In economics, the demand for a product is the amount of

Chapter , Problem 1.5.29

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In economics, the demand for a product is the amount of that product that consumers are willing to buy at a given price. The quantity demanded of a product usually decreases if the price of that product increases. Suppose that a company believes there is a linear relationship between the demand for its product and its price. The company knows that when the price of its product was $3 per unit, the quantity demanded weekly was 500 units, and that when the unit price was raised to $4, the quantity demanded weekly dropped to 300 units. Let represent the quantity demanded weekly at a unit price of dollars. (a) Calculate when = 5. Interpret your result. (b) Find a formula for in terms of . (c) The company raises the price of the good and the new quantity demanded weekly is 50 units. What is the new price? (d) Give an economic interpretation of the slope of the function you found in part (b). (e) Find when = 0. Find when = 0. Give economic interpretations of both these results.