# The GMC company is considering building a new car factory in China. The total (xed) cost of the investment is F = 4.

The GMC company is considering building a new car factory in China. The total (Öxed) cost of the investment is F = 4. When built, the factory will allow to produce y cars at the (variable) cost given byc(y) = 4y2 (4y squared)1a) Does the technology used in the new factory exhibit increasing, decreasing or constant returns to scale (ignore the fixed costs at this point)?b) Find a total costs (TC) of producing 1, 2 and 4 cars. In the graph (y;COST) plot a TC curve, and decompose it into a fixed cost curve and a variable cost curve by adding the two curves to your graph.c) Find the values of the average fixed cost (AFC) for three levels of production y = 1; 2 and 4: Plot a AFC curve in a separate graph. What happens to the AFC when production becomes very large (close to infinity) and when it is very small (close to zero). Explain.d) Find the values of the average variable cost AV C for y = 1; 2 and 4; and mark them in the graph from question c). Connect the three points to obtain the AV C curve.e) Find the values of the average total cost AT C for y = 1; 2 and 4 and mark them in your graph from c). Connect the three points to obtain the ATC curve. What are the values of ATC when the production is very small and very large? Explain which of the two components of ATC – AFC or AVC – dominates in each of the two extremes. Why?f) Find analytically the minimal efficient scale (MES), yMES;ATCMES for the considered car technology.g) Find analytically marginal cost MC curve. In a new graph plot the MC curve, together with the ATC, marking the MES.e) Explain intuitively why or why not the MC curve cuts or does not cut the ATC curve at the MES.f)Harder: find analytically a minimal efficient scale yMES;and ATCMES as a function of F (parameter). How do the two values depend on the level of F?

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