Arthur’s preferences are defined over two basic food groups, beer, x 1 , and ice
ID: 1120742 • Letter: A
Question
Arthur’s preferences are defined over two basic food groups, beer, x1, and ice cream, x2. His utility function is u(x1, x2) = x21 + x2. He has $100 to spend, and each of these goods costs $10 per quart.
a.
Arthur will consume 5 quarts of ice cream and 5 quarts of beer.
b.
Arthur will find that 10 quarts of beer and no ice cream is the best bundle.
c.
Arthur will find that 10 quarts of ice cream and no beer is the best bundle.
d.
Arthur is indifferent between any two points on the line that connects (5, 5) and (10, 10).
e.
Arthur will spend of his income on beer and of his income on ice cream.
ANS: B
Not exactly sure how they got this answer, can someone explain?
a.
Arthur will consume 5 quarts of ice cream and 5 quarts of beer.
b.
Arthur will find that 10 quarts of beer and no ice cream is the best bundle.
c.
Arthur will find that 10 quarts of ice cream and no beer is the best bundle.
d.
Arthur is indifferent between any two points on the line that connects (5, 5) and (10, 10).
e.
Arthur will spend of his income on beer and of his income on ice cream.
Explanation / Answer
u = x12 + x2
Budget line: 100 = 10x1 + 10x2
x1 + x2 = 10
This is a quasilinear utility function which means that x1 & x2 are substitutes, and optimal bundle is in one of the corner points of the linear isoquant touching both axes.
From budget line,
When x1 = 0, x2 = 10 and u = 0 + 10 = 10
When x2 = 0, x1 = 10 and u = (10)2 + 0 = 100
Since utility is higher when x1 = 10 and x2 = 0, this is the optimal bundle.
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