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The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula { q =...

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The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula {eq}q = 102e^{(3p^2 + p)} {/eq}, where q is the demand in monthly sales and p is the retail price in hundreds of yen.

(a) Determine the price elasticity of demand E when the retail price is set at 800. The demand is going (UP/DOWN) by % per 1% increase in price at that price level.

(b) At what price will revenue be a maximum?

(c) Approximately how many paint-by-number sets will be sold per month at the price in part (b)? (Round your answer to the nearest integer.)

Price Elasticity of Demand:

Economists are often concerned with how sensitive the demand for a good with respect to price. In other words, they want to measure the effect on quantity demanded given a small incremental change in price of said good. This is called the price elasticity of demand and can be calculated as follows: {eq}\frac{dQ}{dP} \cdot \frac{P}{Q} {/eq}.

As an addendum, recall that revenue is simply quantity times price, and the way to maximize it is to find it is to solve for the first order condition where the derivative of the revenue function is equated to zero.

Answer and Explanation: 1

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a) {eq}q = 102e-3p^2 + p {/eq}

At {eq}p=8 {/eq}, {eq}q = 102e-3(8)^2 + (8) = 102e -184 \approx 93.26 {/eq}

Furthermore, {eq}\frac{dq}{dp} = -6p +...

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Price Elasticity of Demand: Definition, Formula & Example

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Chapter 3 / Lesson 54
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Learn what price elasticity is. Discover how to find price elasticity of demand, study examples of price elasticity, and examine a price elasticity graph.


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