The elements of labour supply theory can be derived from an expenditure-minimisation approach. Suppose a person’s utility function for consumption and leisure takes the Cobb–Douglas formThen the expenditure-minimisation problem is
a. Use this approach to derive the expenditure function for this problem.
b. Use the envelope theorem to derive the compensated demand functions for consumption and leisure.
c. Derive the compensated labour supply function. Show that ∂lc/∂w> 0.