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Anna71 [15]
3 years ago
13

Olivia likes to eat both apples and bananas. At the grocery store, each apple costs $0.20 and each banana cost $0.25. Olivia’s u

tility function for apples and bananas is given by U(A, B) = 6√AB where MUA = 3√B/A and MUB = 3√A/B . If Olivia has $4 to spend on apples and bananas, how many of each should she buy to maximize her satisfaction? [In the exam, you should be able to calculate MUa and MUb by yourself!] You may also try using the Lagrange optimization method to solve this question.
Business
1 answer:
icang [17]3 years ago
6 0

Answer:

Therefore, Olivia should buy 10 apples and 8 bananas to maximize her utility.

Explanation:

Let A represent the number of apples bought and B represent the number of bananas bought. Therefore since Olivia has $4 to spend:

0.2A + 0.25B = 4       (1)

Also, the tangency condition can be used to find the optimal amount of A to relative to B. It is give as:

MU_A/P_A=MU_B/P_B\\\\\frac{3\sqrt{\frac{B}{A} } }{0.2}= \frac{3\sqrt{\frac{A}{B} } }{0.25}\\\\15\sqrt{\frac{B}{A} }=12\sqrt{\frac{A}{B} }\\\\squaring\ both\ sides:\\\\\frac{225B}{A} =\frac{144A}{B}\\\\225B^2=144A^2\\\\B^2=0.64A^2\\\\Taking\ square\ root:\\\\B=0.8A

Put B = 0.8A in equation 1:

0.2A + 0.25(0.8A) = 4

0.2A + 0.2A = 4

0.4A = 4

A = 10

B = 0.8(A) = 0.8(10) = 8

Therefore, Olivia should buy 10 apples and 8 bananas to maximize her utility.

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5 0
2 years ago
Consider a simple example economy where there are two goods, coconuts and restaurant meals (coconut-based). There are two firms.
tekilochka [14]

A) Product Approach

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Value added = revenue - intermediate costs

Value added coconut producer = $20,000,000 (it does not have intermediate costs)

Value added restaurant = $30,000,000 - $12,000,000 (cost of coconuts)

                                        = $18,000,000

Value added government = $5,500,000 (collected in taxes, $3 million from the restaurant, $1.5 million from the coconut producer, and $1 million from consumers).

GDP = $20,000,000 + $18,000,000 + $5,500,000

        = $43,000,000

B) Expenditure Approach

GDP = Consumption + Investment + Government Spending + Net Exports

Consumption = $8,000,000 in coconuts + $30,000,000 in meals

                       = $38,000,000

Investment = $0

Government Spending = $5,500,000 in government wages

Net Exports = $0 (it is a closed-economy)

GDP = $38,000,000 + $0 + $5,500,000 + $0

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C) Income Approach

Wages = $14,500,000

Corporate Profits  = $24,000,000

Interest income = $500,000

Taxes = $4,500,000

GDP = $43,500,000

e. How does this new piece of information affect your calculations in the expenditure approach? Explain.

GDP under the expenditure approach, would rise by the value of the unsold coconuts ($1 million) as long as the coconuts were harvested in the given year. This is because inventory produced in the given year, is part of that year's GDP.

7 0
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Answer:

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Answer:

Explanation:

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