# Calculating arc elasticity of demand and optimal price

Please help with the following problem:

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.

https://brainmass.com/business/finance/calculating-arc-elasticity-demand-optimal-price-390418

## SOLUTION This solution is **FREE** courtesy of BrainMass!

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%

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