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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?

finguy
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    Without some information on elasticity there is no hope of an answer. Why would the price increase if the demand is low? Wouldn't it have to fall, then stimulating the demand in year 2? – Ross Millikan Jan 09 '14 at 19:30
  • It is a mathematical problem. I am just asking how much a person would have to increase the price to match the expected sales? – finguy Jan 09 '14 at 19:33

1 Answers1

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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.

John
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