C) Where do the average and marginal cost curves intersect? What is the derivati

Question

C) Where do the average and marginal cost curves intersect? What is the derivative of the AC curve and what value does it take at the intersection? What does it tell you about minimum average cost?

2 Short-run costs (6 points) A film studio in Hollywood produces movies according to the function (yes, they can also produce fractions of movies... Think of half a movie as a B-movie or so.) T 0.5 q = F(K, L) = K0 55 /100. In the short run, capital (studios, gear) is fixed at a level of 100. It costs $4,000 to rent a unit of capital and 81,000 to hire a unit of labor (actors, stuntmen, camera crew etc.). (a) What is the fixed cost? What is the variable cost as a function of output q?1 (2) (b) What is the marginal cost (MC) and the average cost (AC) of a movie? What is the average variable cost and average fixed cost? (2) 1Hint: You know what K is. From the production function, you can now determine what L has to be as a function of output q. Once you know what L(q) is, it should be easy to find variable cost.

Explanation / Answer

The average and marginal cost curve intersect where average costs are at its lowest. The derivative of the average cost curve is where the average cost curve attains its lowest point. If the second derivative of the AC curve at that point is positive then this will result in its lowest point. At the lowest point we have marginal cost equal to lowest average cost.

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