Question

Charlie likes both apples and bananas. he consumes nothing else. the consumption bundle where charlie consumes xa bushels of apples per year and xb bushels of bananas per year is written as (xa, xb). last year, charlie consumed 20 bushels of apples and 5 bushels of bananas.

Answer 1

Answer:

the question is incomplete:

It happens that the set of consumption bundles  (xA,xB) such that Charlie is indifferent between (xA,xB) and (20,5) is the set of all bundles such that xB = 100/xA. The set of bundles (xA,xB) such that Charlie is just indifferent between (xA,xB) and the bundle (10,15) is the set of bundles such that xB =  150/xA.

I also found the attached graph.

The requirements are:

1. Is (30,5) ≈ (10,15) true or false?
2. Is (10,15) > (20,5) true or false?
3. Is (20,5) ≥ (10,10) true or false?
4. Is (24,4) ≥ (11,9.1) true or false?
5. Is (11,14) > (2,49) true or false?
6. 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 Charlie weakly prefers to (20,5) a convex  set?
7. Is the set of bundles that Charlie considers inferior to (20,5) a convex set?
8. The slope of Charlie’s indifference curve through a point, (xA,xB), is known as his  ______________ ___ of ___________ at that point.
9. Find Charlie’s marginal rate of substitution at the point (10,10).
10. Find Charlie’s marginal rate of substitution at the point (5,20).
11. Find Charlie’s marginal rate of substitution at the point (20,5).
12. Do the indifference curves you have drawn for Charlie exhibit diminishing  marginal rates of substitution?

Answers:

1. true, they are on the same red line
2. true, (10,15) is on the red line while (20,5) is on the blue line
3. true, they are equivalent since both are on the blue line
4. false, (11,9.1) is on the blue line and (24,4) is on the red line
5. true, (11,14) is on the red line while (2,29) is on the blue portion
6. yes, it is a convex set
7. no, they are not a convex set
8. The slope of Charlie’s indifference curve through a point, (xA,xB), is known as his  RATE of SUBSTITUTION at that point.
9. marginal rate of substitution at (10,10) = -10/10 = -1
10. marginal rate of substitution at (5,20) = -20/5 = -4
11. marginal rate of substitution at (20,5) = -5/20 = -1/4 = -0.25
12. yes, this curves shows diminishing marginal rates of substitutions, e.g. goes from -4 to -1 to -0.25