B.II.2 An optimising consumer has total budget y and consumes two goods, cheese q₁ and bread 92, purchased at the prices p₁ and p2. Suppose that her Marshallian demand for cheese is fi (y, P₁, P2) = max { // - 4,0}, P1 > 0. where A> 0 is a preference parameter. (a) Find the consumer's Marshallian demand for bread. Draw diagrams to illustrate her income expansion paths and the Engel curves for the two goods. What class of preferences do these demands describe? Suppose that the cheese supplier reduces the price of cheese to p₁ - d on purchases above E units (where & pi(A+ E). Explain carefully what bundle of cheese and bread she will choose. How do you know, solely from the information given so far, that she prefers a bundle with 912E to any bundle with q₁ < E? (d) Suppose her preferences are given by utility function u (91, 92) = 91 +A ln q2. Show that this is compatible with the Marshallian demand curves described above. (e) Show that she consumes q₁ > E if y ≥ P₁E +P₁A (P¹ − 1) (In p₁ – In (P₁ – 5)) . Hence draw a diagram showing the path followed by the bundles consumed by the consumer as y increases under the budget constraint with the discount. Comment. (f) How would your analysis change if the cheese supplier made the cheese discount available only to customers who pay a flat fee F to join a club for cheese lovers?
B.II.2 An optimising consumer has total budget y and consumes two goods, cheese q₁ and bread 92, purchased at the prices p₁ and p2. Suppose that her Marshallian demand for cheese is fi (y, P₁, P2) = max { // - 4,0}, P1 > 0. where A> 0 is a preference parameter. (a) Find the consumer's Marshallian demand for bread. Draw diagrams to illustrate her income expansion paths and the Engel curves for the two goods. What class of preferences do these demands describe? Suppose that the cheese supplier reduces the price of cheese to p₁ - d on purchases above E units (where & pi(A+ E). Explain carefully what bundle of cheese and bread she will choose. How do you know, solely from the information given so far, that she prefers a bundle with 912E to any bundle with q₁ < E? (d) Suppose her preferences are given by utility function u (91, 92) = 91 +A ln q2. Show that this is compatible with the Marshallian demand curves described above. (e) Show that she consumes q₁ > E if y ≥ P₁E +P₁A (P¹ − 1) (In p₁ – In (P₁ – 5)) . Hence draw a diagram showing the path followed by the bundles consumed by the consumer as y increases under the budget constraint with the discount. Comment. (f) How would your analysis change if the cheese supplier made the cheese discount available only to customers who pay a flat fee F to join a club for cheese lovers?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:B.II.2 An optimising consumer has total budget y and consumes two goods, cheese q1 and bread q2,
purchased at the prices pi and P2. Suppose that her Marshallian demand for cheese is
i (8, P1. 12) = max {- A, 0.
Pi > 0.
where A > 0 is a preference parameter.
(a) Find the consumer's Marshallian demand for bread. Draw diagrams to illustrate her income
expansion paths and the Engel curves for the two goods. What class of preferences do these
demands describe?
Suppose that the cheese supplier reduces the price of cheese to pi – 8 on purchases above E units
(where d < p1). In other words, buying q1 units of cheese costs pi91 if q1 < E and pi91 – 8(qı – E)
if q1 > E.
(b) Describe the budget set and discuss difficulties in modelling demand for budget sets of this type.
(c) Suppose y > p1(A+ E). Explain carefully what bundle of cheese and bread she will choose.
How do you know, solely from the information given so far, that she prefers a bundle with
q1 > E to any bundle with qı < E?
(d) Suppose her preferences are given by utility function u (q1, 92)
is compatible with the Marshallian demand curves described above.
= q1 + A ln 92. Show that this
(e) Show that she consumes q1 > E if
Pi
y 2 piE +p1A ( - 1) (In p1 – In (p1 – 6)).
Hence draw a diagram showing the path followed by the bundles consumed by the consumer as
y increases under the budget constraint with the discount. Comment.
(f) How would your analysis change if the cheese supplier made the cheese discount available only
to customers who pay a flat fee F to join a club for cheese lovers?
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