An economist is interested in how the price of a certain item affects its monthly sales. At a price of $p, a quantity, q, of the item is sold each month. Suppose that we write q=D(p). Using complete and descriptive sentences, explain the meaning of each of the following statements: a) D(500) = 2,000. b) D'(500) =-25.

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**Price and Demand Analysis**

An economist is interested in how the price of a certain item affects its monthly sales. At a price of $p, a quantity, q, of the item is sold each month. Suppose that we write q = D(p). Using complete and descriptive sentences, explain the meaning of each of the following statements:

**a) D(500) = 2,000**

This statement means that when the price of the item is set at $500, the quantity of the item sold each month is 2,000 units. Essentially, it tells us the number of units demanded by consumers per month when the item's price is $500.

**b) D'(500) = -25**

This statement indicates that at the price point of $500, the rate of change of the quantity demanded with respect to price is -25. In other words, for every dollar increase in the price of the item, the quantity demanded decreases by 25 units. This describes the sensitivity of demand to changes in price at the $500 price level.
Transcribed Image Text:**Price and Demand Analysis** An economist is interested in how the price of a certain item affects its monthly sales. At a price of $p, a quantity, q, of the item is sold each month. Suppose that we write q = D(p). Using complete and descriptive sentences, explain the meaning of each of the following statements: **a) D(500) = 2,000** This statement means that when the price of the item is set at $500, the quantity of the item sold each month is 2,000 units. Essentially, it tells us the number of units demanded by consumers per month when the item's price is $500. **b) D'(500) = -25** This statement indicates that at the price point of $500, the rate of change of the quantity demanded with respect to price is -25. In other words, for every dollar increase in the price of the item, the quantity demanded decreases by 25 units. This describes the sensitivity of demand to changes in price at the $500 price level.
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