Question

If the supply equation is Q = 110 + 8P+0.9p2 (a) find the price elasticity of supply if the current price is 9. (b) estimate the percentage change in supply if the price rises by 2% (Do not round until the final answer. Then round to two decimal places as needed.) (Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

dQ/dP = 8 + 1.8P

(a)

When P = 9,

(dQ/dP) = 8 + 1.8 x 9 = 8 + 16.2 = 24.2

Q = 110 + 8 x 9 + 0.9 x 9 x 9 = 110 + 72 + 72.9 = 254.9

Elasticity of supply (Es) = (dQ/dP) x (P/Q) = 24.2 x (9/254.9) = 0.85

(b)

Es = % Change in supply / % Change in price

0.85 = % Change in supply / 2%

% Change in supply = 0.85 x 2% = 1.70%