1.(a) The diagram below shows indifference curves and budget constraints. BL₁ and BL2denote the original and new budget constraints, respectively, with BL3 as thecompensated budget constraint. The original and new indifference curves are IC₁and IC₂ respectively with the optimisation points marked as A, B and C. Using theinformation shown, explain exactly what this diagram shows, including what hashappened to price and the type of substitution effect.Good YBL2BCX2 X3X₁IC2BL3IC₁BL1Good X (b) Now consider a consumer who faces a utility function of: U(x₁, x₂) =x²x² andprices of P₁, P₂ and an exogenous income of M. Assuming the consumer maximisesutility, find the Marshallian Demand functions. Now assume that the price of goodx₁ 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 ofX₁ rises from £2 to £5. Find the change in demand for both goods due to theincome and substitution effects if we keep purchasing power constant.(d) Suppose that rather than having an exogenous income, M, the consumer now hasan endowment of e₁,e₂ of goods 1 and 2 respectively. How would your Marshalliandemands from part (b) change? (You are not required to find the functions, butsimply need to comment on how they would change). Even if good x₁ is a normalgood, under what circumstances would we be uncertain as to whether demand forgood 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].

An indifference curve refers to a graph showing a combination of 2 goods that give the consumer the…

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

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

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].

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) Suppose there are two goods, X and Y. The price of good X is $5, the price of good Y is $3, and your income is $60. Neatly graph your budget line and label the intercepts. (a) What is the slope of your budget line? (b) How many units of good Y do you give up per unit of good X? (c) Suppose the price of good X rises to $6, show what happens to the budget line and label any new intercepts. (d) What is the new slope of the budget line? How many units of good Y do you now give up per unit of good X? (e) Suppose the price of good X only rises to $6 once you have purchased six units of good X. In other words, it is $5 per unit for the first six units and $6 per unit thereafter. Make a new graph of this "kinked" budget constraint.
5) Consider indifference curves for the consumption of milk and chocolates (you may assume that both are 'goods'). The indifference curves are drawn with the number of chocolate bars on the horizontal axis and pints of milk on the vertical axis. Suppose that at every point, consumer A's indifference curve is flatter than consumer B's. What can you conclude about consumers A and B tastes and preferences?
PROBLEM (1) Suppose a consumer has just enough money to afford the bundle of 3 apples and 2 oranges, and similarly she also has just enough money to afford the bundle of 2 apples and 4 oranges. (a) Denoting the number of apples with x and oranges with y, plot the two given bundles on a graph, and calculate the relative price of apples; px/ py. (b) If she buys only apples with her budget, how many can she buy? If she buys only oranges, how many can she buy? Write down the budget equation for the consumer. (Notice that knowing two points on the budget line, you can write down the budget equation, even though you weren't given the prices nor the income explicitly!) (c) Suppose MUx = 20 and MUY = 30 at some point on the budget line. Is she maximizing utility by choosing this bundle? If not, should she buy fewer apples (and more oranges), or more apples (and fewer oranges), to increase her utility? (d) Forget about (c); instead, you learn that her utility function is u(x,y) = Axy³. What is…
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Subpart 7 only