# Answer to Question #75929 in Microeconomics for Claire

Question #75929

Given the supply function:

Q = 150 + 5P + 0.1√(2)

Find price elasticity of supply when P = 10

Q = 150 + 5P + 0.1√(2)

Find price elasticity of supply when P = 10

Expert's answer

Given, supply function Q = 150 + 5P + 0.1 √(2) ……………………..(1)

At P= 10 equation (1) becomes, Q= 150 + (5×10) +0.1 √(2) = 200.14

Now differentiate equation (1) with respect to P , we get dQ/dP=5

We know price elasticity of supply (e) = dQ/dP ×P/Q = 5×P/Q

Now at P = 10, price elasticity of supply (e)= 5×10/200.14 = 0.2498 (approx.)

(put the value of P and Q at P = 10)

Answer: Price elasticity of supply is 0.2498.

At P= 10 equation (1) becomes, Q= 150 + (5×10) +0.1 √(2) = 200.14

Now differentiate equation (1) with respect to P , we get dQ/dP=5

We know price elasticity of supply (e) = dQ/dP ×P/Q = 5×P/Q

Now at P = 10, price elasticity of supply (e)= 5×10/200.14 = 0.2498 (approx.)

(put the value of P and Q at P = 10)

Answer: Price elasticity of supply is 0.2498.

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