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Consider production function f (x1, x2) = x11/2x21/3. The price of factor 1 is w1 =...

Consider production function f (x1, x2) = x11/2x21/3. The price of factor 1 is w1 = 12

and the price of factor 2 is w2 = 1.

  1. With x̄2 = 8, find the short-run cost function c(y).

  2. Find short-run AC(y), AVC(y), and MC(y) based on the answer to a.

  3. Write out the long-run cost minimization problem to find the cheapest way to produce y units of output.

  4. Write out the Lagrangian for the long-run cost minimization problem.

  5. Solve the long-run cost minimization problem.

  6. Find the long-run minimum cost to produce 10 units of output.

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