Question

Ambrose consumes only nuts and berries. Fortunately, he likes both goods. The consumption bundle where Ambrose consumes x1 units of nuts per week and x2 units of berries per week is written as (x1, x2). The set of consumption bundles (x1, x2) such that Ambrose is indifferent between (x1, x2) and (1, 16) is the set of bundles such that x1 ≥ 0, x2 ≥ 0, and x2 = 20 − 4 √ x1. The set of bundles (x1, x2) such that (x1, x2) = (36, 0) is the set of bundles such that x1 ≥ 0, x2 ≥ 0 and x2 = 24 − 4 √ x1.

1. Plot several points that lie on the indifference curve that passes through the point (1, 16), and sketch this curve. Do the same for the indifference curve passing through the point (36, 0).

2. Shade in the set of commodity bundles that Ambrose weakly prefers to the bundle (1, 16). Is the set of bundles that Ambrose prefers to (1, 16) a convex set?

3. What is the slope of indifference curve at the point (9,12)? At the point (4,16)? (Hint: Recall from calculus the way to calculate the slope of a curve.)

4. Does Ambrose have convex preferences? In another word, does the indifference curves exhibit a diminishing marginal rate of substitution? (Recall that if diminishing MRS is when the slopes of the indifference curves decrease in absolute value as x1 increases).

Answer 1