A consumer has utility function u(L,F) = (L^A)(F^(1-A), where L represents hours of leisure, F is food, and A is a parameter that satisfies 0 < A < 1. The consumer has 24 hours that they can divide between leisure and work. For each hour they work, they gain a salary, s, and each unit of F cost p. They have initial wealth w.

a) Write the consumer's budget constraint

b) Solve the consumer's utility maximization problem

c) Find the condition on the parameters such that the consumer does not work

d) How does the consumer's demand for leisure respond to a change in initial wealth (w)? How does the consumer's demand for leisure respond to a change in salary (s)? Use partial derivatives to answer both questions