R2) The only fruits Dana buys are apples (x) and/or berries (y). She spends $30 on fruits per month. Her utility for fruits is given by u= 4y+xy, with marginal utilities MU. y and MU 4+x. The price of apples is P=$1 and the price of berries is Py = $2. a) Draw her budget line (BL) in a diagram. Show the calculations needed to do so. (Your graph does not need to have accurate scale- simply indicate the relevant values in each axis of the graph). b) In the same diagram, draw her indifference curve (IC) for a utility level of 100. Show the calculations needed to do so. (Hint: Find the combinations on the IC for x=1, x=6, x=16). c) Graphically (without using the mathematical method), find her optimal choice (x*y*). Explain in words how we figure out the optimal choice using the budget line and indifference curves only. (Answer for part (c): approximately (x.y")=(13,8.5))
R2) The only fruits Dana buys are apples (x) and/or berries (y). She spends $30 on fruits per month. Her utility for fruits is given by u= 4y+xy, with marginal utilities MU. y and MU 4+x. The price of apples is P=$1 and the price of berries is Py = $2. a) Draw her budget line (BL) in a diagram. Show the calculations needed to do so. (Your graph does not need to have accurate scale- simply indicate the relevant values in each axis of the graph). b) In the same diagram, draw her indifference curve (IC) for a utility level of 100. Show the calculations needed to do so. (Hint: Find the combinations on the IC for x=1, x=6, x=16). c) Graphically (without using the mathematical method), find her optimal choice (x*y*). Explain in words how we figure out the optimal choice using the budget line and indifference curves only. (Answer for part (c): approximately (x.y")=(13,8.5))
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 8P
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Transcribed Image Text:R2) The only fruits Dana buys are apples (x) and/or berries (y). She
spends $30 on fruits per month. Her utility for fruits is given by
u = 4y+xy, with marginal utilities MUxy and MU, 4+x.
The price of apples is Px=$1 and the price of berries is Py = $2.
a) Draw her budget line (BL) in a diagram.
Show the calculations needed to do so.
(Your graph does not need to have accurate scale-
simply indicate the relevant values in each axis of the graph).
b) In the same diagram, draw her indifference curve (IC) for a utility
level of 100. Show the calculations needed to do so.
(Hint: Find the combinations on the IC for x=1, x=6, x=16).
c) Graphically (without using the mathematical method), find
her optimal choice (x,y*). Explain in words how we figure out the
optimal choice using the budget line and indifference curves only.
[Answer for part (c): approximately (x*,y)=(13,8.5))
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