Consider a representative individual who maximizes , where c is her consumption, h is her hours worked, and . Let w denote the hourly wage and p denote price of consumption.

1. Derive her Marshallian labor supply (i.e. the optimal amount of hours worked as a function of prices).

2. An elasticity is a measurement of the change in one variable as another variable changes. For some pair of variables y, t, the elasticity of y with respect to t is defined as

It measures the percentage change in y when t changes by 1 percent. Derive the elasticity of labor supply using the formula you computed above.

3. Show that