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Unformatted text preview: MP L = dQ/dL = L K 1 * * 2 1 remember that we’ve fixed K=1, and substituting in L=4 leaves us with: MP L = ½ * 1 * ½ = ¼ //home/vdimitrov/16843/625943b21c521351703364700710e2e7932bd68c.doc 1 b) Suppose the firm can hire labor at a wage of $5 per hour and output can be sold at a price of $25 per unit. Determine the profitmaximizing levels of labor and output. i. ( Hint : Remember that the firm maximizes its profit when VMP = P * MP L = w ) Part 1: From the hint, $25 * MP L = $5 Hence, the firm profitmaximizes when MP L = $5 / $25 = 1/5 Part 2: At what point does MP L = 1/5? (Remember, capital is still fixed at K=1) In other words, at what level of labor L does the marginal product of labor = 1/5? MP L = L K 1 * * 2 1 = 5 1 ; since K=1, this simplifies to: 5 2 1 = L so 2 5 = L or L = 25/4 //home/vdimitrov/16843/625943b21c521351703364700710e2e7932bd68c.doc 2...
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 Fall '08
 Crawford,L
 Economics, $5, $6, $12, $25, MPl

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