Question

3. Craig likes both apples and bananas. He consumes nothing else. The consumption bundle where Craig consumes x, bushels of apples per year and Xg bushels of bananas per year is written as (X4, Xg). Last year, Craig consumed 20 bushels of apples and 5 bushels of bananas. It happens that the set of consumption bundles (XA, Xg) such that Craig is indifferent between (XA, Xg) and 0,5) is the set of all bundles such that Xg = 100/XA. The set of bundles (XA.Xg) such that Craig is just indifferent between (XA, XB) and the bundle (10, 15) is the set of bundles such that Xa = 150/XA . a. On the graph below, plot several points that lie on the indifference curve that passes through the point (20,5), and sketch this curve, using blue ink. Do the same, using red ink, for the indifference curve passing through the point (10, 15). b. Use pencil to shade in the set of commodity bundles that Craig weakly bundle (10, 15). Use blue ink to shade in the set of commodity bundles that Craig finds inferior to (20,5). For each of the following pair of bundles denote Craig's preference relation: c. (30,5) and (10, 15) d. (10, 15) and (20,5) e. (20, 5) and (10, 10) f. (24, 4) and (11,9.1) g. (11, 14) and (2, 49) h. A set is convex if for any two points in the set, the line segment between them is also in the set. Is the set of bundles that Craig weakly prefers to (20,5) a convex set? i. What can we infer about Craig's preferences over apples and bananas if he has convex indifference curves? j. Is the set of bundles that Craig considers inferior to (20,5) a convex set? k. The slope of Craig's indifference curve through a point, (XA, XB), is known as his marginal of at that point. 1. Remember that Craig's indifference curve through the point (10, 10) has the equation Xg-100/XA. The slope of this curve is -100/XX. Using this information, find Craig's marginal rate of substitution at the point, (10, 10). m. What is his marginal rate of substitution at the point (5, 20)? n. What is his marginal rate of substitution at the point (20,5)? 0. Do the indifference curves you have drawn for Craig exhibit diminishing marginal rate of substitution?

Answer 1

FEBRUARY 2017 Solutiow ay & (b) 30 Ah Pen Bananas Shading 10 BLUE KSHADING Blue wave 30 ZZZZZZ lo 20 Apples — (c) (30,5) = (10.15) (d) (10,15) > (2015) (e) (20,5) > (10,10) U (24,4) > (11.9.1) g) (11, 14) > (2, 49) sh) Yes 13% (1 opportunity cost of apples is comparatively high for him. M T W T F S S 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 MAR - 2017

FEBRUARY 2012 7 10 No. in (K) The slope of Craig's indifference curve theough a poult ( x) is known as his marginal rate - of substitution at that point 0 MRS at point (10,10) = -). (m) MRS at (5,20) = - 4 (n) RS at (20,5) = -25 Co) Yes. and