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Unformatted text preview: Chapter 2 NAME Budget Constraint Introduction. These workouts are designed to build your skills in de- scribing economic situations with graphs and algebra. Budget sets are a good place to start, because both the algebra and the graphing are very easy. Where there are just two goods, a consumer who consumes x 1 units of good 1 and x 2 units of good 2 is said to consume the consumption bun- dle , ( x 1 ,x 2 ). Any consumption bundle can be represented by a point on a two-dimensional graph with quantities of good 1 on the horizontal axis and quantities of good 2 on the vertical axis. If the prices are p 1 for good 1 and p 2 for good 2, and if the consumer has income m , then she can afford any consumption bundle, ( x 1 ,x 2 ), such that p 1 x 1 + p 2 x 2 ≤ m . On a graph, the budget line is just the line segment with equation p 1 x 1 + p 2 x 2 = m and with x 1 and x 2 both nonnegative. The budget line is the boundary of the budget set . All of the points that the consumer can afford lie on one side of the line and all of the points that the consumer cannot afford lie on the other. If you know prices and income, you can construct a consumer’s bud- get line by finding two commodity bundles that she can “just afford” and drawing the straight line that runs through both points. Example: Myrtle has 50 dollars to spend. She consumes only apples and bananas. Apples cost 2 dollars each and bananas cost 1 dollar each. You are to graph her budget line, where apples are measured on the horizontal axis and bananas on the vertical axis. Notice that if she spends all of her income on apples, she can afford 25 apples and no bananas. Therefore her budget line goes through the point (25 , 0) on the horizontal axis. If she spends all of her income on bananas, she can afford 50 bananas and no apples. Therfore her budget line also passes throught the point (0 , 50) on the vertical axis. Mark these two points on your graph. Then draw a straight line between them. This is Myrtle’s budget line. What if you are not told prices or income, but you know two com- modity bundles that the consumer can just afford? Then, if there are just two commodities, you know that a unique line can be drawn through two points, so you have enough information to draw the budget line. Example: Laurel consumes only ale and bread. If she spends all of her income, she can just afford 20 bottles of ale and 5 loaves of bread. Another commodity bundle that she can afford if she spends her entire income is 10 bottles of ale and 10 loaves of bread. If the price of ale is 1 dollar per bottle, how much money does she have to spend? You could solve this problem graphically. Measure ale on the horizontal axis and bread on the vertical axis. Plot the two points, (20 , 5) and (10 , 10), that you know to be on the budget line. Draw the straight line between these points and extend the line to the horizontal axis. This point denotes the amount of 6 BUDGET CONSTRAINT (Ch. 2) ale Laurel can afford if she spends all of her money on ale. Since ale costsale Laurel can afford if she spends all of her money on ale....
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