{Use of Tech} Demand functions and elasticity Economists use demand functions to describe how much of a commodity can be sold at varying prices. For example, the demand function D(p) = 500 - 10p says that at a price of p = 10, a quantity of D(10) = 400 units of the commodity can be sold. The elasticity E = dD/dp p/D of the demand gives the approximate percent change in the demand for every 1% change in the price. (See Section 3.6 or the Guided Project Elasticity in Economics for more on demand functions and elasticity.)


b. If the price is $12 and increases by 4.5%, what is the approximate percent change in the demand? 

Verified step by step guidance

1. Identify the initial price, which is given as p = 12, and calculate the new price after a 4.5% increase using the formula: new price = initial price * (1 + percent increase).
2. Calculate the new price by substituting the initial price and the percent increase into the formula: new price = 12 * (1 + 0.045).
3. Next, use the demand function D(p) = 500 - 10p to find the initial demand D(12) by substituting p = 12 into the demand function.
4. Calculate the new demand D(new price) by substituting the new price obtained from step 2 into the demand function D(p).
5. Finally, determine the approximate percent change in demand using the formula: percent change in demand = (new demand - initial demand) / initial demand * 100.