讲解 APEC 3002: Managerial Economics Spring 2025讲解 Statistics统计

ApEc 3002

Spring 2025

Cost Function Estimation (CFE) Memo Lab

You’re on the job with the online grocery ordering/delivery service. With plans to expand to new areas of the Metro and the number of orders per week growing in the areas you currently serve.  Your boss has asked you to analyze how expansion will affect the cost side of the business. Over the past six months, the average revenue per order has remained constant at approximately $105. Only recently, however, have combined average costs for warehouse and delivery operations fallen below $100 on average. The investor group that has funded the start-up of the business has expressed concern about the ability of the business to cover costs and provide them with some return on their investment.

You’ve gone to company records for data you can use in your analysis. It’s saved in an Excel worksheet named APEC3002 Memo Lab CFE.xlsx. In addition to data on orders per week (labeled Orders in the worksheet), you’ve asked accounting to provide data on weekly costs. They maintain and have provided cost records on two distinct aspects of your company’s operations. One series of cost figures is for warehouse operations (labeled Warehouse Variable Cost in the worksheet). This includes labor and supply costs for all activities related to ordering product  and assembling grocery orders for customers, as well as the cost of goods sold. The second series of cost figures is for delivery of orders to customers’ homes (labeled Delivery Variable Cost in the worksheet). This includes labor for drivers and dispatchers, fuel, and other vehicle expenses.

Because these two aspects of the overall business may be affected differently by expansion, you’ve decided to examine the cost-output relationships for them separately. Since the period for the analysis is relatively short and all the data are from the same operation, you have decided to ignore prices in your analysis. You’ll simply estimate parameters for two variable cost functions that are simple relationships between cost and output:

VCWH = fWH (Orders) where VCWH stands for Warehouse Variable Cost

VCDEL = fDEL (Orders) where VCDEL stands for Delivery Variable Cost

You can choose the functional form. Cobb-Douglas and polynomial are good candidates. In your write-up (which should be a memo addressed to your boss), you should describe the basic features of your analysis including the purpose and your data sources, explain your choice of functional form, and present your estimation results. The real issue however is – how expansion from nearly 3,500 to as many as 7,000 orders per week will affect costs in the warehouse and for deliveries. Are there economies or diseconomies of scale for these activities? Will average variable costs increase or decrease for these two activities with expansion? What will happen to overall average variable costs per order – i.e., the sum of average variable costs for the two activities? What do your findings suggest about the ability of the business to cover variable costs as your service expands? Should the business expand?

Grading Rubric for Memo Lab