Reference no: EM133271319
LUCAS 1978 MODEL WITHOUT CAPITAL
In the Lucas model, individuals choose between being workers or en- trepreneurs. They differ in their managerial ability x ∈ (0,x ¯).
Entrepreneurs hire workers to produce final goods with the following produc- tion function: y(l,x) = xlα, where l is the number of workers employed. Each worker gets a wage w, independent of their managerial ability. Sup- pose that all markets are perfectly competitive. Set the price of the final good equal to 1.
1. Set up the problem of an entrepreneur. She chooses how many work- ers to employ to maximize profits. Solve for the labor demand of each entrepreneur. How does it depend on x?
2. Substitute l in the profit function. How do profits depend on x? Plot the profit function in a graph with x in the horizontal axis. Plot also the wage in the same graph.
3. What is the optimal choice of individuals? Who will choose to be a worker and who will choose to be an entrepreneur?
4. Find the threshold level x ~ that defines the individuals decision.
5. In equilibrium all markets must clear. Explain in words the labor market clearing condition and how it fixes the wage.
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LUCAS 1978 MODEL WITHOUT CAPITAL
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