Problem 1: Patrick chooses to use his time ‘free-time': (a) working out or (b) reading. Patrick currently has 20 hours a week to allocate to these two activities. It takes Patrick 1.5 hour to work out and .5 hours to read. Patrick enjoys both activities, but he has recently focused more on improving his thought processes; therefore, he spends more time ‘reading'. Patrick feels that the optimal allocation of his time, based upon his budget constraints, is to allocate 12.5 hours to reading and 7.5 hours to working out.
(a) Draw Patrick's budget constraint and optimal consumption bundle such that the number of hours that he spends working out is on the x-axis and the number of hours that he spends on reading is on the y-axis.
(b) Patrick spends more time working out and reading and he becomes more efficient at completing both of these tasks. He can now complete a work out in an hour and he can read the same amount that he previously read in half the time. If the ratio between choosing to read or work out has not changed, please graph his budget constraint and indicate where his knew budget constraint is based upon this new information.
Problem 2. Draw supply and demand curves. Show the impact of an increase in demand on the price and quantity exchanged in the market. Show the impact of a decrease in demand on the price and quantity exchanged in the market.
Problem 3. Currently, the demand equation for baseball bats is Q = 300 - 5P. The current price is $15 per bat. Is this the best price to charge in order to maximize revenues? If not, indicate what price you should charge and quantity that you should produce in order to maximize revenue.
Problem 4. The manager of Viking Sports finds that the price elasticity of baseball bats is -0.77. He wants to hold a sale to get rid of his inventory. What will you advise him (paragraph form)?
Problem 5. A monopoly's demand curve is P = 200 - 3Q and its MC = $15. How many customers should this company serve? What is the price paid by each customer? What will be the company's gross revenue in this venture?
Problem 6: Students are working on an assignment that benefits from teamwork. Barry is a highly analytical person and Jane is a more creative individual. The following chart indicates how long it will take Barry and Jane to complete a task.
Analytical Creative
Barry 5 Hours 8 Hours
Jane 7 Hours 10 Hours
a. Indicate whether Barry or Jane have an absolute advantage completing (1) analytical tasks and (2) creative tasks.
b. Barry and Jane would like to finish the assignment that their instructor gave to them as soon as possible. Does Barry or Jane have a relative advantage in completing either of the tasks? If so, do you feel that they should focus in on their core competencies and split up the tasks to complete the assignment (assume that the ‘workload' is 50% analytical and 50% creative).
Problem 7:
a. Refer to Figure 9.2. What is the Nash equilibrium of this pricing game?
b. Is there a better salutation to this game? If so, what mechanisms would you advise General Electric or Westington put in place to increase the likelihood that both parties agree to the better solution?
Problem 8: A small fitness center that offers only personal training services has the following demand and cost parameters:
Demand: The fitness center has found that it has some discretion in pricing¬¬-that is, it can raise price marginally without drastic reductions in volume. Based on statistical estimates of demand and assuming that external factors stay constant (e.g., price of competitors' services, income levels, etc.), the following relationship exists between the hourly rate for a personal training session (P) and the number of sessions demanded per day (Q):
P = 140 - Q.
Costs: The fitness center finds that its variable costs (e.g., labor) increase at a constant rate of $40 with each additional training session provided per day. Fixed costs such as rent are equal to $200 per day. This yields the following total variable cost (TVC) and total fixed cost (TFC) equations:
TVC = 40Q.
TFC = 200.
Problem 9. Refer to Figure 9.4. The payoffs to each firm (in billions of dollars) and an extensive form game between BP and Shell are shown in the figure. BP has 20 percent of the U.S. gasoline market share and Shell has 16 percent market share. BP and Shell are attempting to determine whether to send geologists to explore Oil Track 20.
(a) Is there a dominant strategy for Shell? What is the dominant strategy, if any, for Shell?
(b) What is the Nash equilibrium or equilibria in this game?
(c) Use the above information to advise BP on whether they should pursue a merger with Shell.
Problem 10: Please provide a graphical example of what could potentially happen to the number of people employed in an economy if the government were to decide to raise the minimum wage; in addition, provide an explanation of what occurs when the minimum wage is increased (theoretical).
