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Assignment #11: Decision Making for Firms in Competitive Markets
Note: This assignment is due on December 2, Wednesday before or in class and will be assessed
for 100 points in total. My office hour is 10am-1pm on Tuesday or by appointment.
Handwriting is required for this assignment. Show the process as how you get the results. Simply put
the numbers from the answer key will result in partial even zero grade. Assignment will be graded
based on the degree of completion and inputs/efforts shown in your work.
We will go through the textbook example “Profit Maximization at Beau Apparel” in section
11.6 in this assignment. I’ve posted a scanned copy of section 11.6 “Implementing the ProfitMaximizing
Output Decision.” Most but not all answers can be found in the handout. The
rest requires your creative inputs. There are five steps in this process/framework of firms’ decision
making to maximize profit.
Implementing the Profit –Maximizing Output Decision
We have learned 1) the consumer behaviour or the demand side of the market, 2) the cost/
production or the supply side of the market, and 3) finally firms’ decision making to maximize
profits, when we combine demand and supply of the market and take the competitive environment
surrounding individual firms (called market structure) into consideration. For this assignment, we
consider price-taking firms in a perfectly competitive market.
A Case Study: Profit Maximization at Beau Apparel
In mid-December 2013, the manager of Beau Apparel was preparing the firm’s production plan for
the first quarter of 2014. Suppose that you are an intelligent consultant hired by the manager to
conduct the economic analysis for an optimal production plan, and then to write a report to the
manager based on your analysis. You will only present the analysis part here.
Go through the following steps and questions, and provide your answers to the questions (read
along the textbook while you are working on these steps and questions):
Step 1.
Forecast the wholesale price of shirts for the first quarter of 2014.
We’ve learned methods for predicting market prices in Chapters 2 and 7. Suppose we
will use the price forecast techniques in Chapter 7.
(a) First, find the appropriate section and case study example in Chapter 7, and give the
titles of the section and the example for price forecasting;
(b) Second, describe how you would forecast the wholesale price of the shirts as follows:
describe the type of data you propose to use, and give the regression equation that
you want to apply for price forecast.
Imagine that you’ve done your forecast and you obtained three prices based on three
different assumptions about market conditions. High: $20; Medium: $15; and Low: $10.
Step 2. Estimate average variable cost (AVC) function, and derive total variable cost
(TVC) function and short-run marginal cost (SMC) function.
We’ve learned how to estimate cost functions in Chapter 10 and in Assignment 10. We
know that we only need to estimate one of the three cost functions, and then we can
derive the other two from the one that is actually estimated.
Based on what you’ve learned in Assignment 10,
(a) First, describe where you would obtain the data to estimate a cost function;
(b) Second, describe briefly how you would calculate AVC from the data that you’ve
collected.
(c) Third, write you regression equation for AVC (suppose after plotting TVC and AVC
data, you found TVC reassembles a cubic function specification, and AVC
reassembles a quadratic specification).
Suppose you’ve done your estimation and estimated AVC function as follows:
AVˆC = 20 − 0.003Q + 0.00000025Q2
(d) Derive TVC function from the above AVC function.
(e) Derive SMC function from the TVC function in part (d) by take derivates of TVC
€ Q.
with respect to
Step 3. Check the shutdown rule: at which market price level, the firm should cease
production for the first quarter of 2014.
(a) Describe the shutdown rule.
(b) Derive the minimum value of AVC. Follow these steps: First, derive the First Order
Condition (FOC) by taking the derivative of AVC with respect to Q, and setting the
derivative equation to zero. Second, solve for Q* from the FOC that you’ve got in
the first step. Third, substitute Q* into AVC function, and you should get a value of
the minimum AVC.
(c) Compare the minimum AVC with the three forecasted prices that you’ve got in Step
1. Should Beau Apparel continue to produce or shut down at the forecasted prices of
$20, $15, and $10, respectively?
Step 4. If Beau Apparel continues its production, what is the optimal production
quantity of shirts for the first quarter of 2014?
(a) Describe decision rule for the optimal output level to maximize profit, given that the
firm decides to produce.
(b) Calculate the output level of shirts at each forecasted price level that is appropriate.
Hint, only calculate the optimal output level when the price is above the shutdown
threshold, i.e., only if Beau Apparel decides to produce.
Step 5. Calculate profit or loss.
Calculate profit or loss based on each forecasted price, $20, $15, and $10 for the first
quarter of 2014.
