How to determine a price point?

[needCalculus]

Hi, I came across an interesting problem. A store sells a product at $.8 per unit for a quantity of <= 5; and if a consumer buys more than 5, the unit price falls to $.6 for incentive selling. But I would hope that we can a find an optimal price model for more sales and maximum profit (supposed this is our goal for now), instead of arbitrarily set the incentive price to .6, that is, how to determine a price point that would generate more sales at maximum profit? Probably, we need cost info here as well, if so, let's say, cost = $.4 per unit.

Is there any simple calculus to solve this problem?

Thanks.

 

[HallsofIvy]

Hi, I came across an interesting problem. A store sells a product at $.8 per unit for a quantity of <= 5; and if a consumer buys more than 5, the unit price falls to $.6 for incentive selling. But I would hope that we can a find an optimal price model for more sales and maximum profit (supposed this is our goal for now), instead of arbitrarily set the incentive price to .6, that is, how to determine a price point that would generate more sales at maximum profit? Probably, we need cost info here as well, if so, let's say, cost = $.4 per unit.

Is there any simple calculus to solve this problem?

Thanks.

Not with just the information you have given. You also need a "demand function", telling how the customer's demand for an item depends upon price.

 

[needCalculus]

@HallsofIvy, thanks for pointing out the need of demand function.

In the meantime, we really don't know what demand would be if we sell this product at $.55 per unit, or at $.6 per unit or at $.65 per unit or at $.7 per unit.
And for simplicity sake, let's say, over the next four weeks, nothing major would impact purchase other than price,
a simplistic approach might be like this:
week 1: selling at $.55
Week 2: at $.6
Week 3: at $.65
Week 4: at $.7

Then we would know total sales for each week and since we know the cost already, we can easily calculate total profit for each week. Then we can deduce that the week that generate most profit is the week that we have set up the best price strategy...
But this approach is like learning from the past, what might be more desirable is a Predictive formula to arrive at a best/optimal price estimation, so that it may be considered/used to set a price for future...