# Suppose Ralph’s long-run economic cost curve is again given by C(q; P) = 300q – 20q 2 + q 3 where…

Suppose Ralph’s long-run economic cost curve is again given by

C(q; P) = 300q − 20q 2 + q 3

where q denotes output in this conveniently single product firm.

(a) Tabulate total and marginal cost for q ∈ {0, 1, 2, 3, …, 20}. Also plot marginal cost for 0 ≤ q ≤ 20; and notice the efficient point is q = 10 units, where average cost for the single product firm is a minimum.

(b) Next consider a particular short-run cost curve given by

C SR(q; P) = F + 290q − 21q 2 + 1.1q 3

Determine F if we are to interpret CSR(q; P) as some short-run cost curve consistent with Ralph’s long-run cost curve and an efficient scale of q = 10 units, so C(10; P) = CSR(10; P).

(c) Plot the resulting marginal short-run cost, for 0 ≤ q ≤ 20. Contrast this with their long-run counterparts. The best way to do this is to plot all four curves on the same graph.

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