Calculate the arc price elasticity of demand for wheat in the two situations: Th

Question

Calculate the arc price elasticity of demand for wheat in the two situations:
The Wheat Market
old price; $3.40/bu
old quantity; 2.5 billion bu
new price; $3.20/bu
new quantity; 2.525 billion bu
Farmer Browns Market
old price; $3.40/bu
old quantity; 28,000 bu
new price; $3.20/bu
new quantity; 35,000 bu

Can you account for the difference in elasticities? (Show Calculations)

Assume that, for a particular demand curve, when price is $60, quantity demanded is 130, and when price is $50, quantity demanded is 175. Without calculating the coefficient of elasticity, is demand over this range elastic or inelastic? How do you know?

Explanation / Answer

Arc price elasticity is calculated using mid point elasticity formula which is based on average quantity and average price.

(change in Q / average Q )
—————————

(change in P / average P)

The Wheat Market
old price; $3.40/bu
old quantity; 2.5 billion bu
new price; $3.20/bu
new quantity; 2.525 billion bu

Change in Q = 2.525-2.5 = 0.025

Average Q = (2.525 + 2.5) / 2 => 2.51

Change in P = 3.20-3.40 => - 0.20

Aveage P = (3.20+3.40 ) / 2 => 3.30

e= ( .025 / 2.51) / (-0.20 / 3.30) = >.099 / .060 => - 1.65 Demadn is highly elastic.

Farmer Browns Market
old price; $3.40/bu
old quantity; 28,000 bu
new price; $3.20/bu
new quantity; 35,000 bu

Change in Q =35000-28000 = 7000

Average Q = (35000 + 2800) / 2 => 31500

Change in P = 3.20-3.40 => - 0.20

Aveage P = (3.20+3.40 ) / 2 => 3.30

e= (7000 / 31500) / (-0.20 / 3.30) = >.22 / .060 => - 3.70 Demadn is more elastic as compared to the awheat amrket.

Price has increased only by 10 units while quantity has decreased largely. It is elastic demand.

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