Suppose K1 and K2 have the following distribution:
Scenario Probability return K1 return K2
w(1)    0.3 -10% 10%
w(2)    0.4 0% 20%
w(3)    0.3 20% -10%

(a) Find the risk of the portfolio with w1 = 30% and w2 = 70%.
(b) Find the risk of the portfolio with w1 = 50% and w2 = 50%.
(c) Which of the portfolios above (in part (a) and (b)), has higher expected returns?

The beta of an all equity firm is 1.6. The beta of debt is 0.2.If the firm changes its capital structure to 60% debt and 40% equity using 10% debt financing, what will be the beta of the levered firm? (Assume no taxes.)

A. 4.0

B. 3.7

C. 3.4

D. 2.8

Complete the following table assuming that (a) MPS = 0.2, (b) there is no government and all saving is personal saving.(mps=marginal propensity to save)

Hint: mps = S1 - S0 / Y1 - Y0

Suppose a family's annual disposable income is 8,000 of which it saves 3,900.

(a) What is their APC (average propensity to consume)? ____________

(b) If their income rises to 9,500 and they plan to save 4,400 , what are their MPS and ____________ MPC? ____________

A game designer claims that there is a 20% chance (or a probability value of 0.2) that an intermediate player will complete the fifth level of a game at the first trial. The game is tested by 8 players of intermediate skills. Assuming events are independent,answer the following questions:

a)What is the probability that only two out of 8 players will pass the game fifth level at the first trial? (NOTE: there are 28 different ways to select 2 players out of 8 players)

b)What is the probability that at least one player out of the 8 players will pass the game fifth level at the first trial?

c)What’s the probability that none of the 8 players will pass the fifth level at the first trial?

Assume that demand for a commodity is represented by the equation P = 10 – 0.2 Q d, and supply by the equation P = 5+ 0.2 Qs where Qd and Q s are quantity demanded and quantity supplied, respectively, and P is the Price. Use the equilibrium condition Qs = Qd a. Solve the equations to determine equilibrium price b. Now determine the equilibrium quantity c. Graph the two equations to substantiate your answers and label these two graphs D1 and S1. 2. Furthermore; assume the demand for this product increases because of a change in income. a. Graph the new demand curve and label as D2 b. What will be the new equilibrium price and quantity compared to the initial one. c. Is this product normal good or inferior good?

Question 1. Suppose ?? is generated by an AR(1) process, such that ?? = 0.2 + 0.5??−1 + ?? ; ??~??(0, ? 2 )

(a) What is the partial autocorrelation function of the above AR(1) process?

(b) Is the above AR(1) process stationary?

(c) Derive E(??)?

(d) Derive V(?? )?

(e) What is the autocorrelation function of the above AR(1) process?

A store that sells calculators finds that the probability that a calculator breaks is 0.2. The problems with calculators breaking is independent to each calculator. (a) If the store sells 100 calculators, find the probability that 80 of the calculators work and 20 break. (b) From the 100 calculators sold, find the probability that the first 20 calculators sold break and the others work. (c) Suppose, once a calculator breaks down, the store is not allowed to sell any more calculators. What is the expected number of calculators they can sell? (d) Continued from part (c), suppose the store already sold 10 calculators and they all work. What is the expected number of calculators they can sell in total?

In the exercise, X is a binomial variable with n = 7 and p = 0.2. Compute the given probability. Check your answer using technology. HINT [See Example 2.] (Round your answer to five decimal places.)

P(1 ≤ X ≤ 3)

a) Suppose a tax on beans of $0.2 per can is levied on firms. As a result of the tax, the equilibrium price increases from $0.4 to $0.5. What fraction of the incidence (tax burden) falls on consumers? On firms? Suppose the supply elasticity is 0.4. What must the demand elasticity be? (8 Points)

(b) If the demand function for orange juice is expressed as Q = 1000 − 400p, where Q is quantity in gallons and p is price per gallon measured in dollars. For what values of prices the demand for orange juice inelastic? (7 Points)

(c) Suppose demand and supply for a good is given by QD = 150 − 2P and QS = 50 + 23P. The government imposes a price oor of $3. What is the quantity bought and sold in the market. (7 Points)

(d) Leonardo is indierent between lahmacun and pizza. Lahmacun sells for $2 and pizza sells for $1 per serving. Assuming that Leonardo has a budget of $10. How will he spend it? Explain your answer by drawing Leonardo's budget line and indierence curves.(8 Points)

A population proportion is 0.2. A sample of size 150 will be taken and the sample proportion p will be used to estimate the population proportion.

Round your answers to four decimal places.

a. What is the probability that the sample proportion will be within ±0.04 of the population proportion?

b. What is the probability that the sample proportion will be within ±0.07 of the population proportion?