A worker is considering how many hours to work, how many hours to enjoy life and how many dollars to consume. Let h represent the number of hours he works, l represent the hours of leisure, and c represent his consumption of stuff in pounds. His preferences are represented by the utility function U = lc . He has 24 hours in a day that he can allocate to working or leisure. Let w denote the hourly wage.

(a) Given that he only has 24 hours in a day, how are l and h related (mathematical expression only)? (5 points)

(b) Given w , how are c and h related (mathematical expression only)? (5 points)

(c) If w is equal to 1, what are the combinations of leisure and consumption that he can achieve? Find the formula for his budget line. Graph the budget line (leisure on the horizontal axis). (5 points)

(d) Calculate the optimal choice. Draw his optimal choice in the previous graph. How many hours will he work? (5 points)

(e) Assume that now the wage decrease to 1 / 2 . Write down the equation for her budget line and graph it. (5 points)

(f) Calculate the optimal choice? How many hours will he work? (5 points)

(g) How did his supply of labor change? What does this tell us about the magnitudes of the income and substitution effects from the change in wages? Please make this brief