1. Charlie likes both apples and bananas. He consumes nothing else. The consmnption bundle where Charlie consumes mg bushels of apples per year and 3:3 bushels of bananas per year is written as (ems-B). Last year, Charlie consumed 2H bushels of apples and 5 bushels of bananas. It happens that the set of consumption bundles (14,333) such that Charlie is indifferent between (mg, mg) and [2!], 5) is the set of all bundles such that 3:3 2 100/134. The set of bundles (In: 125) such that Charlie is just indifferent between (mg. mg) and the bundle (1U, 15) is the set of bundles such that 1:3 2 lag/SEA. (a) Plot several points that lie on the indifference curve that passes through the point (21), 5)1 and sketch this curve. using blue ink. Do the same, using red ink, for the indifference curve passing through the point (10, 15). [[ans: The utility is U = 35:53:14. It is l'iyperbola.]] (b) Use pencil to shade in the set of commodity bundles that Charlie weakly prefers to the bundle [ll], 15). Use blue ink to shade in the set of commodity bundles such that Charlie weakly prefers (20. 5) to these bundles. [[ans: The weakly preferred bundles include all area above the indifference curve (including the curve itself).]] (c) Is the set of bundles that Charlie considers inferior to [2!], 5) a convex set? [[ans: No.\" (d) Obtain the slope of Charlie's indifference curve through a point, (mg, to B)? which is known as his marginal rate of substitution. [[ans: lMRS = llfUA/JUB = :cB/:rA.]] (e) Rernember that Charlie's indifference curve through the point (ll-J, 1U) has the equation 3:3 2 Hill/LEA. Find Charlie 's marginal rate of substitution at the point, (10, 10). [[[ans: ml. (f) 1"J's-"liai- is his marginal rate of substitution at the point (5, 20)? [[ems: *4.\