Suppose that Andrew has the utility function: U(C,M)= C^0.5+M^0.5 , where C represents cupcakes and M represents muffins. Andrew has income of $150. Suppose that the initial price per cupcake is $2 and the price per muffin is $1. At these prices, Andrew spends $100 on muffins. When cupcakes are on sale, each cupcake costs $1. When cupcakes are on sale, Andrew spends $75 on muffins. The price of muffins and Andrew’s income is unchanged throughout.

1. Draw a diagram that illustrates Andrew’s (a) budget constraints, (b) indifference curves, and (c) (d) optimal bundles before and after the change in cupcake price. Place cupcakes on the horizontal axis.

2. Calculate the (a) substitution and (b) income effects resulting from the decrease in the price of cupcakes, and illustrate the substitution and income effects on your diagram in part 1.

3. Are cupcakes a normal or an inferior good for Andrew? Why?

You construct a one-period binomial tree to model the price movements of a stock.

You are given:

1. The length of one period is 6 months.
2. The current price of the stock is 100.
3. The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%.

Suppose:

• u denotes one plus the rate of gain on the stock if the stock price goes up.
• d denotes one plus the rate of loss on the stock if the stock price goes down.
• r denotes the continuously compounded risk-free interest rate.

Which of the following parameters would give rise to an arbitrage opportunity?

1. u=1.011,d=0.822,r=0.05

2. u=1.021,d=0.981,r=0.06

3. u=1.025,d=1.002,r=0.07

4. u=1.028,d=1.010,r=0.08

5. u=1.029,d=1.022,r=0.09

PlEASE PROVIDE EXPLANATION

Industry demand and supply functions for potatoes are as follows:

            Q_D = -1,450 – 25P + 12.5P_W + 0.1Y

            Q_S = -100 + 75P – 25P_W – 12.5P_L + 10R

Where:

Q is number of potato bushels (in millions).

P is the avg. wholesale price of potatoes (in $/bushel).

P_W is avg. wholesale price of wheat (in $/bushel), estimated to be $4.

Y is annual income (GDP in $ billions); estimated to be $15 trillion.

P_L is avg. price of unskilled labor ($/hour); estimated to be $8.

R is avg. annual rainfall (in inches); estimated to be 20 inches.

a) What are the demand and supply curves for potato bushels? (10 points)

b)  Determine if there is a surplus or shortage at P = $1.50 and $2.50 (5 points)

c)   Calculate the equilibrium price/output combination. (5 points)

d)  Do the following events constitute a shift in demand or movement along the demand curve, and in what direction: (5 points)

i. GDP falls by 1%

ii. price rises from $2.00 to $2.50

1. Construct profit diagrams at expiration time to show what position in IBM puts, calls and/or underlying stock best expresses the investor’s objectives described below.

   IBM currently sells for $150 so that profit diagrams between $100 and $200 in $10 increments are appropriate. Also assume that at-the-money puts and calls currently

cost $20 each. The call with strike $140 costs $25 and the call with strike $160 costs $17.

1. (a) An investor wants to benefit from IBM price drops, but does not want to lose more than $20 on the investment.

2. (b) An investor wants to capture profits if IBM price declines and losses if IBM price increases. The investor wants to break even if IBM price does not change.

3. (c) An investor wants to bet that the upcoming IBM earnings announcement is very close to market expectations—meaning that the price will not move by more than $10 dollars.

Bob consumes two goods, gasoline and sandwiches. He has an income of $100 and faces

a price of gasoline of $2 per gallon and a price of sandwiches of $5.

(a) Graph and write the equation for Bob’s budget line.

(b) Bob consumes 4 sandwiches. If Bob’s consumption bundle is just affordable, how

much gas is he consuming?

(c) If Bob consumes the bundle in (b) and the price of sandwiches rises to $8, then by

how much will Bob’s income have to increase so that he can still just afford the bundle

he currently consumes?

(d) Suppose that Bob must spend both money and (ration) coupons to purchase gasoline and

sandwiches. He has 40 coupons and the coupon price of gasoline is 2 and the coupon

price of sandwiches is 1. Show Bob’s budget set. Show Bob’s budget set if his income

were to rise to 250 and if his income were to fall to 30.

4. A nursery is willing to supply 75 plants when the price per plant is $18 and 100 plants when the price per plant is $20.  The price elasticity of supply in this case using the mid-point method would be

a. 2.71 which indicates that the supply is elastic

b. 2.71 which indicates that the supply is inelastic

c. 0.27 which indicates that the supply is elastic

d. 0.27 which indicates that the supply is inelastic

5. Assuming that the price elasticity for a good is 0.3 therefore, a 20% decrease in the price of that good would

a. result in a 0.15 percent increase in the quantity demanded

b. result in a 6 percent increase in the quantity demanded

c. result in a 66 percent increase in the quantity demanded

d. result in a 0.06 percent increase in the quantity demanded

7. In the market of purses a 15 percent change in price causes 20 percent change in quantity supplied. In this situation the price elasticity of supply is

a. 0.74, and supply is inelastic

b. 1.33, and supply is elastic

c. 0.74, and supply is elastic

d. 1.33, and supply is inelastic

1. A. The Table 1 below provides data for the Big Cat Rescue Company. The price of entrance is $60 and Q refers to the number of visitors who can visit the Big Cat Reserve. Calculate TR= Total Revenue, π=profit, MC= Marginal Cost and MR=Marginal revenue and fill in the blanks of the table.

B. Also, calculate TR, MR and π=profit when the entrance price falls to $50.

C. As you look over the completed table, what level of Q maximizes profit when price=$60 and when price=$50?

1. Mustapha maintains a monopoly in the holographic TV market because of its patent,but it is about to expire. The market demand and Mustapha’s production cost are given by:  P = 100 − 0.5? and ?? = 100 + 0.5Q² The equilibrium price and quantity are:

a. Q = 50 units and P = $75.00

b. Q = 75 units and P = $60.00

c. Q = 60 units and P = $60.00

d. Q = 100 units and P = $85.00

2. Mustapha maintains a monopoly in the holographic TV market because of its patent but it is about to expire. The market demand and Mustapha’s production cost are given by:  P = 100 − 0.5? and ?? = 100 + 0.5Q². The monopoly profit is.

a. $3,750.00

b. $2,400.00

c. $3,000.00

d. $2,500.00

3. Aji Fatou owns a rental space in New York and is thinking of opening a restaurant in that space. The total cost of operating the restaurant is C(Q) = 20Q, where Q is the number of customers at the restaurant in a day.

The market demand for restaurants is Q = 100 – p. Aji Fatou has the option of leasing out this space instead of opening a restaurant. The market rent for her property is $600. If Aji Fatou is operating as a perfectly competitive firm. Derive Aji Fatou's Accounting profit and Economic Profit.

a. Accounting Profit = $2,200 and Economic profit =$0.00

b. Accounting Profit = $0.00 and Economic profit = -$600

c.Accounting Profit = $600 and Economic profit =$0

d.Accounting Profit = $2,200 and Economic profit =$1,600

15.

Praveen Co. manufactures and markets a number of rope products. Management is considering the future of Product XT, a special rope for hang gliding, that has not been as profitable as planned. Since Product XT is manufactured and marketed independently of the other products, its total costs can be precisely measured. Next year’s plans call for a $250 selling price per 100 yards of XT rope. Its fixed costs for the year are expected to be $500,000, up to a maximum capacity of 550,000 yards of rope. Forecasted variable costs are $150 per 100 yards of XT rope.

1. Estimate Product XT’s break-even point in terms of sales units and sales dollars. (1 unit = 100 yards) (Do not round intermediate calculations.)

Q3. Consider the following data: S = 100; r = .08; s = .3 on the following two options:

Call 1   Call 2

K = 100;     K = 90

T-t=90 days.      T-t=180 days.

Price: 6.91 16.33

Delta: .58 .78

Gamma: .02 .0138

3.1 A trader just shorted 100 CBOE calls 2.

Calculate the number of shares necessary to create a Delta Neutral position.

3.2 A trader just shorted 100 CBOE calls 2.

Calculate the number of calls 1 and shares of the underlying stock that the trader must hold (long or short) in order to create a Delta-Gamma neutral position

Q4. A trader just shorted 100 of calls 1 and 100 of calls 2 from Q3.

Calculate the delta and the Gamma of this position.

Q5. Consider put 1 and put 2, which are on the same stock and with the same exercise prices and time to expiration as their respective calls from Q3.

Calculate the number of shares covered in put 1 that together with the short calls 1 and 2 from Q3. create a Delta-neutral position.

Q6. Calculate the number of the shares in put 1 and put 2 needed to create a delta-Gamma neutral portfolio consisting of the short calls (call 1 and call 2 from Q3.) and the two puts.