Question

Organic vegetables are traded in a competitive world market, and the world price is USD 9/lb. Unlimited quantities are available for import into the United States at this price. The US domestic supply for various price levels are shown as follows:

Price (USD /lb)	US Supply (million lbs)
3	2
6	4
9	6
12	8
15	10
18	12

What is the equation for supply?

What is the arc elasticity of supply between a price of USD 3/lb and USD 6/lb?

What is the arc elasticity of supply between a price of USD 15/lb and USD 18/lb?

Explain why the elasticity of supply changed as you moved up the supply curve. Think in terms of percentage changes.

Answer 1

• Equation of supply curve:

Q = a + b * P

where Q is quantity sold

a is intercept

b is slope

P is price

2 = a + b * 3 ........ (1)

4 = a + b * 6 ........ (2)

Solving (1) and (2)

2 - 3b = 4 - 6b

3b = 2

b = 0.67

Put value of b in either (1) or (2)

2 = a + 0.67 * 3

a = 0

Supply equation becomes:

Q = 0 + 0.67 * P

Q = 0.67P

• Arc elasticity of supply Quantity sold at $3 (P1) = 2 (Q1) Quantity sold at $6 (P2) = 4 (Q2) Arc elasticity = {(Q2 - Q1) / [(Q1 + Q2) / 2]} / {(P2 - P1) / [(P1 + P2) / 2]} = {(4 - 2) / [(4 + 2) / 2]} / {(6 - 3) / [(6 + 3) / 2]} = 0.67 / 0.67 = 1
• Arc elasticity of supply Quantity sold at $15 (P1) = 10 (Q1) Quantity sold at $18 (P2) = 12 (Q2) Arc elasticity = {(Q2 - Q1) / [(Q1 + Q2) / 2]} / {(P2 - P1) / [(P1 + P2) / 2]} = {(12 - 10) / [(12 + 10) / 2]} / {(18 - 15) / [(18 + 15) / 2]} = 0.18 / 0.18 = 1

Elasticity of supply remains same at all level of points as every change in quantity supplied comes with same change in price.