Question

3. Consider an economy with two people, Yu and Jevon, and two commodities, clothing and food. Currently, Yu and Jevon would both be willing to give up two articles of clothing for five pieces of food. Further, the workers in town can, in a given day, produce either 45 pieces of clothing or 40 pieces of food is the allocation of resources in this economy Pareto efficient? (10 pts) If not, should there be more clothing or more food? (5 pts) (Let the MRS=MUfood/MUclothing=the value of food in terms of clothing=how much clothing we would trade for 1 more food)

Answer 1

For an allocation to be Pareto efficient, the marginal rate of substitution between the goods must be equal to the the marginal rate of transformation between them.

Marginal rate of substitution (MRS) of clothing for food = $\frac{5}{2}$

Marginal rate of transformation(MRT) of clothing for food = $\frac{40}{45}$

The allocation of resources is not Pareto efficient as the MRS is not equal to the MRT.

In this case, MRT<MRS,

so, the production of food should be increased as the rate at which people are consuming food as compared to clothing is more than the rate at which food is being produced as compared to clothing.