Problem 3 (Perfect Complements) Trevor always begins his day with a strawberry milkshake. He makes it by mixing milk (x1) with five strawberries (r2). The secret of a really good milkslhake lies in the optimal proportion of milk and fruit: one glass always comes with five strawberries! a) Plot in a diagram Trevors' preferences (indifference map). Depict three indifference curves that pass through the following bundles (5, 1), (10, 10) and (15,4). What is the MRS at each of these points? b) What utility function represents these preferences (make sure you use right coefficients defining proportion). On the graph from a), indicate the level of utility corresponding to cach indifference curve. c) Multiply your utility function by ten and add to it constant equal to two. How did the indifference map change (explain why)? How was the level of utility associated with the each indifference curve affected?
Problem 3 (Perfect Complements) Trevor always begins his day with a strawberry milkshake. He makes it by mixing milk (x1) with five strawberries (r2). The secret of a really good milkslhake lies in the optimal proportion of milk and fruit: one glass always comes with five strawberries! a) Plot in a diagram Trevors' preferences (indifference map). Depict three indifference curves that pass through the following bundles (5, 1), (10, 10) and (15,4). What is the MRS at each of these points? b) What utility function represents these preferences (make sure you use right coefficients defining proportion). On the graph from a), indicate the level of utility corresponding to cach indifference curve. c) Multiply your utility function by ten and add to it constant equal to two. How did the indifference map change (explain why)? How was the level of utility associated with the each indifference curve affected?
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Preferences and Utility Analysis
Before understanding what is preference and utility analysis, it is very important to understand the terms preference and utility separately.
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Transcribed Image Text:Problem 3 (Perfect Complements)
Trevor always begins his day with a strawberry milkshake. He makes it by mixing milk (x1) with five
strawberries (r2). The secret of a really good nilkshake lies in the optimal proportion of milk and fruit:
one glass always comes with five strawberries!
a) Plot in a diagram Trevors' preferences (indifference map). Depict three indifference curves that
pass through the following bundles (5, 1), (10, 10) and (15,4). What is the MRS at each of these points?
b) What utility function represents these preferences (make sure you use right coefficients defining
proportion). On the graph from a), indicate the level of utility corresponding to cach indifference curve.
c) Multiply your utility function by ten and add to it constant equal to two. How did the indifference
map change (explain why)? How was the level of utility associated with the each indifference curve
affected?
d) Trevor spends $100 per month on his favorite milkshake, and pays $1 for a glass of milk and $1
for one strawberry (they are organic). Find analytically Trevor's demand for milk and strawberries, and
depict it on the graph. Is it interior?
e) The organic strawberries are replaced by genetically modified ones. These are, on average, 2.5 times
larger. Consequently, the optimal proportion of milk to strawberry becomes 1: 2. Plot the indifference
curves for milk and genetically modified strawberries, and write down a utility function that represents
them.
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