Suppose there are two lakes located on a stream. Clean water flows into the first
lake, then the water from the first lake flows into the second lake, and then water from the second
lake flows further downstream. The in and out flow from each lake is 500 liters per hour. The first
lake contains 100 thousand liters of water and the second lake contains 200 thousand liters of water.
A truck with 500 kg of toxic substance crashes into the first lake. Assume that the water is being
continually mixed perfectly by the stream.

a) Find the concentration of toxic substance as a function of time in both lakes.
b) When will the concentration in the first lake be below 0.001 kg per liter?
c) When will the concentration in the second lake be maximal?

Given the following information,
Spot =$100
Risk free = 10%
Maturity = 1 year
Forward contract price =$80
Which arbitrage opportunity will you use to exploit the mispricing?

Question 3

Briefly discuss the implications of the Capital Asset Pricing Model for the relationship between the current spot price of an asset and the discount offered by the seller of a futures contract. (100 words)

What risks are hedged and what risks are unhedged?

Hint: Price vs Quantity risk

Why do airlines avoid hedging 100% of their fuel consumption or avoid being “overhedged”

1) You own the following portfolio and wish to make an index of your portfolio performance. Use an initial index of 100 where appropriate.

a) What is the value of the price weighted index at t = 1 and t = 2?

b) Assuming that t = 1 is the base year (Index = 100), what is the value weighted price at t = 2?

c) Briefly explain the advantages and disadvantages of each type of index.

Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U(D,F) = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $2000. Suppose F is on the horizontal axis and D is on the vertical axis. Her optimal consumption point is given by(partial units are allowed)

1. F = 0 and D = 100

2. F = 5 and D = 20

3. F = 2.5 and D = 10

4. F = 2.5 and D = 20

13. Firms in a perfectly competitive firm make 0 economic profit in the long run.

True or False

14. A firm in a perfectly competitive market, finds that it's MR = MC occurs at Q = 100, at which point the market Price is $8. The firm's ATC = AFC+AVC = $6; Is the firm making a profit or loss at this point of production?

a.Loss of $200

b.profit of $600

C.loss of $600

D. profit of $200

15. A perfectly elastic demand curve has an elasticity of

a. infinity

b. 0

c. 1

d. 100

16. The Cross-Price elasticity of demand Between X and Y will always be negative if the goods are Complements.

True or False

9. The price of an item depends on the order quantity:

It costs $40 to place each order. Annual demand is 3,000 units. Carrying cost is 25 percent of the material price.

What is the optimal order quantity, and what would be its annual total cost? Go to at least two decimal places for your intermediate calculations. Round your answers to the nearest whole number.

The original, first generation Apple Watch was released in 2015. Although the original Apple Watch was designed to compete with various activity trackers at the time, the Apple Watch was sufficiently different for us to assume that there were no close substitutes in 2015.

At the launch Tim Cook announced that the Apple Watch would sell for $500 in the United States and Europe. At that price, q was 1,000, where q was number of watches sold in thousands. An industry group determined that the marginal and average cost of producing the Apple Watch was constant at $100.

1. How much profit did Apple make at the launch of the Apple Watch, given the price and quantity sold (that is, given p=500 and q=1,000)?

In the hope of maximizing its profit, Apple commissioned an economist to estimate demand for the Apple Watch across the U.S. and Europe. The economist determined that the inverse demand function was:

p=600-0.1q.

2. Given the estimated inverse demand, what single price should Apple charge for the Apple Watch in order to maximize its profit?
3. Given that Apple changed the price of the Apple Watch based on the economist’s recommendation, how much profit did Apple make at the new price?

As it turned out, the economist’s estimation actually allowed Apple to distinguish between customers in the United States and customers in Europe, and they were in fact different. These differences were expressed in their different inverse demand functions:

The U.S. market:                              p^A=900-0.25q^A

The European market:                   p^E=400-(1/6)q^E

4. Given the differences across the two groups of customers and assuming that resale across the two continents is impossible, what price should Apple charge in the United States and Europe, respectively?

Given this (group) price discrimination strategy, how much profit did Apple make in each of the two markets? What was total profits earned?

Suppose that Ally Financial Inc. issued a bond with 10 years until maturity, a face value of $1,000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.

a. What was the price of this bond when it was issued? (round to the nearest cent)

b. Assuming the yield to maturity remains constant , what is the price of the bond immediately before it makes it first coupon payment? (Round to the nearest cent)

c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment? (Round to the nearest cent)