What is the maximum revenue and the set of prices that will increase revenue/profit?

Question

Consider a retailer selling a single item. Based on past experience, management estimates the relationship between demand, D, and price, p, by the linear function D = 2,000 – 0.6p. At what price is revenue maximized. What if the retailer can charge two different prices? Can you find a set of prices that will increase profit for this case?

Answer 1

Invert the function so that P= 10,000/3 - 5/3Q.

MR is twice as steep. So MR= 10,000/3 -10/3 Q.

TR is maximised when MR = 0 or 10,000/3 = 10/3Q or Q = 1000. when Q = 1000 we look at demand and see

1000= 2000- 6/10 p or 3/5p = 1000. or P= 5000/3. Any price above 5000/3 will be on the elastic portion of the demand curve.

Hope this helps

Lenny