Question:

3. Consider the CES production function y = (or " + (1-8)r,") over R: where o is some constant satisfying 0 0. (a) Given any isoquant y = C use implicit differentiation to compute the slope dr,/dry (b) Suppose that currently the inputs are equal, ie. I, = r,. Using part (a), determine the value o where increasing the input of r, decreases the input of r, by the same amount (for small enough changes) provided we want to stay on the isoquant. (c) Show that the CES function is homogeneous and determine if it is increasing, decreasing or constant return to scale