Question

This is a simple joint product (economies of scope) problem. (This topic was covered in class, but not in the book, although it is the subject of Exercise 10.1.) You are considering opening a smoothie franchise on 12^th Ave. You will be able to sell 100 smoothies per day, at material costs $2.50 per smoothie and fixed costs (say labor plus rent) of $60 per day. In addition, you have the option of selling on-site music downloads at a supplier cost to you of $0.50 each; you estimate you can sell 200 per day. There is a competing smoothie store, so you will be able to charge no more than $3.00 per smoothie, and internet competition restricts you to charging no more than $0.80 per download.

a) Write the cost function C if you sell only smoothies. Use S to denote the quantity of smoothies (C = f(S) =…). Note: This does not mean the cost if you sell 100 per day; let the quantity of smoothies be a variable (that is, S). Similarly, write the cost function if you sell only downloads D.

C = f(S) =

C = g(D) =

b) Write the cost function if you sell both downloads and smoothies.

C(S,D) =

c) If your revenues exceed your costs, you will go into business. Using the numbers given above, should you go into business? Show your calculation.

d) You are relying on a bank loan. The bank states that you must show that each product that you sell is profitable before they will proceed with the loan. Complete the following reply.

“That’s not the right way to look at my business because …

Answer 1

a) C = f(S) = $2.5S + $60

C = g(D) = $0.50D

b) C (S,D) = $2.50S + $60 + $.50D

c) Max Selling Price of Smothies = $3 per smoothie (100 smoothies per day)

Max Selling Price of downloads = $0.80 per download (200 per day)

Total revenue = 3*100 + 0.80* 200 = $ 300 + $160 = $460

Total Cost = $2.50S + $60 + $.50D = $250 + $ 60 + $ 100 = $ 310

Since revenues exceed costs and we are making a profit of $150 per day, we can go into business.

d) That's not the right way to look at my business because initially the products might not be profitable when sold at a small volume. The fixed cost of $60 remains the same and doesn't change with the quantity of goods sold. Hence at a very low volume sold, I might not be profitable but when the products are sold at greater volumes, the revenes surpass the fixed as well as the variable costs which will make my business profitable Also, the concept of economies of scale should be taken into consideration. As the business grows there is a learning curve involved, and, when my volumes of sale increase considerably, the variable cost per piece will reduce even further ( due to increased efficiencies). This will increase my profits even more in the long run.