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Consider the one-period labor demand model we studied in class.
The XYZ Corporation pro-
duces semiconductor equipment with a production technology that is accurately described by the
production function
Y=100 K^0.4 L^0.6
(a)
What is the marginal product of labor (as a function of K and L)?
(b)
Denote the price of output Y by P and denote the wage rate by W, write down the profit maximization problem of the XYZ Corporation. What is the first-order condition?
(c)
We assume that the amount of capital stock is $100 million, (i.e., K = 100, 000, 000). The price of the product is $11, and the wage for workers is $25,000 per year. What is the optimal labor demand L ? Round to the nearest integer.
(d)
During the last year, South Korean manufactures have entered the U.S. semiconductor market with extraordinary vigor. Because they are lower-cost producers, their entry has driven the gross price of semiconductor equipment in the United States down from $11 to $9. What is the optimal labor demand now? Round to the nearest integer.
(e)
Continue from part (d). Suppose that the government wants to subsidize employment and restore the labor demand to the previous schedule in (c). The subsidy takes the form that for every dollar of wage bill, the government pays b dollars (b < 1). What should b be to restore the labor demand schedule to be the same as in part (c)?
