# Consumer theory and budget line

But the theory of government remained an overarching theoretical concept in continental Europe right to the end of the nineteenth century e. Register Demand Much of the preceeding material in the consumer theory section is focused on the relationship between a consumer's preferences and a utility function that represents these preferences. There are two reasons for this emphasis.

Preferences are a natural psychological concept. Faced with choice alternatives, it is reasonable to expect that a consumer will be able to rank the alternatives.

But when economists evaluate markets, they would like to have a representation of demand. If preferences are represented by a utility function, then demand can be derived from maximization of utility for various prices and income. In this section, we assume that the consumer has preferences that are represented by a utility function, and we then carry out this derivation of demand.

Once demand is represented by a function, it can be used to develop a model of exchange, and it can be combined with the supply functions of firms to model trade in a market.

Utility functions There are several classes of utility functions that are frequently used to generate demand functions.

Each of these utility functions has specific properties and uses which are discussed below after the demand function for each is derived. Diminishing Marginal Rate of Substitution Each of the utility functions examined below Consumer theory and budget line a property called "diminishing marginal rate of substitution.

Figure 10 below demonstrates this idea. The curve in the figure shows a many combinations of commodities X and Y that all result in the same utility. Combinations of X and Y that produce the same utility level are called an "indifference curve. The marginal rate of substitution MRS going from x1, y1 to x2, y2 is 3, since the consumer is willing to give up 3 units of Y to get one additional unit of X.

The MRS going from x2, y2 to x3, y3 is only 1. This reduction in the marginal rate of substitution is one of the main assumptions about preferences or utility beyond the regularity assumptions that were described in earlier sections. Diminishing MRS is both an intuitive condition on preferences, and also a mild assumption, but in almost all cases it is enough to guarantee that the demand for a commodity decreases as its price increases.

The optimal consumption level for each commodity is determined by setting the slope of the indifference curve through a point x, y equal to the slope of the budget line.

Figure 11 shows two consumption points, 'a' and 'b'. At consumption point 'a', the slope of the indifference curve is not equal to the slope of the budget line. Note that at point 'b', the slope of the indifference curve and the budget line are equal, and the utility level is higher than at point 'a'.

Non-optimal consumption point a and optimal point b. The top graph in figure 12 shows three example budget lines and the tangency, with the optimal consumption point for each. Since the price of X for each of the budget lines is different, and the optimal consumption level for X is different in each of the three cases, the relationship between px, the price of X, and the consumption level of X can be traced out.

The lower graph in figure 12 traces out this relationship for a consumer with the indifference curves shown in the top portion of figure The points labeled 'b' and 'c' in both graphs are interpreted similarly.

The points 'a', 'b', and 'c' all lie on the demand graph, which is the bottom graph in figure Optimal consumption points for three different prices top and corresponding demand function bottom.

There is an important feature of the Cobb-Douglas utility function that is apparent in this figure. When the price of X changes, the demand for Y doesn't change.

This means that commodities X and Y are neither substitutes for one another nor complements to one another. Derived demand for Cobb-Douglas utility The graphical derivation of demand described above is useful for understanding what it means to derive demand from a consumer's utility and budget, but an analytical technique is helpful since the demand is then known for many different income levels and for different prices of the other commmodity Y.

The analysis below shows how this is done for the Cobb-Douglas utility function. The simplest way to find the slope of the indifference curve is to use implicit differentiation. Solve this for y' x to get the slope of the indifference curve: Since the slope of the budget line in the figure is 1, point 'b' is the optimal consumption point.

This tangency condition can be substituted into the budget equation to eliminate either x or y so that the demand for one of the commodities can be obtained. CES Utility The Constant Elasticity of Substitution CES utility function is useful because this class of utility functions can be used to model commodities that are either substitutes for one another, or complements of one another.

Derived demand for CES utility The technique for determining demand functions is similar to the technique that was used above to determine the demand for the Cobb-Douglas utility function.

The first step is to determine the slope of the indifference curve through a given point x, yand then set the slope of the indifference curve through x, y equal to the slope of the budget equation.Innovation is a defining feature of novelty in complex technological, sociocultural, and biological systems.

Theories of innovation offer principles on which the practices of innovation are based as well as the connections between theory and practice. A. Introduction. Contents Index End. In their discourses on government, Plato and Aristotle discussed all those problems which were important to an Attic citizen if he were to understand and order his nationwidesecretarial.com encyclopædic approach was also used in theories of government that were developed in the Middle Ages (Rehm L/). Intro Note: Quiz 1 can be picked up at Distribution Center. Second Quiz covers: Preferences, Budget and Optimal Choices.

Core of theory of demand: how does demand change in di⁄erent. The Consumer guide to car tyres. Independent reviews, test results and buying advice.

Consumer theory is the study of how people decide to spend their money, given their preferences and budget constraints. A branch of microeconomics, consumer theory shows how individuals make. Topic 6: Consumer Theory.

The Budget Line Learning Objectives. By the end of this section, you will be able to: Understand budget lines; Explain price ratios; Recreate budget lines after prices and income changes the slope of the budget line, represents the price of x in terms of good y Size Effect.

Consumer Budget: Budget Set, Slope of a Budget Line, Examples