(Solved): 9. The long run total cost for a firm is \( L T C=110,000 Q-200 Q^{2}+Q^{3} \). a. Write an express ...

9. The long run total cost for a firm is \( L T C=110,000 Q-200 Q^{2}+Q^{3} \). a. Write an expression for the long run average cost (LATC). b. Write an expression for the long run marginal cost (LMC) - use calculus: c. Graph the LATC and LMC (plug numbers into the equations you've written - you might want to use Excel to type a formula in.) d. At what output level is the minimum efficient scale of this firm? Label it \( Q^{*} \). You can use the graph or calculus here. You can find the minimum by setting the derivative of LATC \( =0 \) (the place where the slope is 0). You can also think about where the LMC and LATC cross. Show your work in either case... e. Label any areas of increasing retums to scale, decreasing returns to scale and constant retums to scale. f. Suppose the firm is operating at its minimum efficient scale (that's where the demand for the product is). What are the average costs at that level of output? 8 Suppose the government bans (prohibits) firms from exceeding \( Q=50 \). Compare the average costs of production because of this ban compared to the minimum efficient scale. h. Intuitively, why are costs different between \( Q=50 \) and the minimum efficient scale?