Question

3. Suppose a perfectly competitive firm uses capital and labor to produce a single output. The firm's exogenous price for output is Po. The firm's exogenous cost for capital is ro. The firm's exogenous cost for laboris Wo. The firm's production function is given by Q = f(K, L) where: 8f/8K, 8f/8L >0, 82f/8K2, 82f/8L2 <0, and 82f/8K6L = 0 a) Given the profit function for the firm. b) Find the FOC's for K* and L* that allow profit maximization. c) Find the SOC's. d) Find the effects of changing price on K* and L*. e) Find the effects of changing wage on K* and L* f) Find the effects of changing the rental rate of capital on K* and L.

Answer 1

3. (a). Prefit fren) Tre pro - (rok + WOL) T = Pof (K, L) - (Nok twold fuck, w- of a DK dL I (6) Foc's: 20. Po fi(K.L) – y =o a lotilk, L) - Two ao fick,e). at solving the 2 foc's we get k&& L² . (c) sous. 27 - Polerk, c) to blog - Po fick, L) CO a fo de From The sol's. Potrk, L) -roco no Dillmentils wolle Polick, w - Word - - alpotick, 2) – 280 & felk, u) >o. 2 dlofilk, L) – Store & fick, L) >0 opo This imply that increase info will increace Spo po K & L*

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