10.6.2 Products with no external market
Consider the following situation:
SP10.3 Transfer pricing
Due to the expansion of business in Gogoland in recent years, SR Products has set up a marketing division there responsible for selling a new product. The head office and manufacturing plant remain in the United States. The company has estimated that the total cost of manufacturing in the USA and the cost of transportation of the product is given by the function:
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where C=total cost per week in $ and Q¼units sold. This cost appears in the accounts of the manufacturing division.
The total cost for the marketing division in Gogoland is given by:
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This includes the $100 per unit which is the transfer price paid by the marketing division to the manufacturing division. This total cost appears in the accounts of the marketing division. The revenue function for the marketing division is estimated as:
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where R=total revenue per week in $.
a. Calculate the optimal policy for the company as a whole, showing the price, output and overall profits of the firm.
b. Calculate the optimal policies for the marketing division and the manufacturing divisions, assuming a transfer price of $100, showing the overall profit of the firm in each case.
c. Calculate the optimal transfer price in order to make the optimal policies for both divisions the same as that for the company as a whole.
d. What does the above situation imply regarding managerial strategy?
As with all pricing problems discussed so far, the problem can be analysed either graphically or algebraically. In this case an algebraic approach will be used.