Question

In: Economics

A firm has done extensive market research, and has found that on average when they lower...

A firm has done extensive market research, and has found that on average when they lower their price by $6.75, demand for the product increases by 120 units. If sales are 1000 units and the price is $145, what is the price elasticity? What would it be if sales were 3500 units and the price $200? What does the difference in the two elasticities mean?

Solutions

Expert Solution

Case 1

Present Sales = 1000 Units

Price = $145

P1 = 145, Q1 = 1000

When Price is lowered by $6.75, the demand increases by 120 units

P2 = 145 - 6.75 = $138.25

Q2 = 1000 + 120 = 1120 units

Using Midpoint Formuls

Price Elasticity of Demand

= [(Q2 - Q1) / (Q2 + Q1) / 2] / [(P2 - P1) / (P2 + P1) / 2]

= [(1120 - 1000) / (1120 + 1000) / 2 ] / [( 138.25 - 145) / ( 138.25 + 145) / 2]

= ( 120 / 1060) / ( 6.75 / 141.625)

= 0.113 / 0.047

= 2.4

Case 2

When Sales is 3500 units and Price is $200

Q1 = 3500, P1 = $200

When Price is lowered by $6.75, the demand increases by 120 units

Q2 = 3500 + 120 = 3620

P2 = 200 - 6.75 = $193.25

Elasticity of Demand

= [(Q2 - Q1) / ( Q2 + Q1) / 2] / [( P2 - P1) / (P2 + P1) / 2]

= [( 3620 - 3500) / (3500 + 3620) / 2] / [( 193.25 - 200) / ( 193.25 + 200) / 2]

= ( 120 / 3560) / ( 6.75 / 196.625)

= 0.0337 / 0.0343

= 0.98

In first Case the Elasticity of Demnad is 2.4 which is greater than 1. This means that demand is Elastic. When demand is elastic, a percenatge change in price results in larger percentage change in quantity demanded. When demand is elastic, when price increases, there is larger percentage fall in quantity demanded and thus total revenue falls. The vice versa is also true. This means that with fall in price, the total revenue increases.

Revenue Before fall in Price = Price * Quantity = $145 * 1000 = $145000

Revenue After Fall in Price = $138.25 * 1120 = $154840

There is increase in revenue with fall in price. Increase in Revenue = $154,840 - $145,000 = $9840

In Second Case, the Elasticity of Demand is 0.98, which is less than 1. This means demand is inelastic. When demand is inelastic, a given percentage rise in price results a very less percentage decrease in quantity demanded, thus increasing the total revenue. Also, when price decreases, there is very less percenatge increase in quantity demanded, thus decreasing the total revenue.

Revenue Before fall in Price = Price * Quantity = $200 * 3500 = $700,000

Revenue After Fall in Price = $193.25 * 3620 = $699,565

Thus, due to inelastic demand, with the fall in price the total revenue decreases. Decrease in Revenue = $700,000 - $699,565 = $435.

Note: While calculating price elasticity of demand absolute values are considered. So, minus sign is ignored.

Rahul Sunny answered 1 year ago

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