Question

Market research shows that there high-value customers are willing to pay $200 for your house cleaning service and low-value customers are willing to pay $175. High value types represent 40% of the population. If marginal cost is $100, at the optimal price, what are your expected profits per customer?

Answer 1

$185

Step-by-step explanation:

To determine the expected profits per customer at the optimal price, we can use a simple calculation based on the information provided. The key factors to consider are the pricing for high-value and low-value customers, the proportion of each type in the population, and the marginal cost.

Let:

P_h be the price for high-value customers, which is $200.

P_l be the price for low-value customers, which is $175.

Proportion of high-value customers (H) = 40% = 0.40.

Proportion of low-value customers (L) = 60% (since 100% - 40% = 60%).

Marginal cost (MC) = $100.

The expected profit per customer (EP) can be calculated as follows:

EP = (Probability of being a high-value customer × Profit from high-value customer) + (Probability of being a low-value customer × Profit from low-value customer)

EP = (H × P_h) + (L × P_l)

EP = (0.40 × $200) + (0.60 × $175)

EP = $80 + $105

EP = $185

So, at the optimal price, your expected profits per customer would be $185.