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Suppose the Production Function for Widgets Is Given by Y

Question 57

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Suppose the production function for widgets is given by Y = KL - 0.8K2 - 0.2L2 where Y represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labour input.
i)Supposing K = 10, graph the total and average product of labour curves. At what level of labour input does this average product reach a maximum? How many widgets are produced at that point?
ii)Again assuming that K = 10 graph the marginal product of labour (MPL)curve. At what level of labour input does MPL = 0?
iii)Suppose that the capital inputs were increased to K = 20. How would your answers to parts a and b change?

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i)TP(L)= 10L - 80 - 0.2L2, AP(L)= 10 - 8...

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