Conceptual and Computational Questions, Essay Example

For Bea Careful, EU = 0.5+ 0.5= 1.58, which is less than U(5) = = 2.24.  She won’t play.

For Bea Careful, solve EU = P= for P = 0.71. She won’t take the double-or-nothing bet unless P is at least 71%.  For I. M. Wilder, solve EU = (10)2P = 52, P = 0.25.  He’ll take the bet as long as P is above 25%.

NPVb= –27,000 + 5000/(1.09) + 5000/(1.11)2 + 5000/(1.13)3 + 20,000/(1.07)3 = $1,436.48, which is still greater than NPVa.

At e, EU = 410,000; certainty equivalent, at c, is $640. Recall that Eva will only pay $260 to avoid this gamble.

For I. M. Wilder, EU = 0.5(10)2 + 0.5(0) = 50, which is more than U(5) = (5)2 = 25.  He will play.

For Bea Careful, solve EU = P= for P = 0.71.  She won’t take the double-or-nothing bet unless P is at least 71%.  For I. M. Wilder, solve EU = (10)2P = 52, P = 0.25.  He’ll take the bet as long as P is above 25%.

Use formula from page 213 of textbook. At i = 7%, NPVa= $494.53;  at i = 9%, NPVa = – $249.64.  At i = 7%, NPVb = $2,447.54; at i = 9%, NPVb = $1,100.14.  less;  positive, negative.   Solve by trial and error:  ma = 8.32% and mb = 10.743%.

3. TC = $100(89.9) = $8,990. Per-person cost = $8,990/990 = $9.08.
4. TB is slightly less, TB = $101(89.9) + 0.5(1,000 – 101)(89.9) = $49,489.95.  Per-person TB = $49,489.95/1,000 = $49.49.
5. CS is slightly less, CS = $40,410.50. Per-person CS = $40.82. $49.49 – $40.50 = $8.99;  $40.50 – $40.82 = –$0.32 or 32¢ loss;  strong;

This problem is a variation on the adverse selection (lemons) problem. Banks can check the credit histories of their applicants, however, to gain some information on their credit worthiness. pL = (220 – 200)/0.004 = $5,000;  pG = (240 – 200)/0.004 = $10,000. Lemon owners will try to sell at pG = $10,000; price will fall.  At p = $8,000, QL + QG = 220 – 0.004(8,000) + 240 – 0.004(8,000) = 396.  Qs = 400.  Some sellers, who can’t sell their cars, will be disappointed.  Some buyers, who will get stuck with lemons, will be disappointed.

Fair premium = 0.2(40,000) = $8,000.  Yes.  By paying $8,000, this person could wind up at e

NPVb= –27,000 + 5000/(1.09) + 5000/(1.11)2+ 5000/(1.13)3 + 20,000/(1.13)3 = –$1,028.48.