# Economics exam papers Essay

Therefore we know that the consumer chooses the bundle (XSL , 12) = (120, 20). NAME Choice Introduction. You have studied budgets, and you have studied preferences. Now is the time to put these two ideas together and do something with them. In this chapter you study the commodity bundle chosen by a utility-maximizing consumer from a given budget. Given prices and income, you know how to graph a consumer’s budget. If you also know the consumer’s preferences, you can graph some of his indifference curves.

The consumer will choose the “best” indifference curve that he can reach given his judged. But when you try to do this, you have to ask yourself, “How do I find the most desirable indifference curve that the consumer can reach? ” The answer to this question is “look in the likely places. ” Where are the likely places? As your textbook tells you, there are three kinds of likely places. These are: (I) a tangency between an indifference curve and the budget line; a kink in an indifference curve; (iii) a “corner” where the consumer specializes in consuming Just one good.

Here is how you find a point of tangency if we are told

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the consumer’s utility function, he prices of both goods, and the consumer’s income. The budget line and an indifference curve are tangent at a point (XSL , xx) if they have the same slope at that point. Now the slope of an indifference curve at (XSL ,xx) is the ratio -M LU (XSL VIM 1. 12 (XSL , xx (This slope is also known as the marginal rate of substitution. ) The slope of the budget line is -Pl [up . Therefore an indifference curve is tangent to the budget line at the point (XSL ,xx) when M LU (XSL ,xx)/M 1. 2 (XSL ,xx)= Pl /up . This gives us one equation in the two unknowns, XSL and xx . If we hope to solve for the xx, we need another equation. That other equation is the budget equation Pl XSL + up xx = m. With these two equations you can solve for (XSL , xx For equilibrium at kinks or at corners, we don’t need the slope of the indifference curves to equal the slope of the budget line. So we don’t have the tangency equation to work with. But we still have the budget equation.

The second equation that you can use is an equation that tells you that you are at one of the kinky points or at a economics exam papers By cockeye Example: A consumer has the utility function U (XSL ,xx)= min{XSL ,ex. The price of XSL is 2, the price offs is 1, and her income is 140. Her indifference curves are L- shaped. The corners of the L’s all lie along the line XSL = ex. . She will choose a combination at one of the corners, so this gives us one of the two equations we need for finding the unknowns XSL and xx . The second equation is her budget equation, which is ex. + xx = 140.

Solve these two equations to find that XSL = 60 and xx = 20. So we know that the consumer chooses the bundle (XSL , xx ) = (60, 20). When you have finished these exercises, we hope that you will be able to do the following: Calculate the best bundle a consumer can afford at given prices and income in the ease of simple utility functions where the best affordable bundle happens at a point of tangency. Find the best affordable bundle, given prices and income for a consumer with kinked indifference curves. Recognize standard examples where the best bundle a consumer can afford happens at a corner of the budget set. Ђ Draw a diagram illustrating each of the above types of equilibrium. Example: A consumer has the utility function U (XSL ,xx)=xx . The 1 price of good 1 is Pl = 1, the price of good 2 is up = 3, and his income is 180. Then, M LU (XSL ,xx)= ex. xx and M 1. 12 (XSL ,xx)=xx . There fore his marginal rate of substitution -M LU (XSL 1. 12 (XSL -ex. 12/12 = -212 m . This implies that his indifference curve will be 1 tangent to his budget line when -ex. /XSL = -Pl ‘up = -1/3. Simplifying this expression, we have ex. = XSL . This is one of the two equations we need to solve for the two unknowns, XSL and xx .

The other equation is the budget equation. In this case the budget equation is XSL + ex. = 180. Solving these two equations in two unknowns, we find XSL = 120 and * Some people have trouble remembering whether the marginal rate of substitution is -M LU IM 1. 12 or -M 1. 12 IM LU . It isn’t really crucial to remember which way this goes as long as you remember that a tangency happens when the marginal utilities of any two goods are in the same proportion as their prices. 51 Apply the methods you have learned to choices made with some kinds of nonlinear budgets that arise in real-world situations. 5. (O) We begin again with Charlie of the apples and bananas. Recall that Charlie’s utility function is U (XA , CB ) = XA CB . Suppose that the price of apples is 1, the price of bananas is 2, and Charlie’s income is 40. (a) On the graph below, use blue ink to draw Charlie’s budget line. (Use a ruler and Charlie a utility of 150 and sketch this curve with red ink. Now plot a few points on the indifference curve that gives Charlie a utility of 300 and sketch this curve with black ink or pencil. 52 (g) The best bundle that Charlie can afford must lie somewhere on the line you Just penciled in. It must also lie on his budget line.

If the point is outside of his budget line, he can’t afford it. If the point lies inside of his budget line, he can afford to do better by buying more of both goods. On your graph, label this best affordable bundle with an E. This Bananas Red curves happens where XA = 20 and CB = 10. Verify your answer by loving the two simultaneous equations given by his budget equation and the tangency condition. (h) What is Charlie’s utility if he consumes the bundle (20, 10)? Black curve Pencil line 20 it, or never touch it? 10 200. (I) On the graph above, use red ink to draw his indifference curve through (20,10).

Does this indifference curve cross Charlie’s budget line, Just touch Blue budget line 5. 2 (O) Scalar’s utility function is U (X, Y ) = (X + + 1), where X is her consumption of good X and Y is her consumption of good Y . (a) Write an equation for Scalar’s indifference curve that goes through the Y=X+2- Scalar’s indifference curve for U Apples = 36. (b) Can Charlie afford any bundles that give him a utility of 1 50? (c) Can Charlie afford any bundles that give him a utility of 300? 0=36 12 No. 11 8 (e) Neither of the indifference curves that you drew is tangent to Charlie’s budget line. Let’s try to find one that is.

At any point, (XA , CB Charlie’s marginal rate of substitution is a function of XA and CB . In fact, if you calculate the ratio of marginal substitution is M RSI(XA , CB ) = -CB /XA . This is the slope of his indifference curve at , The -1/2 On the axes below, sketch 16 Yes. (d) On your graph, mark a point that Charlie can afford and that gives him a higher utility than 150. Label that point A. Slope of Charlie’s budget line is 4 (give a numerical answer). X (f) Write an equation that implies that the budget line is tangent to an indifference curve at (XA , CB ). -CB /XA = -1/2. There are many solutions to this equation.

Each of these solutions corresponds to a point on a different indifference curve. Use pencil to draw a line that passes through all of these points. (b) Suppose that the price of each good is 1 and that Clara has an income of 11. Draw in her budget line. Can Clara achieve a utility of 36 with this budget? 53 54 c) At the commodity bundle, (X, Y ), Scalar’s marginal rate of substitution is Berries (d) If we set the absolute value of the MRS. equal to the price ratio, we have the equation 15 (e) The budget equation is Red curve Blue line 5 curve (f ) Solving these two equations for the two unknowns, X and Y , we find X= 6. ND Y = 5. 3 (O) Ambrose, the nut and berry consumer, has a utility function U (XSL 4 XSL +xx , where XSL is his consumption of nuts and xx is his consumption of berries. (a) The commodity bundle (25, O) gives Ambrose a utility of 20. Other points that give him the same utility are (16, 4), (9, 16 and (O, 20 Plot these points on he axes below and draw a red indifference curve through them. 25 Nuts (f) Now let us explore a case where there is a “boundary solution. ” Suppose that the price of nuts is still 1 and the price of berries is 2, but Ambrosia’s income is only 9.

Draw his budget line (in blue). Sketch the indifference curve that passes through the -2/3. (b) Suppose that the price off unit of nuts is 1, the price off unit of berries is 2, and Ambrosia’s income is 24. Draw Ambrosia’s budget line with blue ink. How many units of nuts does he choose to buy? Units. (h) Which is steeper at this point, the budget line or the indifference curve? Units. (d) Find some points on the indifference curve that gives him a utility of 25 and sketch this indifference curve (in red). (e) Now suppose that the prices are as before, but Ambrosia’s income is 34.

Draw his new budget line (with pencil). How many units of nuts will 16 units. He choose? How many units of berries? Indifference curve. (I) Can Ambrose afford any bundles that he likes better than the point (9, O)? (c) How many units of berries? -1/2. (g) What is the slope of his budget line at this point? 5. 4 (1) Nancy Learner is trying to decide how to allocate her time in studying for her economics course. There are two examinations in this course. Her overall score for the course will be the minimum of her scores on the two examinations. She has wants to get as high an overall score as possible.

She knows that on the first examination if she doesn’t study at all, she will get a score of zero on it. For every 10 minutes that she spends studying for the first examination, she will increase her score by one point. If she doesn’t study at all for the second examination she will get a zero on it. For every 20 minutes she spends studying for the second examination, he will increase her score by one point. 9 units. 55 (a) On the graph below, draw a “budget line” showing the various combinations of scores on the two exams that she can achieve with a total of 1,200 minutes of studying.

On the same graph, draw two or three “indifference curves” for Nancy. On your graph, draw a straight line that goes through the kinks in Nanny’s indifference curves. Label the point where this line hits Nanny’s budget with the letter A. Draw Nanny’s indifference curve through this point. Score on test 2 56 for the first examination, her score on this exam will be XSL = ml 15. If she spends mm minutes studying for the second examination, her score on this exam will be xx = ran 110. Cores on the two exams that she can achieve with a total of 400 minutes of studying. On the same graph, draw two or three “indifference curves” for Nancy. On your graph, find the point on Nanny’s budget line that gives her the best overall score in the course. (b) Given that she spends a total of 400 minutes studying, Nancy will maximize her overall score by achieving a score of “L” shaped indifference examination and on the first on the second examination. (c) Her overall score for the course will then be Budget line 120 Score on test 1

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