Maximizing Profit: how high will our campus store price its goods?

Maximizing Profit: how high will our campus store price its goods?

Alice, Congyi, Isha and Linda

We all know that the MHC campus store is expensive. It is a monopoly on MHC apparels such as sweatshirts and (weirdly enough) bandeaus and can thus self-determine the prices of these goods. As a monopoly, facing downward sloping demand curve, how does our campus store determine the prices of everyday goods? Also at what price and quantity does it maximize profit?

With changing seasons, people are becoming sick more often. Since DayQuil is one of the few options on campus to combat a cold or the flu and Mount Holyoke students can rarely afford taking time off to fully nurse their illness. Lets look at an example of how the Campus store may set price to maximize profits. Let the inverse aggregate demand function for DayQuil from the campus store be P = 24 - 4Q, and the cost function as C (Q) =Q²-2Q. Since the Store is situated on campus, it does not have to worry about paying rent; thus, for now, the fixed cost is zero. So the question is at what price and quantity would the Campus Store maximize their profit?

We know that the campus store is a monopoly. If the campus store wants profit maximization, the optimal price and quantity would be where their Marginal Revenue (MR) equals to their Marginal Cost (MC.)
 (As demonstrated in the graph)

So, let’s do profit maximization for the Campus Store, this way we can get the price and quantity

We know, P=24-4*Q and C (Q) = Q^2-2*Q

Total Revenue = (24-4Q)*Q = 24Q-4Q^2

Marginal Revenue = 24-8Q.

                      

Max (Q) = P*Q- C(Q) = 24Q-4Q^2 - (Q^2-2*Q)                                                      

FOC : 24-8Q-2Q+2 = 0

                     24-8Q = 2Q-2                                             

                            Q = 2.6                                                                                              

So P = 24-4Q = 13.6                       

Now the Profit (π)= TR-TC

                               = P*Q – C (Q) = (13.6*2.6 ) - ( 2.6²-- 2*2.6)

                              = 23.4

From this example of the Campus Store and the product DayQuil, we maximized the profit and got profit of 23.4, Price as 13.6 and Quantity as 2.6. At this quantity the marginal revenue is equal to the marginal cost. Therefore this would be the optimum price at which Campus store could maximize its profits.