Problems on Monopoly Behavior

Here are some problems on monopoly behavior.  Answering Problems 1-4 
will be easier if you have worked the homework problem on pages 237 
and 238 of the text.


    1.  A monopolist faces a demand function that can be described by the
        equation P=505-15Q where P is the price that the monopolist
        charges per unit of output and Q is the number of units that the
        monopolist can sell at that price. The monopolist's total costs
        are 25Q and its marginal cost is 25.  The following expression
        expresses the monopolist's profit as a function of the number of
        units sold: 

        (a) 505-15Q-25 
        (b) 505-30Q 
        (c) 480Q-15Q2 
        (d) 505Q-15Q2-15 
        (e) None of the above 

(Hint: Profit is Total Revenue Minus Total Cost)

    2.  The monopolist found in the previous problem has a marginal
        revenue curve that is described by the equation (where MR stands
        for marginal revenue): 

        (a) MR=505-15Q 
        (b) MR=505-25Q 
        (c) MR=520+25Q 
        (d) MR=505-30Q 
        (e) MR=530-40Q 

    3.  Where quantity is measured on the horizontal axis and dollars on
        the vertical axis, the marginal cost curve of the monopolist of
        the previous two problems is  

        (a) an upward-sloping line through the origin with slope 25. 
        (b) a horizontal line at a height of $25. 
        (c) a vertical line at a quantity of 21. 
        (d) an upward-sloping line through the origin with slope 50. 
        (e) a vertical line at quantity 16 

    4.  In order to maximize its profits, the monopoly of the preceding
        questions should sell a quantity of  

        (a) 32 units 
        (b) 16 units 
        (c) 166.67 units 
        (d) 83.33 units 
        (e) 40 units 

(Hint: For what quantity does marginal revenue equal marginal cost?)


    5.  Bozoworks, a software company, has exclusive rights to sell the
        game Space Morons. Bozoworks spent $2500 getting the program 
        ready to market. Its only remaining costs are the cost of
        distributing the copies of Space Morons to buyers. This costs $5
        per copy. If Bozoworks sells Q copies, its total costs will be
        $2500+5Q. Nobody is willing to pay more than $90 for a copy of
        Space Morons. If Bozoworks offers to sell Space Morons at price
        p, all buyers with buyer values of p or greater will buy and all
        buyers with buyer values below p will not buy.  There are 37
        demanders who have buyer values of  $90  for a copy of Space
        Morons. For every dollar that the price falls below $90, Space
        Morons picks up one more buyer. Thus there is 1 demander with
        buyer value $89, one with buyer value $88, one with buyer value
        $87, and so on. Bozoworks' marginal revenue from increasing its
        sales from 37 to 38 is:  

        (a) $90 
        (b) $3,330 
        (c) $45 
        (d) $52 
        (e) $180 

(Hint: To increase sales from 37 to 38, Bozoworks will have to cut
 the price it gets for every unit it sells by $1)

    6.  Which of the following formulas gives the highest price at which
        Bozoworks can sell Q copies of Space Morons, where 37<Q<127?  

        (a) P=90-2Q 
        (b) P=127-Q 
        (c) P=90-2Q 
        (d) P=90-Q 
        (e) None of the above 

(Hint: At what price can it sell 37 units, 38 units, 
39 units...? Do you see the pattern?)


    
                         Answers


         1.   C     
         2.   D     
         3.   B     
         4.   B    
         5.   D     
         6.   B