7. Work It Out. Consider an economy with two sectors: manufacturing and services. The demand for labor in manufacturing and the demand for labor in services are described by the following equations: Lm = 200-6Wm 100 - 4WS Ls = where L is labor (in number of workers), W is the wage (in dollars), and the subscripts denote the sectors. The economy has 100 workers who are willing and able to work in either sector. a. If workers are free to move between sectors, what is the relationship between Wm and W₁? b. Suppose that the condition in part (a) holds, and wages adjust to equilibrate labor supply and labor demand. Calculate the wage and employment in each sector. c. Suppose a union establishes itself in manufacturing and pushes the manufacturing wage to $25. Calculate employment in manufacturing. d. In the aftermath of the unionization of manufacturing, all workers who cannot get the highly paid union jobs move to the service sector. Calculate the wage and employment in services. - e. Now suppose that workers have a reservation wage of $15 — that is, rather than take a job at a wage below $15, they would rather wait for a $25 union job to open up. Calculate the wage and employment in each sector. What is the economy's unemployment rate?

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