cities derived in (c) is 0 2. Given the production function of q = / 0.25 /0.25 ,v is the unit price for k, w is the unit price for 1, and P is the unit price for output, (a). (5 points) Derive the contingent input demand function for labor , that is, the demand function for labor contingent on a particular output level q. (b). (10 points) Derive the total cost function. This should be a function of q, v and w. (c). (10 points) Derive the profit function. This should be a function of P, v and w. (d). (5 points) Derive the total demand function for labor /, that is, the demand function for labor that doesn't depend on the output level q. It should be a function of P, v and w only. (e). (10 points) Decompose the effect of a change in w on / into an output effect and a substitution effect