Problem 1. Lolita. Lolita, an intelligent and charming Holstein cow, consumes only two goods, cow feed (made of ground corn and oats) and hay. Her preferences are represented by the utility function U(91,92) = 9192, where q₁ is her consumption of cow feed, and q2 is her consumption of hay. The indifference curves for this function are smooth, strictly convex, and downward sloping. Note that such a utility function is called a generalised Cobb-Douglas utility function. It describes the same preferences as the utility function (q₁)0.5 (92)0.5. Lolita has been instructed in the mysteries of budgets and optimisation and always maximises her utility subject to her budget constraint. Lolita has an income I = $120 that she is allowed to spend as she wishes on cow feed and hay. a) Calculate Lolita’s optimal bundle if the price of cow feed is pº₁=$1 and the price of hay is p2=$1. Call this bundle A and show it on a graph (put cow feed on the horizontal axis). b) Suppose that the price of cow feed increases to pew₁-$4 and the price of hay stays the same at p2=$1. Calculate Lolita's new optimal bundle of cow feed and hay (call it bundle B). Show it on the same graph. c) If at new prices (pnew₁-$4 and p2=$1) Lolita has just enough income to achieve the same utility as in part (a), what bundle will she buy? Calculate this new bundle D and show it on the graph. Calculate the income required to buy bundle D.
Problem 1. Lolita. Lolita, an intelligent and charming Holstein cow, consumes only two goods, cow feed (made of ground corn and oats) and hay. Her preferences are represented by the utility function U(91,92) = 9192, where q₁ is her consumption of cow feed, and q2 is her consumption of hay. The indifference curves for this function are smooth, strictly convex, and downward sloping. Note that such a utility function is called a generalised Cobb-Douglas utility function. It describes the same preferences as the utility function (q₁)0.5 (92)0.5. Lolita has been instructed in the mysteries of budgets and optimisation and always maximises her utility subject to her budget constraint. Lolita has an income I = $120 that she is allowed to spend as she wishes on cow feed and hay. a) Calculate Lolita’s optimal bundle if the price of cow feed is pº₁=$1 and the price of hay is p2=$1. Call this bundle A and show it on a graph (put cow feed on the horizontal axis). b) Suppose that the price of cow feed increases to pew₁-$4 and the price of hay stays the same at p2=$1. Calculate Lolita's new optimal bundle of cow feed and hay (call it bundle B). Show it on the same graph. c) If at new prices (pnew₁-$4 and p2=$1) Lolita has just enough income to achieve the same utility as in part (a), what bundle will she buy? Calculate this new bundle D and show it on the graph. Calculate the income required to buy bundle D.
Chapter1: Making Economics Decisions
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Transcribed Image Text:Problem 1. Lolita.
Lolita, an intelligent and charming Holstein cow, consumes only two goods, cow feed (made
of ground corn and oats) and hay. Her preferences are represented by the utility function
U(91,92) = 9192, where q₁ is her consumption of cow feed, and q2 is her consumption of hay.
The indifference curves for this function are smooth, strictly convex, and downward sloping.
Note that such a utility function is called a generalised Cobb-Douglas utility function. It
describes the same preferences as the utility function (q1)0.5 (92)0.5.
Lolita has been instructed in the mysteries of budgets and optimisation and always maximises
her utility subject to her budget constraint. Lolita has an income I = $120 that she is allowed
to spend as she wishes on cow feed and hay.
a) Calculate Lolita's optimal bundle if the price of cow feed is pº₁-$1 and the price of hay
is p2 $1. Call this bundle A and show it on a graph (put cow feed on the horizontal
axis).
b) Suppose that the price of cow feed increases to pew₁-$4 and the price of hay stays the
same at p2=$1. Calculate Lolita's new optimal bundle of cow feed and hay (call it
bundle B). Show it on the same graph.
c) If at new prices (pnew₁-$4 and p2=$1) Lolita has just enough income to achieve the
same utility as in part (a), what bundle will she buy? Calculate this new bundle D and
show it on the graph. Calculate the income required to buy bundle D.
d) What are the total, income and substitution effects (on cow feed) of an increase in the
price of cow feed from $1 to $4? Show them on a graph.
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