Budget Constraint Graph

5 Key excerpts on "Budget Constraint Graph"

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  eBook - ePub

  Alternative Principles of Economics

  • Stanley Bober(Author)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  Now that we have the foundation of this indifference–ordinal ranking approach, we move to arrive at the rule for utility maximization based on this, and then to derive the consumer demand curve. The construction of this curve is merely a reflection of a consumer adjusting to an external event so as to maintain one’s maximizing position, and the event is a change in the price of the good for which we want to derive the curve. Before the event occurs, the consumer has chosen a particular basket of goods that presumably mirrors the highest attainable level of utility, and the basic elements of this choice are obviously the individual’s set of preferences as represented by an indifference map, the prices of the individual goods composing the basket, and the individual’s money income. Before setting out the solution to this choice problem, it should be reiterated and emphasized that the solution here (and in the context of the marginal utility cardinal analysis as well) is based on what we can consider as “independence of preferences.” Each consumer is concerned only with one’s own consumption pattern; the utility or satisfaction derived from a particular purchase is attributable to the individual’s own experience. In the solution to the choice problem the consumer is presumed not to be concerned or indeed influenced by what is going on elsewhere, that is, by the choices being made by other consumers. In Principles texts the student is shown an aggregate or market demand curve adjacent to individual demand curves and is told that points on the aggregate curve are found by summing horizontally the individual demand curves. The individual consumers behind the individual curves are considered to be in their own box, making their own decisions, and not at all being influenced by the behavior of the others. Certainly in an understanding of consumer demand this is one perception that we will want to question. But let us get back to the mainstream indifference model.

  Figure 4.8

  The consumer faces a host of combinations of goods that one may want to purchase and that we see as being reflected in the indifference map. What one would like to do is but one half the problem. The other and more telling half is what the consumer can do at the time of making the choice. The essence of the consumption choice is to narrow down the choices from all possible choices to those that are economically attainable. And what is attainable is dependent on the constraints facing the consumer—those being the prices of the goods and one’s available income. Figure 4.9 illustrates such a budget constraint.

  Figure 4.9

  We set out the constraint as

  telling us that the amount of spending on goods A and B cannot exceed the consumer’s available income. The expenditure of less than one’s full income generates the purchase of sets of baskets that lie within the dotted-lines area under the constraint line. The use of one’s total available income (given prices) places one on the budget constraint line. This line evidences what is attainable (what the consumer can do), for it shows the set of combinations of A and B that can be purchased given the “objective” data of prices and income. The placement of the budget line is determined by finding the intercepts on the A and B axes. For example, if the consumer were to spend all income on good B , then the amount purchased would be given by

  M/pB

  ; likewise, if we were to set B = 0, we determine the good A budget intercept as

  M/pA .

  There are some features of this line that we should mention. An increase in money income with unchanged prices clearly shifts the line to the right, enlarging the available set of baskets. Clearly a change in the price of one of the goods, given unchanged money income, alters the slope of the constraint line as it changes one of the intercepts. Furthermore, if we were to double income and also double price, the available set of possible purchases would not change; the intercepts remain the same and the equation of the constraint line, of course, remains unchanged as well. So the set of commodity A and B baskets available to the consumer depends on relative prices (

  pB /pA

  ) and on the real value or purchasing power of money (

  M/pB , M/pA

  ). We should note that the slope of our constraint line is (−

  pA /pB

  ).6

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  eBook - ePub

  Microeconomics For Dummies

  • Lynne Pepall, Peter Antonioni, Manzur Rashid(Authors)
  • 2016(Publication Date)
  • For Dummies

    (Publisher)

  the dual.

  What’s most important is the conclusion that you can derive from knowing something about utility (see Chapter 4 ) and something about the budget constraints and how the two have to be related. The relation between the two that is important in this case is that the highest level of utility possible for a constrained consumer occurs when the indifference curve is tangent to the budget constraint. Therefore the slope of the utility curve and the slope of the budget constraint are equal at that point.

  The slope of the indifference curve is the marginal rate of substitution (MRS), as in Chapter 4 , and the slope of the budget constraint is the relationship between the two prices (–p 1 /p 2 ). Given that these have to be equal at the optimal choice for the consumer, you know that the optimizing consumer’s best point occurs when

  You need to know this equation for Chapter 6 ’s full discussion on consumer optimization and for Chapter 9 , which looks into the famous supply and demand model.

  Passage contains an image Chapter 6

  Achieving the Optimum in Spite of Constraints

  In This Chapter

  Breaking down the effect of a change in prices into income and substitution effects

  How consumers’ preferences are revealed

  Comparing income and substitution effects

  The single most important part of microeconomics is the constrained optimization model, which is based on the idea that people act to achieve the best they can, given some kind of constraint that limits their choice. This way of looking at people’s decisions runs through most of the microeconomic syllabus, finding its way into all sorts of things from consumer choice to environmental or health economics. Yet its roots lie in the way economists look at individual decision-making.

  To microeconomists, people optimize.

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  Health Economics

  An Industrial Organization Perspective

  • Xavier Martinez-Giralt, Pedro Barros(Authors)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  .

  Formally, consider a two-good economy and a consumer i with a utility function Ui (q

  i1

  , q

  i2

  ) and income yi . Given prices p = (p1 , p2 ), the individual's feasible set is given by the consumption plans qi = (q

  i1

  , q

  i2

  ) ∈X satisfying

  The problem of the consumer is to select a feasible bundle qi to maximize utility given (p, yi ), that is,

  Figure 2.5 Solution to the consumer's decision problem.

  Assuming the utility function is strictly concave we can use the Lagrange method of optimization and solve the following problem:3

  The corresponding system of first-order conditions is, From (2.2) and (2.3) we obtain,

  This expression is of particular importance. The left-hand side of (2.5) tells us the rate at which the consumer is willing to exchange consumption of good 1 by consumption of good 2. This is called the marginal rate of substitution. Therefore, in equilibrium the relative prices determine the marginal adjustment of the optimal consumption bundle. Figure 2.5 (b) illustrates the characterization of the optimal bundle. A variation of the relative prices means a variation of the slope of the budget constraint and thus an adjustment of the optimal consumption plan.

  The remaining first-order condition (2.4) tells us that in equilibrium the consumer exhausts the income, so that the solution to the consumer's problem lies in the budget constraint. This should not be surprising because the individual does not derive utility from holding money.

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  eBook - ePub

  Economics for Investment Decision Makers

  Micro, Macro, and International Economics

  • Christopher D. Piros, Jerald E. Pinto(Authors)
  • 2013(Publication Date)
  • Wiley

    (Publisher)

  The set of options available is bounded by the budget constraint, a negatively sloped linear relationship that shows the highest quantity of one good that can be purchased for any given amount of the other good being bought. Analogous to the consumer’s consumption opportunity set are, respectively, the production opportunity set and the investment opportunity set. A company’s production opportunity set represents the greatest quantity of one product that a company can produce for any given amount of the other good it produces. The investment opportunity set represents the highest return an investor can expect for any given amount of risk undertaken. Consumer equilibrium is obtained when utility is maximized, subject to the budget constraint, generally depicted as a tangency between the highest attainable indifference curve and the fixed budget constraint. At that tangency, the MRS XY is just equal to the two goods’ price ratio, P X / P Y —or that bundle such that the rate at which the consumer is just willing to sacrifice good Y for good X is equal to the rate at which, based on prices, she must sacrifice good Y for good X. If the consumer’s income and the price of all other goods are held constant and the price of good X is varied, the set of consumer equilibria that results will yield that consumer’s demand curve for good X. In general, we expect the demand curve to have a negative slope (the law of demand) because of two influences: income and substitution effects of a decrease in price. Normal goods have a negatively sloped demand curve. For normal goods, income and substitution effects reinforce one another. However, for inferior goods, the income effect offsets part or all of the substitution effect

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  Behavioural Economics and Experiments

  • Ananish Chaudhuri(Author)
  • 2021(Publication Date)
  • Routledge

    (Publisher)

  Suppose X costs $20 per unit (P X = $20) while Y costs $10 per unit (P Y = $10). (So maybe X is a film ticket and Y is a large tub of popcorn.) How many of each can she afford? What if she spent her entire $100 on X? Since X costs $20 each, she can buy 5 of these. How about Y? She can buy 10 of these since they cost $10 each. This allows us to draw Ana’s budget constraint. She can buy either 5 units of X or 10 units of Y, or any combination of the two that add up to $100. Figure 1.6 shows this budget constraint. At one extreme, Ana buys 5 of X and zero of Y; at the other extreme, she buys 10 of Y and zero of X. If we join these two extreme points (or the two intercepts) with a straight line, then this is Ana’s budget constraint. She can choose either of the two extremes, or, more likely, another intermediate point on the line such that the total is $100. For instance, she can buy 4 units of X, costing $80, and 2 units of Y, costing $20, for a total of $100. Or 3 of X costing $60 and 4 of Y costing $40, etc. The line is negatively sloped because, in order to buy more of one good, Ana needs to give up some of the other. We will refer to a possible pair of choices of X and Y as a “consumption bundle”. Figure 1.6 Ana’s budget constraint Figure 1.7 shows that the absolute slope of the budget constraint is given by the ratio of the two prices (P X /P Y). This is because the slope of a line is given by the rise over the run. In this case, the rise is (Income/P Y) while the run is (Income/P X). Simple algebraic manipulation shows that this is the same as (P X /P Y). Of course, this is the absolute slope (or the magnitude of the slope) since the actual slope is negative. Given the supposed values of P X and P Y, this value is equal to ($20/$10) which is 2

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