a "constant elasticity of substitution" (CES) production function, Y = F(K,L) = A(Kº + L), where a < 1. What condition is necessary for the CES production function to exhibit constant returns to scale?

Answer 1

I suppose that output is generated by the production function - y = f(K, L, M) = AK 1-2-B.22 MB Now suppose we raise , ks L and m by a scalas constant z'. i.c. f ( ZK, ZL, ZM) = A (2 k) * ( 22 je (Zm) P = 21-x-8 +2+B. ;-a-port TAKIT-P MB = ZY Hue, raising both A inputs K, L and m by scalar Z increases output by the same proportion Z. tuce the production function exhibits constant returns to scale. 17 2 Now, CEs production function is given by: Y= F (KL) - Ackat Lap here we raisc both k and L by a scalar constant Z. Now, F (2K, ZL) = A (lz klx + 2LR = A[ z***+222x70 = A ZKPJ KX+ 27 B = ZXP AT A KT+ LXIB = 240 y. Hue for the production function to entibet constant returns to scale LB should be equal to 1.ie. 2 B = 1 ce it a B= 1 then increasing both k and Lby So Colar with increases out but by Zo hence the Hunces it Cs CamScanner

constant retums to scale production function will enhibit it 2B = 1: Scanned with CamScanner