Question

Your startup company Fabulous Fudge Inc. enters a new market. Your marketing consultants estimate the daily demand for your chocolate bars as


q(p) = 2000; if p < 1;
1000(-p^2 + 2p + 1); if 1 <= p < 2;
1000(p^2 - 6p + 9); if 2 <= p < 3;
0; if 3 <= p:

Here q denotes the quantity demanded per day and p the price per chocolate bar in dollars.
(a) Sketch the graph of demand q(p) as a function of price p.
(b) Compute the price elasticity of demand E(p).
(c) Determine the range of prices p for which demand is elastic, inelastic and unit elastic.
(d) If the price per chocolate bar is

Answer 1

Your startup company Fabulous Fudge Inc. enters a new market. Your marketing consultants estimate the daily demand for your chocolate bars as


q(p) = 2000; if p < 1;
1000(-p^2 + 2p + 1); if 1 <= p < 2;
1000(p^2 - 6p + 9); if 2 <= p < 3;
0; if 3 <= p:

Here q denotes the quantity demanded per day and p the price per chocolate bar in dollars.
(a) Sketch the graph of demand q(p) as a function of price p.
(b) Compute the price elasticity of demand E(p).
(c) Determine the range of prices p for which demand is elastic, inelastic and unit elastic.
(d) If the price per chocolate bar is 1:2$ and you wish to increase your revenue, should you increase or decrease the unit price?
(e) Determine the price(s) p at which the instantaneous rate of change of revenue with respect to price is zero.