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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The Answer of 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?

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