1. Useful for class assignment # 1
Appendix to Chapter 4
Review material on the opportunity cost and the marginal rate of substitution (MRS)
Useful for class assignment # 1

2. Constant opportunity cost
The opportunity cost of one coconut is measured by the number of sacrificed fish all while remaining on the same Production Possibilities Frontier (PPF).

3. Constant opportunity cost
Fish
We need to give up the production of 40 fishes to produce the first 20 coconuts. The opportunity cost = - 40y/20x= -2y/x = slope of the PPF. Therefore, the physical cost of one extra coconut is 2 fishes.
Coconuts

4. Constant opportunity cost
Fish
40 fishes must be sacrificed to produce the next 20 coconuts. The opportunity cost = - 40y/20x= -2y/x =slope of the PPF. Notice, the opportunity cost of one unit of coconut is also 2 fishes.
The opportunity cost is constant.
Coconuts

5. Increasing opportunity cost
Fish
We need to give up the production of 4 fishes to produce the first 20 coconuts. The opportunity cost = - 4y/20x= -0.2y/x = slope of the line connecting E1 to E2.
Coconuts

6. Increasing opportunity cost
Fish
To produce the next 20 coconuts, the production of 12 fishes must be forgone. The opportunity cost = -12y/20x= -0.6y/x = slope of the line connecting E2 to E3.
Coconuts

7. Increasing opportunity cost
Fish
We need to give up the production of 20 fishes to produce 12 additional coconuts. The opportunity cost = - 20y/12x= -1.6y/x = slope of the line connecting E7 to E8. 40
The opportunity cost is increasing. The more units of x are produced, the higher the opportunity cost of each extra unit.
Coconuts

8. The opportunity cost of small increments of x (coconuts)
Fish
When the variations in x become smaller (tend to zero), the opportunity cost is equal to the slope of the tangent at the point of variation.
Coconuts

9. Decreasing marginal evaluation (MRS)
Fish
From the point of view of the consumer, the value of one coconut is measured by the number of fish that she is ready to sacrifice all while maintaining the same level of satisfaction, i.e. remaining on the same indifference curve.
Coconuts

10. Decreasing marginal evaluation
Fish
The consumer is ready to sacrifice 22 fishes in exchange for 14 additional coconuts. The marginal evaluation = Marginal Rate of Substitution (MRS)= -22y/14x = -1.57y/x = slope of the line linking E1 to E2.
Coconuts

11. Decreasing value
Fish
The consumer is ready to sacrifice 8 fishes in exchange for 8 extra coconuts. The marginal evaluation= MRS= -8y/8x = -1y/x = slope of the line linking E2 to E3.
The value given by the consumer to a good is decreasing. The more x is consumed, the less its value in terms of y.
Coconuts

12. Marginal evaluation for small increments of x (coconuts)
Fish
When the variations in x become smaller (tend to zero), the marginal evaluation or MRS corresponds to the slope of the tangent at the point of variation.
Coconuts