Question

7. Consider a utility function:U(c,l) = (1) log (c) +log (l), 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 effects.