Setting Up a Utility Maximization Problem via Substitution
A consumer has a utility function U(X, Y) = X^(0.5) * Y^(0.5). Their income is $100, the price of good X is $2, and the price of good Y is $5. To solve for the optimal consumption bundle using the substitution method, you first need to express the utility function in terms of a single variable. Write the new utility function as a function of only good X after performing the substitution.
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.3 Doing the best you can: Scarcity, wellbeing, and working hours - The Economy 2.0 Microeconomics @ CORE Econ
Ch.5 The rules of the game: Who gets what and why - The Economy 2.0 Microeconomics @ CORE Econ
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Marginal Rate of Transformation (MRT) as the Wage Rate (w)
Calculating an Optimal Consumption Bundle
Optimal Consumption Bundle Calculation
A consumer is choosing between two goods, food (F) and clothing (C). At their current consumption bundle, their marginal rate of substitution of food for clothing (MRS_FC) is 4. The price of food is $10 per unit, and the price of clothing is $2 per unit. To maximize their utility, this consumer should:
A consumer is choosing between apples (A) and bananas (B). At their current consumption bundle on their budget line, their marginal rate of substitution of apples for bananas (MRS_AB) is 3. The price of an apple is $2 and the price of a banana is $1. This consumer is currently maximizing their utility.
A consumer aims to maximize their satisfaction from consuming two goods, X and Y, subject to a limited income. Arrange the following mathematical steps in the correct logical order to find the consumer's optimal consumption bundle using the tangency condition.
A consumer seeks to maximize their satisfaction from consuming two goods, X and Y, given their prices (Px, Py) and income (I). Match each mathematical expression with its corresponding economic concept in this constrained choice problem.
Evaluating Solution Methods for Consumer Optimization
For an interior solution to a consumer's utility maximization problem, the optimal consumption bundle is found on the budget line at the point where the marginal rate of substitution is equal to the ratio of the two goods' ____.
Setting Up a Utility Maximization Problem via Substitution
A student is solving for a consumer's optimal bundle of two goods, X and Y. The consumer's utility is given by U(X,Y) = XY, the price of X is $2, the price of Y is $4, and their income is $80. The student's work is shown below:
- Budget Constraint: 2X + 4Y = 80
- Marginal Rate of Substitution (MRS): Y/X
- Condition for Optimum: Y/X = 80
Which statement best identifies the conceptual error in the student's approach?
A consumer is choosing between apples (A) and bananas (B). At their current consumption bundle on their budget line, their marginal rate of substitution of apples for bananas (MRS_AB) is 3. The price of an apple is $2 and the price of a banana is $1. This consumer is currently maximizing their utility.