Question

If the supply equation is Q = 80 +9P+0.9P? (a) find the price elasticity of supply if the current price is 7 (b) estimate the percentage change in supply if the price rises by 5%. (a) (Do not round until the final answer. Then round to two decimal places as needed.) (b) % (Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

Answer :

a) Supply function = Q = 80 + 9P + 0.9P^2

When P = 7;

Supply = Q = 80 + 9*7 + 0.9*7*7 = 187.1

Differentiating Q with respect to P, we get ;

dQ/dP = 9 + 2*0.9*P = 9 + 1.8P

When P = 7 ;

dQ/dP = 9 + 12.6 = 21.6

Price elasticity of supply = (dQ/Q) / (dP/P) = (dQ/dP) * (P/Q) = 21.6 * (7/187.1) = 0.808

Answer a) 0.808

b) Current Price = 7

Increase in price = 5%

New price = 7 + 0.05*7 = 7.35

New Quantity = 80 + 9*7.35 + 0.9*7.35*7.35 = 194.77

Change in Quantity = 194.77 - 187.1 = 7.67

Percentage change = (7.67/187.1) * 100 = 4.10%

Answer b) 4.10%