You have 100 Christmas trees.  PN = 30 – QN  PD = 75 – QD How many trees do I sell in November and December? (PN is the price for November, PD is the price of trees in December).

 Answer: Profit = Price x Quantity Therefore, profit in November = QN(30 – QN) = 30QN – QN2 Differentiate to find the marginal profit: = 30 – 2QN Set marginal profit to 0 (maximised your profit): 30 – 2QN = 0  Therefore, 2QN = 30  Therefore the quantity sold in November is 15 Repeat process for December• The most important thing to remember with a question like this (which will not appear in an exam but helps conceptualise the concept of profit maximisation) is that what you differentiate you find the rate of change between two variables. • By differentiation price with respect to quantity you find the marginal profit of the two. • Importantly, this will result in an excess number of trees remaining, so selling all of the stock is not the route to profit maximisation. Restricting supply to where MR=0 is.