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# Calculating arc elasticity of demand and optimal price

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Stinging Pesticides, Inc., provides scorpion control services, to residential and business customers in the El Paso area. The company recently raised its service price from \$70 to \$80 per annual treatment. As a result, sales fell to 37,500 from 52,500 treatments in the year earlier period.

A. Calculate the arc price elasticity of demand for SPI service.
B. Assume that the arc price elasticity (from Part A) is the best available estimate of the point price elasticity of demand. If marginal cost is \$48 per unit for labor and materials, calculate SPI's optimal markup on price and its optimal price.

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Please refer attached file for complete solution. Expressions typed with the help of equation writer are missing here.

A. Calculate the arc price elasticity of demand for SPI service.
Initial Price=P1=\$70
Final Price=P2=\$80
Initial sales=Q1=52500
Final Sales=Q2=37500
Arc Elasticity of demand=

B. Assume that the arc price elasticity (from Part A) is the best available estimate of the point price elasticity of demand. If marginal cost is \$48 per unit for labor and materials, calculate SPI's optimal markup on price and its optimal price.

Marginal Cost=MC=\$48
Price elasticity of demand=Ep=-2.5
Optimal Price = (Ep/(1 + Ep))* MC
=(-2.5/(1-2.5))*48
=\$80

Optimal Markup=P-MC=(80-48)=\$32

Mark up percent on Marginal cost=Markup/MC=32/80=40%

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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