Sp06_EC41_W09

Sp06_EC41_W09 - EC 41 UCLA Fall 2008 Sample Problems #6; RE...

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EC 41 UCLA Fall 2008 – Sample Problems #6; RE Chapters 5 & 6 We will skip Chapters 8 and 9 and end the class with section 10.1 1) Flip a fair coin and consider the number of flips required for the first head. If we graph probability of first head on the vertical axis, and number of flips on the horizontal, what type of distribution is this? 2) Flip a fair coin. Consider the number of flips required for the first head. What it the probability of getting the first head on the 6 th toss (i.e., 5 tails in a row, followed by a head)? probability 3) (similar to problem 5.91 on page 357) Consider tossing a coin. Draw the probability that the first Head is on the Xth toss to the right (up to X = 5) a) What is the probability that the first Head is on the second toss? b) What is the probability that the first head is on the third toss? number of tosses to get the first “head” 4) a) A Geometric series can be written; a 0 + a 1 + a 2 + a 3 + …. . If 0<a<1, this sum = a 1 1 . What is the sum of the geometric series if a =.2? ______ if a = .1? _______ b) If a = marginal propensity to consume = .9, what is the Keynesian Autonomous Spending Multiplier? (assume Consumption is only spending category affected by income) c) Suppose the consolidated balance sheet of all commercial banks in an economy is (all values in millions of $): Assets Liabilities and Owners Eq . Reserves 20 (Checkable) Deposits 100 If the required reserve ratio (set by the Fed) is .2 (banks must keep Securities 20 Owners Equity 20 an amount in Reserves = to 20% of deposits), what is the increase Loans 80 in deposits if reserves increase by 10 (say by an open market purchase of securities by the Fed)? d) Suppose a bond pays out $100 per year, every year and the interest rate is 5%. What is the price of this bond just after a payment is made (one year until the next $100 payment)? Use: present value of an amount, PV = future amount/(1+interest) t where t is the number of periods in the future when the amount will be received, and the sum of geometric series). 5)
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Sp06_EC41_W09 - EC 41 UCLA Fall 2008 Sample Problems #6; RE...

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