In "Cast Away Islands", there is only one company, "Allelectronics", which produces TV. It is the sole employer of engineers in "Cast Away Islands". The labor supply curve of engineers is w=30+L and the production function for making TV is Q=8L. Due to the free trade policy of Cast Away Islands, TV market is perfectly competitive and Allelectronics takes the TV price as given at P=5.
(a) How many worker "Allelectronics" hire? What is the wage rate? How many TVs does Allelectronics produce?
It was recently found out that Cast Away Islands was building a nuclear weapon secretly. As a result WTO imposed severe economic sanctions. There is no more free trade and Allelctronics now has a monopoly power in domestic TV market. The domestic demand for TV is P= (57/2 - 1/2Q).
(b) How many worker "Allelectronics" hire? What is the wage rate? How many TVs does Allelectronics produce? What is the price for TV?
(c) Graph the labor market with L on x-axis, w on y-axis. Draw labor supply curve, marginal expenditure function, labor demand curve. You can assume that w= ∂TR(L)/∂L is the labor demand function. To get ∂TR(L)/ ∂L, first write down the total revenue function only in terms of L (use the production function to substitute Q), then differentiate it with respect to L.
(d) What is the welfare loss in the labor market compared to the case where the engineer labor market is competitive?