Exercise 4 - 30 pts

Consider the following economy with production. There is a worker endowed with 1 unit of time, which can be allocated either to leisure or labor. There is a firm with a technology that turns a worker's labor (the complement of his leisure) into bread. That technology satisfies:

b(l) = l1/2

where l [0,1] denotes the worker's labor and b(l) is the amount of bread produced as a function of labor input. The worker's utility function from labor supplied and bread consumed is:

u(l,b)=ln(b)l, 0<<2

1. What is the set of Pareto optimal allocations in this economy? (15 pts)
2. Provide prices and an allocation that, together, constitute a competitive equilibrium in this economy. (15 pts)