What is the point elasticity of the demand function p plus 4q equl to 80 at 10 and 400?

Answer 1

To answer this question you must know two things: 1) the point elasticity formula, and 2) the demand equation. 1) the point elasticity formula says: dQ/dP X P/Q is the point elasticity at a price (P) and the corresponding Quantity (Q) -P is the price you are evaluating the elasticity at, and Q is found by evaluating the demand equation at the price (P) -dQ/dP is the derivative of Q with respect to P 2) The demand equation for this particular problem is: P+4Q=80 The Answer: Step one: differentiate the demand equation with respect to P - to do this you must algebraically solve the demand equation for Q P+4Q=80 4Q=80-P Q=20-0.25P -next you must differentiate with respect to P dQ/dP=-0.25 Step 2: plug derivative into formula -now, refering back to the original formula, you have: -0.25 X P/Q Step 3: Plug in the values for P/Q - in this problem, they want you to evaluate the elasticity at price 10 and price 400 Price at 10: Elasticity(10)= -0.25 X (10/17.5)=-0.4375 or 0.4375 (elasticities are always positive) Now, the step above is very simple, all I did is multiplied the derivative of the demand function by the price over the quantity demanded evaluated at the price by the the demand function. All that is happening is I am following the point elasticity formula outlined at the top. Price at 400: Elasticity(400)=-0.25 X (400/-80)=1.25 And there you have it!