Two Individuals, Dave and Bob, Consume Two Goods, X and Y

question 100

Essay

Two individuals, Dave and Bob, consume two goods, X and Y. The utility functions for the two individuals are given as:
Bob's utility function:
U_B = 30X^0.25Y^0.75
Dave's utility function:
U_D = 50X^0.5Y^0.5
Bob is currently consuming 5 units of X and 10 units of Y. Dave is currently consuming 12 units of X and 8 units of Y. The current prices of X and Y are $10 and $15, respectively.
a. Determine the marginal rate of substitution for each individual.
b. In light of the information given above, have the two individuals achieved exchange equilibrium? Would it be possible to make one individual better off without harming the other? If the individuals have achieved exchange equilibrium, are other equilibrium combinations of X and Y between the individuals possible?

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Definitions:

Environmental Regulations

Rules and standards set by authorities to control the impact of human activities on the environment.

Utilities

Essential services provided by public and private sectors such as water, electricity, gas, and sewer services.

Taxes

Compulsory financial charges or some other type of levy imposed upon a taxpayer by a governmental organization in order to fund government spending and various public expenditures.

Northern Mexico

A geographical region of Mexico, often characterized by its vast deserts, maquiladoras (manufacturing plants), and proximity to the United States border.