3 years ago

I need help with #14

Mathematics

1 answer:

kodGreya [7K]3 years ago

7 0

35 brownies were brought to class by Lauren

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Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x 2y 8 , where x is the number of apples consumed a

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Answer:

16 apples.

Step-by-step explanation:

$U(x, y) = x^2y^8$

$MU_x =\frac{\partial U}{\partial x} = 2xy^8\\MU_y = \frac{\partial U}{\partial x} = 8x^2y^7\\$

Price of apples, Px=$4

Price of tomatoes, Py=$3

Ratio of their Marginal Utilities

$\frac{MU_x}{MU_y} = \frac{Px}{Py}$

$\frac{y}{4x} = \frac{4}{3}$

$y=\frac{16x}{3}$

Since Natalie’s income is $320

320 = xPx+yPy

$320=4x + 3*\frac{16x}{3} \\320= 4x+16x = 20x\\x=\frac{320}{20} = 16\\Also\\y=\frac{16x}{3}=\frac{16X16}{3}=\$85.33$

Since x=16, Natalie will consume 16 apples.

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A small business lost $6200 in its first year, lost $2150 in its second year, and earned $4780 in its third year. Overall, in th

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Overall, they lost $3570

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3 years ago