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Managerial Economics- Elasticity Concepts

You have taken a job as pricing manager for a very fine men's clothing line that sells high-end, tailored shirts, suits, etc. The firm is interested in increasing its revenues. Because it is a "high-end" clothier, your boss does not what to have a "sale" on shirts or sweaters; he would actually rather increase the prices on either the firm's tailored shirts or the firm's hand-knit sweaters.

You know that depending on the elasticity of demand, it is possible to increase the prices for shirts or sweaters, sell fewer units but actually increase your revenues.

The last time you increased the prices on your shirts and sweaters, the shirts went from $300 each to $320 each and the sweaters went from $400 each to $430 each.

The corresponding change in demand was: Shirts dropped from an average sales of 260 a month to 242, while sweaters dropped from an average sales of 200 a month to 188.

Calculate the price elasticity of demand for shirts and sweaters.

Which one, shirts or sweaters, has a demand elasticity that will allow you to increase the price, sell fewer units BUT still increase your revenues?

Take what was chosen and increase the price 10% from the current price (the current price is $320 for shirts and $430 for sweaters) and show the new quantity demanded at that price as we did in class. Also, show that the new total revenue will be greater than then old total revenue.

Solution Preview

Please refer attached file for missing formulas.

Solution
First we calculate arc price elasticity of demand for shirts.
Average P=(300+320)/2=310
Average Q=(260+242)/2=251

Ep(shirts) = percentage change of P/percentage change of Q = Average P/Average Q = 242-260/320-300 * 310/251 = -18/20 * 310/251 = - 1.11

Now we calculate the arc price elasticity of demand for sweaters
Average P=(400+430)/2=415
Average Q=(200+188)/2=194

Ep(sweaters) = percentage change of P/percentage change of Q = 188 - 200/430 - 400 * ...

Solution Summary

Solution depicts the steps to estimate the price elasticity of demand for shirts and sweaters in the given case. It also analyzes the effect of price changes on the total revenue.

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