A8+Derived+Demand+and+Long+Run+Cost+Function

A8+Derived+Demand+and+Long+Run+Cost+Function - electricity...

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Frank Chapter 10 (Blue Book) Assume the production function q = 16K .5 N .25 represents a family farm. In this case, the family owns acres of land (N) that it can farm or rent each year. The rental rate for the land is f. The family can also lease machinery time from the local cooperative equipment shed. The charge for the machine use is r. The family’s harvest in thousands of bushels is represented by q. What is the derived demand for land and capital? (6 points) What is the average cost function? (9 points)
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Derived Demand (1) Solve for either K* or L* as a function of w, v, and q ii) Place Derived Demands into the Cost Equation yielding TC = f(w, v, q) iii) Changes in input prices (1) If one input price rises, you will see a substitution of inputs, if possible. The degree of which depends on: (a) The input’s share of costs (b) The ability to substitute ( σ ) (c) The book uses the example of copper and aluminum wiring for
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Unformatted text preview: electricity transmission. This brings up the question of what really is the input, copper wiring or high conductivity material with a tensile (?) strength above X. If the latter is chosen, did prices really rise that much? Answers mp N = 4 K 1/2 N-3/4 mp K = 8 K-1/2 N 1/4 mp N = w = 4 K 1/2 N-3/4 mp K r 8 K-1/2 N 1/4 K = 2 (f/r) N N = (1/2) (r/f) K q = 16 K 1/2 ((1/2) (r/f) K) 1/4 q = 2 15/4 r 1/4 f-1/4 K 3/4 K 3/4 = 2-15/4 r-1/4 f 1/4 q K* = 2-5 r-1/3 f 1/3 q 4/3 q = 16 (2 (f/r) N) 1/2 N 1/4 q = 2 9/2 f 1/2 r-1/2 N 3/4 N 3/4 = 2-9/2 f-1/2 r 1/2 q N* = 2-6 f-2/3 r 2/3 q 4/3 TC = rK + fN TC = r (2-5 r-1/3 f 1/3 q 4/3 ) + f (2-6 f-2/3 r 2/3 q 4/3 ) TC = 2-5 r 2/3 f 1/3 q 4/3 + 2-6 f 1/3 r 2/3 q 4/3 TC = (2-5 + 2-6 ) r 2/3 f 1/3 q 4/3 TC = (3/64) r 2/3 f 1/3 q 4/3 ATC = TC/q = (3/64) r 2/3 f 1/3 q 4/3 )/q ATC = (3/64) r 2/3 f 1/3 q 1/3...
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A8+Derived+Demand+and+Long+Run+Cost+Function - electricity...

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