Answer key
Expected Value Specialty Line= 0.3(400,000) + 0.5(230000) + 0.2(20000) = 239000
b. Variance for Discount line = 1,501,000,000
Standard deviation = 38,743
Variance for Specialty line = 16,809,000,000
Standard deviation = 129,650
The discount store opportunity is far less risky.
c. The specialty store offers a higher expected return but not in proportion to the increased risk.
Expected payoff = $166.67 + $58.33
= $225
b. The utility from $400 is square root of 400 = 20. The utility from $100 is square root of 100 = 10
Expected utility = (20)(5/12) + (10)(7/12) = 14.16
c. Utility from $169 is 13. The utility from rolling the dice (14.16) is greater than the utility from a certain $169; therefore, Connie will turn down the $169 alternative prize and roll the dice.
d. The cash payment that will yield 14.16 is calculated as follows:
14.16 = square root (I)
200.51 = I
Connie is indifferent between a cash payment of $200.51 and a roll of the dice. A payment of $200.52 is preferred to the roll of the dice.
Qd - (5 – Pd)/0.005 = 1000 – 200 Pd
Qf – (3 – Pf)/0.00075 = 4000 – 1333.33 Pf
Q = 5000 – 15333.33 Pf 0 ≤ Pd ≤ 5
0 ≤ Pf ≤ 3
b. Domestic buyers enter market at Pd ≤ 5
Foreign buyers enter market at Pf ≤ 3
c. At P = $2.50 per pound:
Qd = 1000 – 200(2.5) = 500 pounds a day
Qf = 4000 – 1333.33(2.5) = 666.68 pounds a day
Q = 5000 – 1533.33(2.5) = 1166.68 pounds a day
Check Qd + Qf = Q
d. At P = $4 per pound, only domestic buyers enter market; so world demand equation is not appropriate to use. We must use only domestic demand equation
Qd = 1000 – 200(4) = 200 pounds a day
b. Right-angle indifference curves.
c. Straight line downward sloping indifference curves
d. Indifference curve is a circle
b. Optimal mix of X and Y:
MRS = Px/Py
Y/X = 9/12 = 0.75
John should consume 0.75 times as much Y as X.
c. John’s current mix is not optimal. Currently he is consuming 0.67 Y for each X.
1600- 125P = 440 + 165 P
1160 = 290 P
P = 4
Q = 1600 – 125(4) = 1100
b. For Price Elasticity of Demand = -125 times 4/1100 = -0.45 (approximately)
For Price Elasticity of Supply = 165 times 4/1100 = 0.60 (approximately)
c. Calculate Qd and Qs at the $4.50 price
Qd = 1037.5
Qs = 1182.5
Surplus = Qs – Qd = 1182.5 – 1037.5 = 145 million bushels that government would be forced to buy.
25 – 0.005Q + 0.15(10) = 5 + 0.004Q
21.5 = 0.009Q
Q = 2388.9 units per week
At Q = 2388.9, P = $14.56 per unit
b. Since we can solve for quantity demanded as a function of prices
Q = (25 + 0.15 PY – PX
We see that there is a positive
relationship between Q and PY.
An increase in price of good Y generates an increase in quantity
demanded for good X at any value of PX, which implies that goods X
and Y are substitutes.