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ECON 1100: Intermediate Economics

Assignment #7

Due Thursday 11/02/2023 by 9:30 am

Answer the following questions clearly and completely. Be sure to show your work - we need to be able to see how you arrived at your answers so that we can understand your thought process and give full (partial credit if warranted). Be sure to upload your assignment to Gradescope before the deadline. You are welcome and encouraged to work in groups as long as the work you hand in is your own! Do not hesitate to stop by office hours if you have any questions or merely wish to talk through any aspect of the problems. Work hard and goodluck!

1.   The New Age firm produces clean coal. New Age’s production function is given by q  = LS, where L denotes labor and S denotes its cutting-edge machinery. The price of labor is given by the wage, w, and price of machinery is denoted ps. Suppose that in the short run number of machines is fixed atS(̅) =  1 while L is variable.

a.    Write  down  the  expression  for  the  short-run  production  function.  In  no  more  than  two  sentences, describe the fundamental difference between the short-run and long-runtime horizons in production.

b.    Invert the short-run production and derive variable costs, VC(q) = wL(q), where labor is a function of the level of output L(q). Next derive fixed costs and the short run cost function, C(q).

c.    Compute the marginal productivity of labor (MPL) and show that MPL is diminishing, i.e.    < 0. d.    Compute marginal cost (MC(q) = ) and show that it is increasing, i.e., .    > 0.

e.    Show that a diminishing MPL  is implies that MC is increasing.

f.     Show that the marginal productivity of labor (MPL) is less than the average product of labor (APL). And show that MPL  < APL  implies that there is a diminishing APL, i.e.  < 0.

g.    Find a formula for the level of output (q), which will depend on (be a function of) wand ps, where average cost is minimized? What is the impact of an increase in fixed costs on the cost minimizing level of output (q) and why?