COMM 220 Lecture Notes - Lecture 4: Production Function
21 Oct 2015
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Comm 220 practice problem set 2 solutions. When the inputs are doubled, output increases by less than double. This production function exhibits decreasing returns to scale. 8 (b) when k=8, q = f(8,l) = 6l1/2 + 3(8)2/3 = 6l1/2 + 12. Apl = q/l = 6/l1/2 + 12/l (c) mpl = dq/dl = 0. 5(6)l-1/2 = 3/l1/2: (a) mpl = dq/dl = 20 0. 1l. Apl = q/l = 80/l + 20 0. 05l (b) apl reaches its maximum when apl = mpl. L = (80/0. 05)0. 5 = 40, where apl reaches its maximum. At l = 40, mpl = 20 0. 1(40) = 16: (a) mrtslk = mpl/mpk = 250(0. 5)k0. 75l 0. 5 / 250(0. 75)k 0. 25l0. 5 = 2k/3l. When the inputs are doubled, output increases by more than double. This production function exhibits increasing returns to scale. Since l is in the denominator, as l increases, mpl decreases. For example, for any given value of k:
