Question

6) You are working for a button factory that faces the following demand curve for its buttons: (14 marks)

   $bVrjWPE97aYAAAAASUVORK5CYII=$

1. Calculate elasticity of demand at a price of $10 and $40. How should the firm adjust prices in each case to increase revenue and why?
2. Calculate the price that maximizes revenue.

Answer 1

a) Price elasticity of demand = dq/dp * p/q

= -(1/p) * p/q

= -1/q

Now price elasticity at P = 10 is PED = -1/(4 - ln(10)) = -0.59

When price is P =40, PED = -1/(4 - ln(40)) = -3.21

In case the price is 10, the price should be reduced to increase revenue since PED is less than 1 making demand inelastic.

In case the price is 40, the price should be increased to increase revenue since PED is more than 1 making demand elastic.

b) Revenue = price x quantity

R = 4p - p*ln (p)

Revenue is maximized when R'(p) = 0

4 - p*(1/p) - ln (p) = 0

ln(p) = 3

This gives p = 20

Hence the revenue maximizing price is 20.