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3 pages/≈825 words
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MLA
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Mathematics & Economics
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English (U.S.)
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Economic Problems: Utility Maximization Assignment (Coursework Sample)
Instructions:
economic problems
Q1: Let I=6,000, U(X, Y) =X3Y, PX=2, Py=3. Find the optimal combination of X and Y that maximizes utility.
Q2: In theory, what is the optimality condition for a consumer, i.e. what condition must hold when the consumer has maximized production? Please express your answer using relevant ratios and not specific numbers.
Q3: Suppose the consumer chooses a combination of X and Y where the marginal rate of substitution of X for Y is equal to 2/3. Should the consumer adjust her choice of consumption? Explain. If so, should the consumer choose more or less of X and/or Y?
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Date of Submission
Utility Maximization Assignment
Q1: Let I=6,000, U(X, Y) =X3Y, PX=2, Py=3. Find the optimal combination of X and Y that maximizes utility.
Since the expenditure cannot exceed income I, the proportions of good X and Y consumed must be equal to 6000.
Amount spent on good X= Px* X = 2X
Amount spent on good Y= Py*Y = 3Y
Therefore, 2X + 3Y≤ 6000
For maximum utility, it is assumed that the consumer will spend all the income on all the goods. Therefore, the budget constraint becomes
2X+3Y = 6000
U(X, Y) = X3Y
For maximization, we follow four key steps
Max U(X, Y) = X3Y
Subject to
2X + 3Y= 6000 => 2x+...
Name of the Professor
Name of the Course
Date of Submission
Utility Maximization Assignment
Q1: Let I=6,000, U(X, Y) =X3Y, PX=2, Py=3. Find the optimal combination of X and Y that maximizes utility.
Since the expenditure cannot exceed income I, the proportions of good X and Y consumed must be equal to 6000.
Amount spent on good X= Px* X = 2X
Amount spent on good Y= Py*Y = 3Y
Therefore, 2X + 3Y≤ 6000
For maximum utility, it is assumed that the consumer will spend all the income on all the goods. Therefore, the budget constraint becomes
2X+3Y = 6000
U(X, Y) = X3Y
For maximization, we follow four key steps
Max U(X, Y) = X3Y
Subject to
2X + 3Y= 6000 => 2x+...
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