The marketing team at Widgets Inc. is trying to determine the optimal price for
ID: 413387 • Letter: T
Question
The marketing team at Widgets Inc. is trying to determine the optimal price for a new product it has recently developed, code named “The Unicorn.” Management estimates that at a price of $30 per unit, it will sell 650,000 units. If it lowers the price to $27 it expects sales to increase to 875,000 units, and at a price of $24 it anticipates sales of one million units.
Because “The Unicorn” is based on entirely new technology, management expects there to be a substantial learning (i.e., production) curve. At a production volume of 650,000 units, management forecasts average costs of $15 per unit. At a production level of 875,000 units, costs will average $13 per unit; and at production volume of one million units costs should average $12 per unit.
Fixed costs will total $8 million per year, regardless of the level of production.
With this information in mind, what is the optimal price for the new product? Show your work and explain.
Explanation / Answer
In order to find the optimum price level, let us calculate the variable costs for different price level given:
Step 1: Calculating Total cost (TC) for all three levels using the formula:
TC = Average Cost (AC) * Number of Units
At price level 30: TC = 15 * 650,000
= $ 9,750,000
At price level 27: TC = 13 * 875,000
= $ 11,375,000
At price level 24: TC = 12 * 1,000,000
= $ 12,000,000
Step 2: Calculating Variable Cost (VC) for all the three levels using the formula:
VC = TC – FC
At price level 30: VC = 9,750,000 – 8,000,000
= $ 1,750,000
At price level 27: VC = 11,375,000 - 8,000,000
= $ 3,375,000
At price level 24: VC = 12,000,000 – 8,000,000
= $ 4,000,000
Calculations are presented in tabular form as well for clear understanding:
Price per unit
No. of units
AC per unit
FC per unit
TC
VC
30
650,000
15
8,000,000
9,750,000
1,750,000
27
875,000
13
8,000,000
11,375,000
3,375,000
24
1,000,000
12
8,000,000
12,000,000
4,000,000
As per the above calculations, the Optimal Price for the new product is $ 30, as at this level the Total Cost as well as Variable Cost is the minimum ($1,750,000), as compared to other levels. And the price charged is said to be optimal when the cost involved with it is the minimum.
Therefore: Optimal Price = $ 30
Price per unit
No. of units
AC per unit
FC per unit
TC
VC
30
650,000
15
8,000,000
9,750,000
1,750,000
27
875,000
13
8,000,000
11,375,000
3,375,000
24
1,000,000
12
8,000,000
12,000,000
4,000,000
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