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Condition for an Increasing Utility Function
The 'more is better' principle implies that utility rises with an increase in desirable goods like free time () and consumption (). This is mathematically expressed by requiring the partial derivatives of the utility function for both goods to be positive. Therefore, for the utility function to be increasing, the marginal utility of free time () and the marginal utility of consumption () must be greater than zero. When these conditions are met, it is said that utility 'depends positively' on both free time and consumption.
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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
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Condition for an Increasing Utility Function
An individual's well-being is determined by two desirable things: hours of free time and units of consumption. A fundamental assumption is that their well-being increases if they get more of one of these things without having less of the other. If this individual currently has a combination of 20 hours of free time and 100 units of consumption, which of the following new combinations would unambiguously result in a higher level of well-being based only on the information provided?
Preference Consistency Analysis
Evaluating a Utility Scenario
Consider an individual whose satisfaction depends on two desirable goods: apples and oranges. According to the principle that 'more is better', this individual can be equally satisfied with a bundle of 15 apples and 10 oranges as they are with a bundle of 15 apples and 11 oranges.
An individual's satisfaction depends on two desirable goods: weekly consumption () and daily hours of free time (). Their current situation is represented by the bundle (c=500, t=10). Match each of the following new bundles of goods to the statement that correctly describes the change in the individual's satisfaction relative to their current situation, based only on the principle that 'more is better'.
An individual's satisfaction is determined by the quantities of two desirable goods they consume: concert tickets and restaurant meals. They currently have a bundle A, consisting of 5 tickets and 10 meals. They are then presented with a new bundle B, consisting of 5 tickets and 12 meals. The level of satisfaction from bundle B will be ______ than the level of satisfaction from bundle A.
The 'More is Better' Assumption in Economic Models
Evaluating a Proposed Satisfaction Model
An individual's satisfaction is determined by two desirable goods: weekly hours of leisure and weekly income. Their current situation is Bundle X: 15 hours of leisure and $400 of income. Consider three alternative bundles: Bundle A (15 hours, $450), Bundle B (14 hours, $400), and Bundle C (16 hours, $350). Based only on the principle that more of a desirable good is better, which statement correctly describes the relationship between these bundles?
An individual's satisfaction is derived from two desirable goods: digital music albums and streaming movie subscriptions. Based only on the principle that having more of a desirable good is always better, arrange the following bundles from the one that provides the least satisfaction to the one that provides the most satisfaction.
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Shape of an Indifference Curve
Positive Parameters in Cobb-Douglas Function and Positive Marginal Utility
An individual's satisfaction is derived from consuming two desirable goods, Good X and Good Y. This means that, all else being equal, their satisfaction should increase if they acquire more of Good X, and it should also increase if they acquire more of Good Y. Given that the quantities of X and Y are always positive, which of the following mathematical functions, U(X, Y), correctly represents this relationship for all possible positive quantities of X and Y?
Mathematical Verification of a Preference Principle
An individual's preferences for two items, apples (A) and bananas (B), are described by the utility function U(A, B) = 15A - 2B. According to this function, this individual always gains more satisfaction from consuming an additional apple, and also always gains more satisfaction from consuming an additional banana.
Evaluating a Utility Function Model
An individual's preferences are represented by a utility function, U(X, Y), where X and Y are quantities of two different goods. Match each utility function below with the correct description of its marginal utilities, assuming the quantities of X and Y are always positive.
Analyzing Preferences for Goods and Bads
Evaluating Player Satisfaction Models in Game Design
Interpreting the Mathematics of Preferences
For a utility function representing an individual's preferences for two desirable goods, the 'more is better' principle is mathematically expressed by the condition that the ______ for each good must be positive.
An individual's satisfaction from consuming two goods, X and Y, is represented by the utility function U(X, Y) = 20X - X² + 10Y. Assuming the quantities of both goods must be positive, for which range of values for good X does this function satisfy the 'more is better' principle with respect to both goods?