labor and marginal product/cost

  1. You collect the following production data for your firm:
Q
a.   Which functional form (linear, quadratic, cubic) is most suitable to your data? Construct a scatter diagram but be sure to just do the dots, don’t include the lines that connect them. Then, play around with the trendline feature and include what you consider to be the best trendline.

b.   Using OLS, estimate the firm’s short-run production function. Comment on the strength of the regression results.

c.   Calculate the Q, AP, and MP for L = 8 workers.

d.   At 8 workers, is SMC rising or falling, and how do you know?

L

198 2
1,310 6
408 3
65 1
1,984 9
990 5
1,386 7
712 4
1,678 11
1,710 10

 

  1. Straker Industries estimated its short-run costs using a U-shaped average variable cost function of the form and obtained the following results. Total fixed cost (TFC) at Straker Industries is $820.
Adjusted R Square 0.710
  Coefficients Standard Error t Stat P-value
Intercept 41.80 4.04 10.35 0.000
Q -2.34 0.89 -2.64 0.017
Q^2 0.17 0.04 4.15 0.001

 

  1. What level of output (Q) is associated with the minimum AVC? What is the value of AVC at this minimum?
  2. Determine equations for ATC, TC, and SMC. Graph one scatterplot of Q vs. TC, and another scatterplot of Q vs. ATC, AVC, and SMC.
  3. When output is 16, how much is TC, AVC, ATC, and SMC?
  4. At what amount of output does labor change from exhibiting increasing returns to decreasing returns?
  5. Do Applied Problem #10 on page 442 about grocery stores and gasoline stations. NOTE: the question is not asking if grocery stores compete with gas stations, but whether individual grocery stores are competitive with each other, and whether individual gas stations are competitive with each other.

 

  1. Suppose the market demand and supply functions are QD = 220 – 1.6P and QS = 4P – 116. You have just graduated and moved to this city; as a new MBA and an entrepreneur, you are considering entering the market for this product.
  2. Determine the equilibrium price and quantity in this market.
  3. You’ve researched and found that most firms in the market currently experience costs such that TC = 30 + 65Q – 14Q2 + 2.4Q3. Determine whether or not you should enter this market. Use graphs to support your answer.
  4. Due to unforeseen delays, you don’t enter the market. However, a year later the market supply has changed to QS = 4P – 60. Are you surprised at this shift in supply?
  5. Given the new supply conditions, determine whether or not you should enter the market.

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