Charlie likes two goods, pears and kiwis, and consumes no other goods. We write his consumption bundle as (pears, kiwis), so that pears are the x variable and kiwis the y variable. Last month, Charlie consumed 20 pears and 5 kiwis. The indifference curve through this bundle is described by y = 100/x. Furthermore, you are told that the set of bundles for which he is indifferent between them and a new bundle at (10, 15) is the set of bundles with y = 150/x.
(a) Plot the two indifference curves. Note the slope at the two points given.
(b) Are the following true or false? (No explanation needed here, but it's all or nothing for credit.)
i. (30, 5) ~ (10, 15)
ii. (10, 15) ~ (20, 5)
iii. (20, 5) ~ (10, 10)
(c) Is the set of bundles Charlie weakly prefers to (20, 5) convex?
(d) Recall the indifference curve through the point at (20, 5) is defined by y = 100/x. This has a slope for any given x of -100/x^2. What is the marginal rate of substitution at
i. (10, 10)
ii. (5, 20)
iii. (20, 5)
(e) Do these preferences represent diminishing marginal rate of substitution?