Slope of an Indifference Curve
The slope of an indifference curve is derived by keeping utility constant. For small changes, the total change in utility is: Rearranging this equation gives the slope of the indifference curve: Because the marginal utilities for desirable goods are positive ( and ), the right-hand side of the equation is negative. This demonstrates that indifference curves for such goods are always downward-sloping.
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Slope of an Indifference Curve
An individual's satisfaction is determined by a function of two variables: hours of free time and units of consumption. Assume that having more of either variable always increases satisfaction. If this individual experiences a small decrease in their hours of free time, what change in consumption is necessary for their overall level of satisfaction to remain exactly the same?
Maintaining Utility with Changing Variables
For an individual whose satisfaction depends on free time and consumption (where more of each is preferred), the small increments formula implies that if they reduce their free time by one small unit, their overall satisfaction will remain constant as long as they also increase their consumption by exactly one small unit.
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The total change in an individual's satisfaction from small adjustments to their consumption of two goods can be approximated by adding the 'satisfaction effect' of the change in the first good to the 'satisfaction effect' of the change in the second good. If the individual's overall satisfaction remains unchanged after these adjustments, what must be true about the two individual 'satisfaction effects'?
An individual's well-being is determined by the amount of time they spend on two activities: work and leisure. Currently, the additional well-being they would gain from one more hour of leisure is greater than the additional well-being they would gain from one more hour of work. If this individual decides to work one hour more and take one hour less of leisure, what will be the net effect on their overall well-being?
The Condition for Constant Satisfaction
An individual's satisfaction is derived from two goods: coffee (c) and donuts (d). Currently, the additional satisfaction they get from one more cup of coffee is 15 units, while the additional satisfaction from one more donut is 5 units. If this person gives up one cup of coffee and receives three donuts in exchange, what is the approximate net change in their total satisfaction?
According to the principle of small increments, if an individual's consumption of two goods changes in such a way that their overall level of satisfaction remains constant, the gain in satisfaction from the increase in one good must be ______ by the loss in satisfaction from the decrease in the other good.
Evaluating a Proposed Exchange
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Learn After
A small furniture company builds custom wooden chairs. The owner is analyzing the business's expenses to understand how they behave. Which of the following groups of expenses will increase in total as the company decides to build more chairs each month?
A consumer's satisfaction from consuming good X and good Y is represented by the utility function U(X, Y) = X²Y. If the consumer is currently consuming 2 units of good X and 10 units of good Y, what is the slope of their indifference curve at this point?
A consumer is analyzing their preferences between coffee (measured on the horizontal axis) and tea (measured on the vertical axis). At their current consumption bundle, the slope of their indifference curve is -2. What is the correct interpretation of this value?
A person's satisfaction depends on two factors: hours of leisure (which they enjoy) and hours of exposure to air pollution (which they dislike). If an indifference curve is drawn with hours of leisure on the horizontal axis and hours of pollution on the vertical axis, what will its shape be? Analyze the relationship based on the fact that the slope of the curve is determined by the negative ratio of the marginal utilities of the two factors.
Analysis of a Convex Indifference Curve
True or False: A consumer is choosing between two goods, Apples (plotted on the vertical axis) and Bananas (plotted on the horizontal axis). If, at their current consumption bundle, the additional satisfaction they get from one more Apple is exactly half the additional satisfaction they get from one more Banana, then the slope of their indifference curve at that point is -2.
Interpreting Consumer Trade-offs
A consumer's satisfaction is determined by their consumption of two goods: Good X (plotted on the horizontal axis) and Good Y (plotted on the vertical axis). At their current consumption bundle, the consumer has reached a point of satiation with Good X, meaning an additional unit of Good X provides zero additional satisfaction. However, they would still gain positive satisfaction from an additional unit of Good Y. Based on the principle that the slope of an indifference curve is the negative rat
Derivation and Economic Intuition of the Indifference Curve Slope
A consumer's preferences for two goods, Tacos (on the horizontal axis) and Burritos (on the vertical axis), are represented by indifference curves. Match each slope value of an indifference curve at a specific consumption bundle with the correct interpretation of the consumer's preferences at that bundle.
A consumer is analyzing their preferences between coffee (measured on the horizontal axis) and tea (measured on the vertical axis). At their current consumption bundle, the slope of their indifference curve is -2. What is the correct interpretation of this value?