Sarah and Jane are two representative individuals living in an economy that produces two goods, X and Y. Sarah's and Jane's utility functions are given as:
Sarah: U^S = 100X^0.5Y^0.5
Jane: U^J = 50X^0.4Y^0.6
The market determined prices of X and Y are $10 and $20, respectively. Current outputs are 58 units of X per time period and 36 units of Y. Jane's current income is $600 per time period, while Sarah's income is $700 per time period.
a. Write expressions for Sarah and Jane's marginal rates of substitution.
b. Determine the quantities of X and Y that Sarah and Jane should consume in equilibrium.
c. Do the values calculated in part (b) satisfy the conditions for equilibrium in exchange? Explain using numbers.
d. Examine your answers in parts (b) and (c). If equilibrium has not been achieved, what would be necessary to reach equilibrium? If equilibrium has been achieved, comment on the process by which equilibrium was reached.

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The Answer of Sarah and Jane are two representative individuals living in an economy that produces two goods, X and Y. Sarah's and Jane's utility functions are given as: Sarah: U^S = 100X^0.5Y^0.5 Jane: U^J = 50X^0.4Y^0.6 The market determined prices of X and Y are $10 and $20, respectively. Current outputs are 58 units of X per time period and 36 units of Y. Jane's current income is $600 per time period, while Sarah's income is $700 per time period. a. Write expressions for Sarah and Jane's marginal rates of substitution. b. Determine the quantities of X and Y that Sarah and Jane should consume in equilibrium. c. Do the values calculated in part (b) satisfy the conditions for equilibrium in exchange? Explain using numbers. d. Examine your answers in parts (b) and (c). If equilibrium has not been achieved, what would be necessary to reach equilibrium? If equilibrium has been achieved, comment on the process by which equilibrium was reached.

Sarah and Jane Are Two Representative Individuals Living in an Economy