Consider a utility function: U (c,`) = (1)log(c) + log(`), where > 0.

(a) Suppose that the consumer has one unit of time, w = 0.75, = 0.8, and T = 1.0.

Determine the consumer's optimal choice of consumption and leisure, and show this in

a diagram.

(b) Now suppose that wage double, i.e. w = 1.5. Again, determine the consumer's optimal

choice of consumption and leisure. Use a graph to show how and why the consumer's

optimal consumption bundle changes, with reference to income and substitution eects.