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For following two production functions: (1) Q = L1/4 K (2) Q = 2L + 4K...

For following two production functions: (1) Q = L1/4 K (2) Q = 2L + 4K a) Determine whether factor L is subject to diminishing marginal returns? What about K? b) Calculate the MRTS. c) Determine returns to scale: CRS, IRS or DRS. Show how you arrive at your answers. For function (2) also draw a few representative isoquants; fully label your graph.

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1) Q = 24K E a Now marginal product of labore MPL = 20 = £ L - 3/4 K Now 2 (MPL) = - + x3) VA = 2 2 2 h k so MPK = 0o = 24 2we double double both. L and k Now , Le) Now we Q121,2%) = (22)%4 (2K) = (2) 4+ LY4K = (2) LuK CS Scanned with = (2) Q I CamShunce the increasing sing production re returs to scale As (2) 5/4 > 2, 1 fm ction enhibits (IRS) iso quart equation of - 2)16:8 + Q = 20 14.187 8.4 F.Q Q=10 labor (2) Q = 2L+4K Now Marginal product of MPL = GQ = 2 d (MPL) =0 Marginal product of capLand K is not subject to diminishing retums. (6) MATS - MPLE - Ź 0.5 . (e) Now doubling both Land K we get, P Q (21, 2K) = 21 Joining home ina horizontal and untical in Ancept we get iso quant (2=10) Now wh. q=20 equation of iso quant 20= 22 +4K hor

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