下面的北美精算师2001年11月真题Course2（第三节课），请相关备战精算师人士赶快消化掉。
　　21. In a perfectly competitive market, the market supply and demand functions are:
　　Supply: P = 4Q
　　Demand: P = 100 . Q
　　where P is price and Q is quantity.
　　The total variable cost function (TVC) for an individual firm is:
　　TVC = 76q + q2
　　where q is the quantity produced by the firm.
　　What is the output for the firm?
　　(A) 0
　　(B) 2
　　(C) 8
　　(D) 20
　　(E) 38
　　Course 2, November 2001 23
 
　　22. A firm.s market value balance sheet is as follows:
　　Asset Value 500 Debt 200
　　Equity 300
　　Firm Value 500 Firm Value 500
　　The risk-free rate of interest is 3.5%, bequity is 1.2, bdebt is 0.2, and the return on the
　　market portfolio is 14.4% .
　　Calculate the company.s cost of capital.
　　(A) 5.7%
　　(B) 7.2%
　　(C) 10.0%
　　(D) 12.2%
　　(E) 16.6%
　　Course 2, November 2001 24
 
　　23. Suppose purchasing power parity exists between the United States and the United
　　Kingdom. The current inflation rates are 3.0% in the U.S. and 5.0% in the U.K.
　　The current nominal exchange rate is 2.0 dollars per pound.
　　What is the expected exchange rate one year from now?
　　(A) 1.20
　　(B) 1.96
　　(C) 2.00
　　(D) 2.04
　　(E) 3.33
　　Course 2, November 2001 25
 
　　24. David can receive one of the following two payment streams:
　　(i) 100 at time 0, 200 at time n, and 300 at time 2n
　　(ii) 600 at time 10
　　At an annual effective interest rate of i, the present values of the two streams are equal.
　　Given vn = 0.75941, determine i .
　　(A) 3.5%
　　(B) 4.0%
　　(C) 4.5%
　　(D) 5.0%
　　(E) 5.5%
　　Course 2, November 2001 26
 
　　25. A stock currently has a price of 45.00 and pays no dividends. One year from now, there
　　is a 50% probability that the price of the stock will be 30.00 and 50% that it will be
　　greater than 40.00 .
　　The risk-free rate is 4% .
　　Calculate the price of a one-year European call option with an exercise price of 40.00 .
　　(A) 4.81
　　(B) 6.35
　　(C) 9.81
　　(D) 10.00
　　(E) 11.35
　　Course 2, November 2001 27
 
　　26. Joe’s budget line is defined by the equation y = .0.5x + 18, where y is the quantity
　　of meat and x is the quantity of bread.
　　If Joe’s income increases, what will happen to the slope and the y-intercept of his
　　budget line?
　　(A) Both the slope and the y-intercept will increase.
　　(B) The slope will increase while the y-intercept will remain unchanged.
　　(C) The slope will decrease while the y-intercept will remain unchanged.
　　(D) The slope will remain unchanged while the y-intercept will decrease.
　　(E) The slope will remain unchanged while the y-intercept will increase.
　　Course 2, November 2001 28
 
　　27. A man turns 40 today and wishes to provide supplemental retirement income of 3000 at
　　the beginning of each month starting on his 65th birthday. Starting today, he makes
　　monthly contributions of X to a fund for 25 years. The fund earns a nominal rate of 8%
　　compounded monthly.
　　Each 1000 will provide for 9.65 of income at the beginning of each month starting on his
　　65th birthday until the end of his life.
　　Calculate X.
　　(A) 324.73
　　(B) 326.89
　　(C) 328.12
　　(D) 355.45
　　(E) 450.65
　　Course 2, November 2001 29
 
　　28. Payments are made to an account at a continuous rate of (8k + tk), where ere 0≤t≤10 .
　　Interest is credited at a force of interest δt = 1
　　8 + t
　　.
　　After 10 years, the account is worth 20,000 .
　　Calculate k .
　　(A) 111
　　(B) 116
　　(C) 121
　　(D) 126
　　(E) 131
　　Course 2, November 2001 30
 
　　29. Suppose a consumer.s income increases and, at the same time, the price of X decreases.
　　Further suppose that in the new situation the consumer purchases less X than before.
　　Which of the following must be true?
　　(A) X is a normal good.
　　(B) X is an inferior good.
　　(C) X is a Giffen good.
　　(D) X is a luxury good.
　　(E) X is a good for which the compensated demand curve
　　is steeper than the uncompensated demand curve.
　　Course 2, November 2001 31
 
　　30. Nate intends to invest in two different stocks, X and Y .
　　Stock X has an expected return of 10% and a standard deviation of Z .
　　Stock Y has an expected return of 20% and a standard deviation of 1.5Z .
　　After investing in both stocks, the expected return on Nate.s two-stock portfolio is 12%
　　and the standard deviation is Z .
　　Calculate the correlation between the returns on Stocks X and Y .
　　(A) 0.50
　　(B) 0.53
　　(C) 0.56
　　(D) 0.60
　　(E) 0.63
　　Course 2, November 2001 32
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