Q1. Determine the value-maximizing order quantity when the buyer's total value from purchasing Q units of output is B = 30Q - Q2‚ and the seller's cost of producing Q units is C = 0.5Q2.
Q2. A would-be acquirer is preparing to make a first-and-final tender offer to acquire target Company T. The acquirer judges that Company T's reservation value is somewhere between $60 and $90 per share, with all values in between equally likely. Under its own management, the acquirer predicts that the target will be worth $100 per share. Should the firm offer $90 per share to assure that Company T will sell out? Determine the offer that maximizes the acquirer's expected profit.
Q3. A manager reveals that she has a utility function U = 100M - 2M2, for 0 ≤ M ≤ 25, where 'U' stands for Utility, 'M' stands for Money. Is this person risk averse, risk neutral, or risk loving?
Q4. Consumer surveys indicate that 40% of newspaper readers read automobile ads and 5% of those who read the ads actually purchase automobiles. On the other hand, 50% of magazine readers read automobile ads but only 3% of those who read the ads actually buy a car. Among those who do not read either newspaper or magazine auto ads, 1% buys cars anyway. Sixty percent of the population reads newspapers, while 20 percent primarily read magazines. Compute the overall percentage of the population that purchases automobiles in a given year. (To aid your analysis, you might wish to draw a decision tree listing appropriate probabilities for the three aforementioned reading segments.)
Q5. Stake Gold Mines has the option to purchase a parcel of land adjacent to its current mining operations in a Western state. The seller's best and final price is $3 million. If the land has commercial mineral deposits, Stake Gold estimates its value at $5 million. If there are no deposits, the estimated value is $2 million. A preliminary look at the land leads Stake Gold to believe that the chance of mineral deposits is 50:50.
(a) Given this information, should Stake Gold purchase the land? For a fee of $200,000, the seller has agreed to let Stake Gold collect extensive mineral samples on the site. Based on past experience, if there are minerals present, the samples will provide a favorable indication 80% of the time. If no minerals are present, the samples will (falsely) give a favorable reading 40% of the time.
|
|
Growth
|
Recession
|
Total
|
|
+
|
0.4
|
0.1
|
0.5
|
|
-
|
0.3
|
0.2
|
0.5
|
|
Total
|
0.7
|
0.3
|
|
Determine Pr(M|F) and Pr(M|U). (Here, M denotes mineral deposits, NM denotes no mineral deposits, F denotes favorable samples, and U denotes unfavorable samples.)
(b) Should Stake Gold pay $200,000 for the right to collect samples?
Q6. A firm hires an economist to conduct market research and determine demand for a new product. If the test is correct and the firm launches the product, it earns a profit of $600,000. If the firm launches the product when there is weak demand, it incurs a loss of $250,000.
|
|
Strong
|
Weak
|
Total
|
|
Accurate
|
0.2
|
0.2
|
0.4
|
|
Inaccurate
|
0.3
|
0.3
|
0.6
|
|
|
0.5
|
0.5
|
1.0
|
What is the firm's expected profit from an accurate and inaccurate test respectively? What can you conclude about the quality of the market research?