Price of Product

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Suppose an item costs $ \$10$. The expected demand for 4 years are:

$$ \text{1st year}: 5$$ $$ \text{2nd year}:10 $$ $$ \text{3rd year}:1 $$ $$ \text{4th year}:2 $$

The actual demand is: $$ \text{1st year}: 3$$ $$ \text{2nd year}:12$$ $$ \text{3rd year}:2 $$ $$ \text{4th year}:8 $$

What would the price of the item have to be for each year to match the expected sales? For example, in the first year, the actual demand of $3$ is less than the expected demand $5$. This suggests that the item price of $10$ will increase in year 2 etc. So we have:

$$ \text{Price 1st year}: \$ 10$$ $$ \text{Price 2nd year}: ?$$ $$ \text{Price 3rd year}:? $$ $$ \text{Price 4th year}:? $$

The cumulative expected demand is:

$$\text{1st year}: 5$$ $$\text{2nd year}: 15$$ $$\text{3rd year}: 16$$ $$\text{4th year}: 18$$

so that the total expected sales is $\$180$.

The cumulative actual demand is:

$$\text{1st year}: 3$$ $$\text{2nd year}: 15$$ $$\text{3rd year}: 17$$ $$\text{4th year}: 25$$

so that the total actual sales is $\$ 250$.

At year 1, how can a person change the price to match the expected sales after the first year?

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This depends entirely on what your demand is as a function of price. That, in turn, is based on the distribution of what your potential customers are willing to pay.

You might sell four at $\$20$ but you might also sell four at $\$100$. There's no way to determine that based on the information you've supplied. At the very least, the demand model should be some function of price and years on market.