h6_ans - ½ J ½ = 30 J For q=150 J = 25 For q=300 J = 100...

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1 The Colorado College Department of Economics and Business Block 7 Econ 207 HW 6 ans. 1. (a) MP L =dq/dL = 1; MP K = dq/dK = 2 RTS = MP L /MP K = ½ Thus the isoquant has constant RTS. It is downward sloping and linear. Foe every unit of labor, half the amount of capital is employed. (b) Since RTS = ½; w /v = 1. RTS < w/v MP L /W < MP K /L The manufacturer will use only K . For q = 20, K = 10; q = 40, K = 20; q = 60, K = 30. The manufacturer’s expansion path is simply the K axis . (c) Now RTS = ½; w /v = 1/3 with v = $3. RTS > w/v MP L /w > MP K /v Here the manufacturer will use only L . For q = 20, L = 20; q = 40, L = 40; q = 60, L = 60. Now the manufacturer’s expansion path is the L axis . 2. (a) q = 900
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Unformatted text preview: ½ J ½ = 30 J For q=150, J = 25 For q=300, J = 100 For q=450, J = 225 (b) q =30 J J = q 2 /900 TC = w S S+w J J = 40(900)+80(q 2 /900) = 36000+ 8q 2 /90 L K Slope = 1/2 2 For q=150, TC = 38000 For q=300, TC = 44000 For q=450, TC = 54000 . (c) MC = d(TC)/dq = 16q/90 For q=150, MC = 26.67 For q=300, MC = 53.33 For q=450, MC = 80 . 3. (a) q = 2 K L × K = 100, q = 2 100 . L × q = 20 . L 400 20 2 q L q L = ⇒ = STC = w L +r K = 4(q 2 /400) + 1(100) = q 2 /100 + 100 SAC = 100/q + q/100 . SMC = q/50 (b) If q=25, STC = 106.25 , SAC = 4.25 , SMC = 0.5 If q=50, STC = 125 , SAC = 2.5 , SMC = 1 If q=100, STC = 200 , SAC = 2 , SMC = 2 ....
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