An individual has a utility function, U = A (a log L + Blog C) +z where (A, a, B, E) are constants, L is leisure, and C is consumption. She wants to maximize utility subject to the budget constraint, V + w(1 - L) > PC where V is non-labor income, w is the wage, and p is the price associated with the consumption good. Derive mathematically how her optimal choice of L and C depend on A and E. Provide intuition for your answer as well