Answer to Question #269009 in Microeconomics for David

Question

The estimated equation for the Japanese Densuke Watermelon supply curve is Q = 100 + 0.8 p

where p is the price in dollars per kilogram and Q is the quantity supplied in tons per year. What is the price elasticity of supply at the points on the supply curve where the prices are p = $10 , p = $20, p = $200, and p = $500 and p → $∞ per kg? Draw the supply curve and show these elasticities on the diagram.

Answer 1

Solution:

Price elasticity of supply = $\frac{\partial Q} {\partial P}\times \frac{P}{Q}$

$\frac{\partial Q} {\partial P}$ = 0.8

When P = 10: Q = 100 + 0.8(10) = 100 + 8 = 108

Price elasticity of supply = $0.8\times \frac{10} {108} = 0.07$

 

When P = 20: Q = 100 + 0.8(20) = 100 + 16 = 116

Price elasticity of supply = $0.8\times \frac{20} {116} = 0.14$

 

When P = 200: Q = 100 + 0.8(200) = 100 + 160 = 260

Price elasticity of supply = $0.8\times \frac{200} {260} = 0.62$

 

When P = 500: Q = 100 + 0.8(500) = 100 + 400 = 500

Price elasticity of supply = $0.8\times \frac{500} {500} = 0.8$

 

When P = ∞: Price is constant at any given quantity

Price elasticity of supply = ∞

 

This is depicted by the below supply curve showing the price elasticity of supplies: