What do we mean by a production function Interpret the follo

What do we mean by a \"production function\"? Interpret the following production functions (a) Q= 50LiKi (b) Find the equation for an isoquant for the production function given in Question 1(a). Prove that it is downward sloping and convex

Solution

The isoquant is given for a particular production function. Thus the equation of the isoquant is given by the production function itself which is Q=50L^(3/4)*K^(1/4). The marginal productivity of labour is given by mpl=37.5*L^(-1/4)*K^(1/4). The second derivative is <0. Similarly for capital is given by mpk=(50/4)L^(3/4)^*K^(-3/4). Thus the second derivative is <0 and so the isoquant is convex in labour and capital and downward sloping.