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Derive demand function from utility function: Kevin has the utility function for goods x and y as u(x,y)=x^1/3y^2/3, The price of good x is $2 each, and the price of good y is $5 each. Kevin has a total income of S120. (A) Write down Kevin's budget constraint. (B) Derive Kevin's demand function for x and y

User SergGr
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Final answer:

To derive Kevin's demand function for goods x and y, we need to consider his budget constraint. The budget constraint represents the combinations of goods x and y that Kevin can afford given his income and the prices of the goods.

Step-by-step explanation:

To derive Kevin's demand function for goods x and y, we need to consider his budget constraint. The budget constraint represents the combinations of goods x and y that Kevin can afford given his income and the prices of the goods. In this case, the price of good x is $2 and the price of good y is $5, and Kevin has a total income of $120.

The budget constraint equation can be written as:

2x + 5y = 120

where x represents the quantity demanded of good x and y represents the quantity demanded of good y.

To derive Kevin's demand function for x and y, we need to solve the budget constraint equation for x in terms of y and for y in terms of x.

To solve the budget constraint equation for x in terms of y, we can rearrange the equation as:

x = (120 - 5y) / 2

This is Kevin's demand function for good x, which tells us the quantity of good x Kevin will demand at different prices of good y and given his income.

To solve the budget constraint equation for y in terms of x, we can rearrange the equation as:

y = (120 - 2x) / 5

This is Kevin's demand function for good y, which tells us the quantity of good y Kevin will demand at different prices of good x and given his income.

User Vanilla Face
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