1. (a) The diagram below shows indifference curves and budget constraints. BL₁ and BL₂ denote the original and new budget constraints, respectively, with BL3 as the compensated budget constraint. The original and new indifference curves are IC₁ and IC₂ respectively with the optimisation points marked as A, B and C. Using the information shown, explain exactly what this diagram shows, including what has happened to price and the type of substitution effect. Good Y BL2 B C X2 X3 A X₁ IC2 BL3 IC₁ BL₁ Good X
1. (a) The diagram below shows indifference curves and budget constraints. BL₁ and BL₂ denote the original and new budget constraints, respectively, with BL3 as the compensated budget constraint. The original and new indifference curves are IC₁ and IC₂ respectively with the optimisation points marked as A, B and C. Using the information shown, explain exactly what this diagram shows, including what has happened to price and the type of substitution effect. Good Y BL2 B C X2 X3 A X₁ IC2 BL3 IC₁ BL₁ Good X
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:1.
(a) The diagram below shows indifference curves and budget constraints. BL₁ and BL2
denote the original and new budget constraints, respectively, with BL3 as the
compensated budget constraint. The original and new indifference curves are IC₁
and IC₂ respectively with the optimisation points marked as A, B and C. Using the
information shown, explain exactly what this diagram shows, including what has
happened to price and the type of substitution effect.
Good Y
BL2
B
C
X2 X3
X₁
IC2
BL3
IC₁
BL1
Good X
![(b) Now consider a consumer who faces a utility function of: U(x₁, x₂) =x²x² and
prices of P₁, P₂ and an exogenous income of M. Assuming the consumer maximises
utility, find the Marshallian Demand functions. Now assume that the price of good
x₁ increases to P₁. Find the Hicksian demands and explain what they show.
(c) Assume that the price of x₂ is held fixed at £4 and income is £200, but the price of
X₁ rises from £2 to £5. Find the change in demand for both goods due to the
income and substitution effects if we keep purchasing power constant.
(d) Suppose that rather than having an exogenous income, M, the consumer now has
an endowment of e₁,e₂ of goods 1 and 2 respectively. How would your Marshallian
demands from part (b) change? (You are not required to find the functions, but
simply need to comment on how they would change). Even if good x₁ is a normal
good, under what circumstances would we be uncertain as to whether demand for
good x₁ will fall or rise, following any change in its price? Explain your answer.
[Hint: consider whether the consumer is a demander or supplier of the good].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2080afbe-6e16-483d-b107-fad4884c2af0%2Fb0da3545-29f7-403a-8831-1c3c0bf2b0d7%2Fcns4w29_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Now consider a consumer who faces a utility function of: U(x₁, x₂) =x²x² and
prices of P₁, P₂ and an exogenous income of M. Assuming the consumer maximises
utility, find the Marshallian Demand functions. Now assume that the price of good
x₁ increases to P₁. Find the Hicksian demands and explain what they show.
(c) Assume that the price of x₂ is held fixed at £4 and income is £200, but the price of
X₁ rises from £2 to £5. Find the change in demand for both goods due to the
income and substitution effects if we keep purchasing power constant.
(d) Suppose that rather than having an exogenous income, M, the consumer now has
an endowment of e₁,e₂ of goods 1 and 2 respectively. How would your Marshallian
demands from part (b) change? (You are not required to find the functions, but
simply need to comment on how they would change). Even if good x₁ is a normal
good, under what circumstances would we be uncertain as to whether demand for
good x₁ will fall or rise, following any change in its price? Explain your answer.
[Hint: consider whether the consumer is a demander or supplier of the good].
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