SECTION OVERVIEW: Chapter 10 continues our analysis of production and cost by applying
regression techniques to empirically estimating production and cost functions (similar to
chapter 7’s estimation of demand functions). Given the typical theoretical shape of
production and cost curves, it describes cubic functions for the total, average, and marginal
equations. Chapter 11 merges production and cost (supply) information with demand
functions in situations of perfect competition to reveal how firms set prices and quantities.
LEARNING GOALS: Upon completing this section, we will be equipped to take data and estimate
regressions to specify production or cost functions, and interpret the quality of the results.
These results will allow us to make more informed decisions, such as determining
diminishing returns to labor and marginal product/cost. We will also understand the
theoretical determinants of short-run and long-run production and pricing decisions in
perfectly competitive markets.
1. You collect the following production data for your firm:
Q
L
a. Which functional form (linear, quadratic, cubic) is most
198
2
suitable to your data? Construct a scatter diagram but be sure
1,310
6
to just do the dots, don’t include the lines that connect them.
Then, play around with the trendline feature and include what
408
3
you consider to be the best trendline.
65
1
b. Using OLS, estimate the firm’s short-run production function.
1,984
9
Comment on the strength of the regression results.
990
5
c. Calculate the Q, AP, and MP for L = 8 workers.
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7
d. At 8 workers, is SMC rising or falling, and how do you
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4
know?
1,678
11
1,710
10
2. 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
AVC a bQ cQ 2
Industries is $820.
Adjusted R Square
0.710
Coefficient
Standard
s
Error
t Stat
P-value
41.80
4.04
10.35
0.000
Intercept
-2.34
0.89
-2.64
0.017
Q
0.17
0.04
4.15
0.001
Q^2 a. What level of output (Q) is associated with the minimum AVC? What is the value of AVC
at this minimum?
b. Determine equations for ATC, TC, and SMC. Graph one scatterplot of Q vs. TC, and
another scatterplot of Q vs. ATC, AVC, and SMC.
c. When output is 16, how much is TC, AVC, ATC, and SMC?
d. At what amount of output does labor change from exhibiting increasing returns to
decreasing returns? ECON 705 Module 5 Assignment End-of Module Assessment due: Aug. 6th, 11:59 pm 3. 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.
4. 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.
a. Determine the equilibrium price and quantity in this market.
b. 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.
c. 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?
d. Given the new supply conditions, determine whether or not you should enter the market.