Consider the utility function U(c, l)=((c+1)l), Let the wage rate, non-labor income, maximum time available, and price of the consumption good c be denoted by w, I, T, and p, respectively. Let the optimal consumption and leisure be denoted by c* and l * , respectively.

1Define and calculate the reservation wage w*.

2Prove that l * = T if w < w*. Interpret this result.

3Draw the labor supply curve (plot w against h, where h = T - l ) and highlight the key features of the curve. Is it possible for the labor supply curve to be backward bending? Explain.

4Suppose there is now a fixed cost of work F > 0. Calculate the reservation wage Prove that w** > w*. What is the economic interpretation of this result?