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hjlf
3 years ago
10

Ellie is spending her entire income on goods X and Y. Her marginal utility from the last unit of X is 100 and the marginal utili

ty from the last unit of Y that she consumes is 50. ​Ellie's utility is only maximized if
Business
1 answer:
defon3 years ago
6 0

Answer:

The price of good X is twice the price of good Y

Explanation:

Utility can be defined as the amount of satisfaction that one can derive from consuming a product.

Marginal utility is the additional utility derived from consuming an extra unit of a product.

Total Utility is the total satisfaction one derives from consuming all units of a product.

Because consumers are rational and they want to spend the least amount to get maximum utility, they are at equilibrium at the point where Marginal Utility of product X divided Price of X is equal to the Marginal Utility of product Y divided by Price of Y.

So for utility to be maximized it means that the price of good X has to be twice the price of good Y.

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Assuming two investments have equal lives, a high discount rate tends to favor Group of answer choices the investment with even
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3 years ago
You are interested in valuing a 2-year semi-annual corporate coupon bond using spot rates but there are no liquid strips availab
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Answer:

Following are the solution to this question:

Explanation:

Assume that r_1  will be a 12-month for the spot rate:

\to 1.25 \% \times \frac{100}{2} \times 0.99 + \frac{(1.25\% \times \frac{100}{2}+100)}{(1+\frac{r_1}{2})^2}=98\\\\\to \frac{1.25}{100} \times \frac{100}{2} \times 0.99 + \frac{(\frac{1.25}{100} \times \frac{100}{2}+100)}{(1+\frac{r_1}{2})^2}=98\\\\\to \frac{1.25}{2} \times 0.99 + \frac{(\frac{1.25}{2} +100)}{(1+\frac{r_1}{2})^2}=98\\\\\to 0.61875 + \frac{( 0.625 +100)}{(\frac{2+r_1}{2})^2}=98\\\\\to 0.61875 + \frac{( 100.625)}{(\frac{2+r_1}{2})^2}=98\\\\\to 0.61875 + \frac{402.5}{(2+r_1)^2}=98\\\\

\to 0.61875 + \frac{402.5}{(2+r_1)^2}=98\\\\\to 0.61875 -98 = \frac{402.5}{(2+r_1)^2}\\\\\to -97.38125= \frac{402.5}{(2+r_1)^2}\\\\\to (2+r_1)^2= \frac{402.5}{ -97.38125}\\\\\to (2+r_1)^2= -4.13\\\\ \to r_1=3.304\%

Assume that r_2  will be a 18-month for the spot rate:

\to 1.5\% \times \frac{100}{2} \times 0.99+1.5\%  \times \frac{100}{2} \times \frac{1}{(1+ \frac{3.300\%}{2})^2}+\frac{(1.5\%  \times  \frac{100}{2}+100)}{(1+\frac{r_2}{2})^3}=97\\\\\to \frac{1.5}{100} \times \frac{100}{2} \times 0.99+\frac{1.5}{100}  \times \frac{100}{2} \times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(\frac{1.5}{100}  \times  \frac{100}{2}+100)}{(1+\frac{r_2}{2})^3}=97\\\\

\to \frac{1.5}{2}  \times 0.99+\frac{1.5}{2}\times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(\frac{1.5}{2} +100)}{(1+\frac{r_2}{2})^3}=97\\\\\to 0.7425+0.75 \times \frac{1}{(1+ \frac{\frac{3.300}{100}}{2})^2}+\frac{(0.75  +100)}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4925 \times \frac{1}{(1+0.0165)^2}+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4925 \times \frac{1}{(1.033)}+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\

\to 1.4925 \times 0.96+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4328+\frac{(100.75 )}{(1+\frac{r_2}{2})^3}=97\\\\\to 1.4328-97= \frac{(100.75 )}{(1+\frac{r_2}{2})^3}\\\\\to -95.5672= \frac{(100.75 )}{(1+\frac{r_2}{2})^3}\\\\\to (1+\frac{r_2}{2})^3= -1.054\\\\\to r_2=3.577\%

Assume that r_3  will be a 18-month for the spot rate:

\to 1.25\% \times \frac{100}{2} \times 0.99+1.25\% \times \frac{100}{2} \times \frac{1}{(1+\frac{3.300\%}{2})^2}+1.25\%\times\frac{100}{2} \times \frac{1}{(1+\frac{3.577\%}{2})^3}+(1.25\% \times \frac{\frac{100}{2}+100}{(1+\frac{r_3}{2})^4})=96\\\\

to solve this we get r_3=3.335\%

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