Quiz7_F10_Key - The firm can lower the cost while...

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3550 F10 Quiz 7 Key 1. Assume a firm is operating on its expansion path in the short run: Q = 6 1/2 *L 1/2 *K 1/2 Where: K is fixed at 10, L = 15, Q = 30, MRTS = 2/3, P L = $40, P K =$60 a. (3) Graph their production isoquant and isocost curves, label all relevant part of the graph. Now assume that because of an increase in the price of the good in the market, they decide to increase production in the short run to 42.426 b. (2) How much labor will they need to hire in the short run to produce Q = 42.426? Rewrite the production function with K=10 and Q=42.426. 42.426=(6*L*10) 1/2 Î 42.426 2 =60L L=1800/60=30 c. (3) Will the firm want to change its input mix in the long run? Explain how you know. Yes. From the graph above the firm is not operating on the expansion path any more.
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Unformatted text preview: The firm can lower the cost while maintaining the Q=42.426 by hiring more K and less L . (moving along the isoquant) d. (2) Describe the difference in marginal cost between the short run and long run. That is, explain which is higher, and why. 29 . 48 426 . 12 600 30 426 . 42 1200 1800 1 2 1 2 = = − − = − − = Δ Δ = Q Q TC SRTC Q SRTC SRMC 30 426 . 42 1200 2 1 2 1 2 − − = − − = Δ Δ = LRTC Q Q TC LRTC Q LRTC LRMC From the graph above we know LRTC 2 <SRTC 2 =1800. Therefore, LRMC <SRMC =48.29. L LR a b c 30 15 10 1200/60=20 1800/60=30 Q=30 Q=42.426 L K...
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