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:

Stock Repurchases

The act of a company buying back its own shares from the marketplace, potentially to increase the value of remaining shares.

IRS

Internal Revenue Service, the U.S. government agency responsible for tax collection and tax law enforcement.

SEC Regulations

The rules and regulations enforced by the Securities and Exchange Commission (SEC) that govern securities and financial markets in the United States.

Stock Market Crash

A rapid and significant decline in the stock market prices, which can lead to a widespread panic among investors and significantly affect the overall economy.