Consider the following production function Y zK 13 N 23 a S

Consider the following production function: Y = zK ^1/3 N ^2/3

(a) Setup the rm’s maximization problem (taking K as xed) and solve for the labour demand Nd in terms of exogenous variables K, w, z (The marginal product of labour is MP_N = (1 )KN given a Cobb-Douglas production function such as Y = zKN¹);

(b) How does the labour demand change with respect to i. an increase in w; ii. a decrease in z;

Solution

I think the production function must be Y = zK^1/3N^2/3

So Marginal Product of labour = MPN = dY/dN = zK^1/3*2/3N^1/3

As w (wage rate) changes, Labour will change accordingly. if W increases, Labour will be reduced.

As z decreases, MPN will also increases (as seen from MPN equation) and as a result demand for labour also increases.