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alisha [4.7K]
3 years ago
9

Maurice has the following utility function: U (X Y) =20X+80Y-X^2-2Y^2, where X is his consumption of CDs with a price of ​$11 an

d Y is his consumption of movie​ videos, with a rental price of ​$2. He plans to spend ​$50 on both forms of entertainment. Determine the number of CDs and video rentals that will maximize​ Maurice's utility.
Business
1 answer:
Schach [20]3 years ago
8 0

Answer:

1 CD and 19 movie videos

Explanation:

This is a quadratic programming problem. Given the utility function, product price and budget constraint. the following relation between X and Y is:

Y =\frac{50-11X}{2}

When that is inserted in the utility function, the function is:

U(X) = -X^{2} -420X+200-\frac{121X^{2}-1100X+2500 }{2}

In order to find the maximization parameter X, the first derivative of the function is needed (leveled with zero), and it is:

-123X + 130 = 0

The value for X is 1,06 which can be rounded to 1. From the first relation, we see that Y is 19.

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Album Co. issued 10-year $200,000 debenture bonds on January 2. The bonds pay interest semiannually. Album uses the effective in
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Nancy sold three capital assets that were held for investment. She sold stock in ABC Corporation for a gain of $10,000; stock in
wlad13 [49]

Answer:

D) $3,000 deduction against ordinary income with a $5,000 capital loss carried forward to offset income for next year

Explanation:

Note: This question is not complete as it does not include the options. The complete question is therefore presented before answering the questions follows:

Nancy sold three capital assets that were held for investment. She sold stock in ABC Corporation for a gain of $10,000; stock in XYZ Corporation for a gain of $2,000; and corporate bonds for a loss of $20,000. Assuming all of the investments had a long-term holding period, how will the transactions be treated for tax purposes?

A) Gain of $12,000 taxed at 15% and a loss of $20,000 deductible against ordinary income

B) Net loss of $8,000 that is fully deductible against ordinary income in the current year

C) Net loss of $8,000 that results in no deduction in the current year, but can be carried forward to offset capital gains for the next year

D) $3,000 deduction against ordinary income with a $5,000 capital loss carried forward to offset income for next year

The explanation to the answer is therefore presented as follows:

The first step is to compute the net capital gain (loss) is as follows:

Particulars                                                                            $  

Gain from the sale of stock in ABC Corporation          10,000

Gain from the sale of stock in XYZ Corporation            2,000

Loss from the sale of corporate bonds                     <u>  (20,000)  </u>

Net capital gain (loss)                                              <u>     (8,000)  </u>

In the US, individuals are allowed to use up to $3,000 to reduce their taxable income in the first year of the loss, while the remaining capital losses will be carried over to the next years.

From the net capital gain computed above, the correct option is D. That is, the $8,000 loss will be treated for tax purposes as a $3,000 deduction against ordinary income in the current year with the remaining $5,000 capital loss carried forward to offset income for next year.

6 0
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