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.
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.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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' = 100Xº.5Y0.5
MUx = 50X-0.5Y0.5
MUy = 50X°.5Y-0.5
Sarah: US = 50X0.4Y0.6
MUX = 20X-0.6Y0.6
MUy = 30X0.4Y•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.
d. Draw an Edgeworth box with Jane in the lower left to illustrate your answers to (b) and (c).
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