Question

imagine that the short-run price elasticity of supply for farmer's corn is 0.3, while long - run price elasticity of supply is 2.
1. if prices for corn fall 30%, what are the short-run changes in quantity supplied?
2. what are the short-run and long run changes in quantity supplied if prices rise by 15%?
3. what happens to the farmer's revenues in each of these 4 situations?

Answer 1

Elasticity of supply = % Change in quantity supplied / % Change in price

(1)

0.3 = % Change in quantity supplied / (-30%)

% Change in quantity supplied = (-30%) x 0.3 = -9% (Decrease)

(2)

(a) For short run,

0.3 = % Change in quantity supplied / 15%

% Change in quantity supplied = 15% x 0.3 = 4.5% (Increase)

(b) For long run,

2 = % Change in quantity supplied / 15%

% Change in quantity supplied = 15% x 2 = 30% (Increase)

(3) Let initial revenue (R) = P x Q

When price falls by 30%, in long run, % Change in quantity supplied = 2 x (-30%) = -60% (Decrease)

(Case I: Short run, Price falls 30%)

New revenue (R1) = 0.7P x 0.91Q = 0.637 x PQ

% Change in revenue = (R1/R) - 1 = [(0.637 x PQ) / PQ] - 1 = 0.637 - 1 = -0.363 = -36.3% (Decrease)

(Case II: Long run, Price falls 30%)

New revenue (R1) = 0.7P x 0.4Q = 0.28 x PQ

% Change in revenue = (R1/R) - 1 = [(0.28 x PQ) / PQ] - 1 = 0.28 - 1 = -0.72 = -72% (Decrease)

(Case III: Short run, Price rises 15%)

New revenue (R1) = 1.15P x 1.045Q = 1.20175 x PQ

% Change in revenue = (R1/R) - 1 = [(1.20175 x PQ) / PQ] - 1 = 1.20175 - 1 = 0.20175 = 20.175% (Increase)

(Case IV: Long run, Price rises 15%)

New revenue (R1) = 1.15P x 1.3Q = 1.495 x PQ

% Change in revenue = (R1/R) - 1 = [(1.495 x PQ) / PQ] - 1 = 1.495 - 1 = 0.495 = 49.5% (Increase)