accounting73
14.10.2019 •
Business
Harmonâs utility function is u(x1, x2) = x1x2. his income is 100 dollars. the price of good 2 is p2 = 4. good 1 is priced as follows. the first 15 units cost 4 dollars per unit and any additional units cost 5 dollars per unit. what consumption bundle does alex choose?
a. (12.5, 12.5)
b. (25,12.5)
c. (12.5, 25)
d. (15, 10)
e. none of the above.
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Ответ:
Option (a) is correct.
Explanation:
U(x1, x2) = x1x2
Income = 100 dollars
Therefore,
Alex budget constraint is $100.
(a) (12.5, 12.5)
Cost of this bundle = 12.5 × $4 + 12.5 × $4
= $50 + $50
= $100
(b) (25, 12.5)
Cost of this bundle = 15 × $4 + 10 × $5 + 12.5 × $4
= $60 + $50 + $50
= $160
This bundle is not possible because of budget constraint.
(c) (12.5, 25)
Cost of this bundle = 12.5 × $4 + 25 × $4
= $50 + $100
= $150
This bundle is not possible because of budget constraint.
(d) (15, 10)
Cost of this bundle = 15 × $4 + 10 × $4
= $60 + $40
= $100
Hence, it is possible to buy bundle (a) and (d).
Utility function for (a) and (d) bundle:
(a) (12.5, 12.5)
Utility = 12.5 × 12.5
= 156.25
(d) (15, 10)
Utility = 15 × 10
= 150
Therefore,
Alex will choose bundle (a) (12.5, 12.5) because this will give maximum utility.
Ответ:
Bond Price = $1143.533636 rounded off to $1143.53
Explanation:
To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,
Assume that the face value or par value of the bond is $1000.
Coupon Payment (C) = 1000 * 0.07 * 6/12 = $35
Total periods (n) = 9 * 2 = 18
r or YTM = 0.05 * 6/12 = 0.025 or 2.5%
The formula to calculate the price of the bonds today is attached.
Bond Price = 35 * [( 1 - (1+0.025)^-18) / 0.06] + 1000 / (1+0.025)^18
Bond Price = $1143.533636 rounded off to $1143.53