Constant elasticity of demand

Question

Given: Q = aP^b

For P₀ = 200, b = -1.5, Q₀ = 1000, solve for a to get a = 2828427

b is the constant elasticity of demand

Now suppose P rises to P₁=250; for given values of parameters a and b, new value of Q is Q₁=715.5418

%chg(Q) = (Q₁-Q₀)/Q₀ = -0.28446

%chg(P) = (P₁-P₀)/P₀ = 0.25

So elasticity = %chg(Q) / %chg(P) = -1.14

But elasticity is supposed to be constant at -1.5!!!

What am I doing wrong?

Answer 1

Dear student, your calculation is perfect. The reason that your elasticity is not coming -1.5 is that here the question setter has calculated elasticity based on the mid point formula.

As you would be knowing that by mid point formula, while calculating elasticity, we use the average of the two values in the denominator which calculating the percentage changes.

So,

%chg(Q) = (Q1-Q0)/{(Q1+Q0)/2} [the only difference here is that in denominator, we take average of Q1 and Q0 and not Q0]

Similarly,

%chg(P) = (P1-P0)/{(P1 + P0/2)}

Now when you solve it again by using this mid point formula, you will get elasticity as -1.5

I hope this clears your doubt. Still if you have any doubt, you can contact me. Also, If you have any tutoring requirement in any subject of economics, then do contact me.

Thanks

Shubham