HW10

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Econ 300
Assignment 10

Universal Widget produces high-quality widgets at its plan in Nevada for sale throughout the world. The cost function for total widget production $\left( q\right)$ is given by:

$\displaystyle TC$ $\displaystyle =$ $\displaystyle 10q$

$\displaystyle MC$ $\displaystyle =$ $\displaystyle 10.$

Widgets are demanded only in Australia (where the demand curve is given by and and Lapland (where the demand curve is given by and $MR=30-\frac{q}{2}$ .) If Universal Widget can control the quantitites supplied to each market, how mnay should it sell in each location in order to maximize total profits? What are these profits? Graph your results.
The demand function for football tickets for a typical game at a large Midwestern university is . The university has a clever and avaricious (i.e., greedy, grasping ) athletic director who sets his ticket prices so as to maximize revenues. The university's football stadium holds 100,000 spectators.
1. Write down the inverse demand function.
2. Write expressions for total revenue and marginal revenue as a function of the number of tickets sold.
3. Use blue to draw the inverse demand function and red to draw the marginal revenue function. Also draw a vertical blue line representing the capacity of the stadium.
4. What price will generate the maximum revenue? What quantity will be sold at this price?
5. At this quantity, what is the marginal revenue? At this quantity, what is the price elasticity of demand? Will the stadium be full?
6. A series of winning seasons caused the demand curve for football tickets to shift upward. The new demand function is What is the new inverse demand function?
7. Write an expression for marginal revenue as a function of output. Use red to draw the new demand function and use black to draw the new marginal revenue function.
8. Ignoring stadium capacity, what price would generate maximum revenues? What quantity would be sold at this price?
9. As you noticed above, the quantity that would maximize total revenue given the new higher demand curve is greater than the capacity of the stadium. Clever thought the athletic director is, he cannot sell seats he hasn't got. He notices that his marginal revenue is positive for any number of seats that he sells up to the capacity of the stadium. Therefore, in order to maximize his revenue he should sell ______ tickets at a price of ________.
10. When he does this, his marginal revenue from selling an extra seat is _______. The elasticity of demand for tickets at this price quantity combination is _________.
The following conversation was overhead during a microeconomics cram session. Student A: ''In order to maximize profits, a monopolist should obviously produce where the gap between price and average cost is the greatest.'' Sutdent B: ''No, that will only maximize profit per unit. To maximize total profits, the firm should produce where the gap between price and marginal cost is the greatest since that will maximize monopoly power and hence profits.'' Can you make any sense of this drivel? What concepts, if any, have these students not grasped sufficiently?
A monopolist faces a market demand curve given by

$\displaystyle Q=70-P.$

The monopolist's marginal revenue curve is given by

$\displaystyle MR=70-2Q.$
1. If the monopolist can produce at consumer average and marginal costs of what output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits?
2. Assume instead that the monopolist has a cost structure where total costs are described by
  
  $\displaystyle TC=0.25Q^{2}-5Q+300$
  
  and marginal cost is given by
  
  $\displaystyle MC=0.5Q-5.$
  
  With the monopolist facing the same market demand and marginal revenue, what price-quantity combination will be chosen now to maximize profits? What will profits be?
3. Assume now that a third cost structure explains the monopolist's position with total costs given by
  
  $\displaystyle TC=0.333Q^{3}-26Q^{2}+695Q-5800$
  
  and marginal costs given by
  
  $\displaystyle MC=Q^{2}-52Q+695.$
  
  Again, calculate the monopolist's price-quantity combination that maximizes profits. What will profits be?
4. Graph the market demand curve, the MR curve, and the 3 MC curves from and Notice that the monopolist's profit-making ability is constrained by (1) the market demand curve it faces (along with its associated MR curve) and (2) the cost structure underlying its production.
Suppose that the market for hula hoops is monopolized by a single firm.
1. Draw the initial equilibrium for such a market.
2. Suppose now that the demand for hula hoops shifts outward slightly. Show that, in general (contrary to the competitive case), it will not be possible to predict the effect of this shift in demand on the market price of hula hoops.
3. Consider three possible ways in which the price elasticity of demand might change as the demand curve shifts outward - it might increase, it might decrease, or it might stay the same. Consider also that marginal costs for the monopolist might be rising, falling, or constant in the range where MR=MC. Consequently, there are nine different combinations of types of demand shifts and MC slope configurations. Analyze each of these to determine for which cases it is possible to make a defninite prediction about the effect of the shift in demand on the price of hula hoops.
Suppose a textbook monopoly can produce any level of output it wishes at a constant MC and AC of $5 per book. Assume that the monopoly sells its books in two different markets that are separated by some distance. The demand curve in the first market is given by

$\displaystyle Q_{1}=55-P_{1}$

and the curve in the second market is given by

$\displaystyle Q_{2}=70-2P_{2}.$
1. If the monopolist can maintain the separation between the two markets, what level of output should be produced in each market and what price will prevail in each market? What are total profits in this situation?
2. How would your answer change it it only cost demanders $5 to mail books between the two markets? What would be the monopolist's new profit level in this situation? How would your answer change if mailing costs were $0?
Ronald Coase has conjectured that a monopoly that produces a durable good (one that lasts more than a single period) has less monopoly power than a monopoly that produces a good that is consumed quickly ecasue teh durable good monopoly must face competition from its own used goods. Explain the general types of considerations that a monopoly producer of a durable good would have to consider in choosing a profit-maximizing output level.
What is a ''natural monopoly''? Why does electric power distribution of local telephone service have the characteristics of a natural monopoly? Why might this be less tru for electric power generation or long-distance telephone service?