3. 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 follows: Jane: U' = 100X0.5Y0.5 MUX = 50X-0.5y0.5 MUy = 50X0.5Y-0.5 Sarah: US = 50X04Y0.6 MUx = 20X-0.6Y0.6 MUy = 30X04Y-0.4 The market prices of X and Y are $10 and $20, respectively. Current outputs are 58 units of X and 36 units of Y. Jane's current income is $600, while Sarah's income is $700. a. Write out an expression for each consumer's marginal rate 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.

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