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1. Explain why the marginal cost curve must cross the average cost curve at the minimum of the average cost.
Consider the following production function: f(L,K) = (L^1/2+ K^1/2)^2 . The short run value of capital is K ¯ = 4, and the input prices are w = 2 for labor and r = 1 for capital.
2. Derive the short run average cost, marginal cost, and average variable cost functions. (Hint: Before you start, what is the output if L = 0?)
3. Check that the short run average cost reaches its minimum for q = 9. What is the minimum value of the short run average cost? (Hint: To check the minimum of the SRAC, show that the derivative of the SRAC function is equal to zero at q = 9.)
4. Verify analytically that at q = 9, the SRMC and the SRAC intersect. (Hint: Simply show that the two functions take the same value at q = 9.)
5. At what point do the short run MC and the short run AVC curve intersect? Comment.
This document contains various important questions and their appropriate answers in the subject field of Economics.
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