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Solution to a Constrained Choice Problem
First-Order Condition
A 'first-order condition' is a necessary condition that a solution to an optimization problem must satisfy. It is termed 'first-order' because it is derived from the first derivatives of the functions involved. This condition helps locate potential optimal points, which are often found on the boundary of a problem's constraint. For example, in a consumer choice problem, the first-order condition can be expressed as MRS = MRT, or, when using the substitution method, it is found by setting the first derivative of the objective function to zero.
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
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Optimal Choice as a Balance Between Two Trade-Offs
First-Order Condition
A decision-maker wants to achieve the most satisfaction possible from consuming two goods, but has a limited budget. The best possible consumption bundle for this individual is located at a point that represents a combination of goods which is:
Characteristics of an Optimal Choice
Identifying the Optimal Consumption Bundle
In a constrained choice problem where an individual aims to maximize their satisfaction, any point on the feasible frontier represents an optimal solution.
A decision-maker is choosing between different combinations of outcomes but is limited by a boundary of what is possible (the feasible frontier). Their goal is to find the combination that gives them the most satisfaction, represented by a series of satisfaction curves. Match each location on a conceptual graph of this problem with its correct description.
Evaluating an Optimal Choice Strategy
For a decision-maker seeking to maximize their satisfaction subject to limitations, the optimal choice occurs at a point on the feasible frontier where it is just touching, or tangent to, the highest attainable ________.
A person is trying to find the best combination of two goods to consume to achieve the most satisfaction, given they have a limited budget. Arrange the following steps in the logical order required to identify this single best combination.
Evaluating a Consumer's Choice
Analyzing a Sub-Optimal Choice
Learn After
Uniqueness of a First-Order Condition Solution from Concave Functions
Angela's Optimization Problem as a Tenant vs. an Independent Farmer
Conditions for a Unique, Maximum Solution from a First-Order Condition
General Form of the First-Order Condition
Finding an Optimum for a Single-Variable Function using First and Second-Order Conditions