Absence of an Interior Solution to the First-Order Condition
In some optimization problems, the functions defining the model, such as the utility function (v) and the feasible frontier function (g), may be shaped in a way that their derivatives do not intersect within the feasible range of the choice variable. For example, in Angela's case, this would mean no solution exists for free time (t) between 0 and 24 hours. When this occurs, there is no 'interior' solution that satisfies the first-order condition, necessitating an examination of the boundaries of the feasible set.
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Introduction to Microeconomics Course
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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Corner Solution
A farmer is deciding how many hours per day to spend on leisure (
t), where the possible range is0 ≤ t ≤ 16. The remaining hours are spent working to produce grain. For any choice oftwithin this range, the farmer's marginal rate of substitution (the amount of grain they are willing to give up for an extra hour of leisure) is always greater than their marginal rate of transformation (the amount of grain they would actually lose by taking an extra hour of leisure). Given this information, what is the farmer's optimal number of leisure hours?Profit-Maximizing Advertising Budget
Profit-Maximizing Advertising Budget
Optimal Allocation Decision
A firm is choosing its level of production,
q, which can be any value between 0 and 100 units. For any level of production in this range, the marginal revenue gained from selling one more unit is always less than the marginal cost of producing it. Based on this, the firm's profit-maximizing strategy is to find the production level within the 0-100 range where the difference between marginal cost and marginal revenue is smallest.Optimal Allocation without a Tangency Point
Optimal Study Time Allocation
Analyzing an Optimization Problem with a Boundary Solution
Optimal Time Allocation without an Interior Solution
An individual is deciding on an amount of an activity (
x) to undertake, where the feasible range is0 ≤ x ≤ 100. For each scenario below describing the relationship between the marginal benefit (MB) and marginal cost (MC) of the activity, match it to the optimal choice ofxthat maximizes net benefit. Assume that forx > 0, MB is a decreasing function ofxand MC is an increasing function ofx.