Introduction to Microeconomics- L1 EG – University of Orleans
Tutorial n.2
For each question of Exercise 1, use one of the empty graphics that you printed (cf. question bexercise 1 of Tutorial 1).
Exercise 1. Consider the data of Exercise 1-Tutorial 1. Let 𝑝𝑥 and 𝑝𝑦 the prices of goods X and Y, and
R the agent’s revenue.
1- Suppose that R=100 euros, 𝑝𝑥 = 𝑝𝑦 =5 euros:
a- Define and draw the budget set.
b- Which is the consumer’s optimal choice?
2- For 𝑝𝑥 = 𝑝𝑦 =5 euros, define and draw the income-offer curve (or income expansion path). Consider
as levels of revenue those which correspond to the optimal choice for each of the five indifference
curves of Exercise 1 of Tutorial 1. Build the Engel curves for goods X and Y. Compute the income
elasticity of the demand of goods X and Y. Comment.
3- Suppose now that R=132, 𝑝𝑥 =12 and 𝑝𝑦 =7 euros. Determine the optimal choice. Suppose that 𝑝𝑦
increases to 12 euros. Disentangle and explain the effects of this price change.
4- Suppose that R=100 and 𝑝𝑦 =5 euros. Determine the optimal choices when 𝑝𝑥 is equal to 4, 5, 10
and 20, respectively. Draw the income-offer curve and the demand curve of good X. Which are the
price elasticities of demand of X along this last curve? Compute the cross-price elasticity of demand.
5- Which is the optimal choice for R=125, 𝑝𝑥 = 5 and 𝑝𝑦 = 35 euros. What happens if 𝑝𝑦 increases?
(Show the associated income and substitution effects).
Exercise 2. The demand of good X is: X = -5R2+55R+50, where R is revenue.
a- We study this function for 2≤R≤9.5. Draw the corresponding Engel curve.
b- Compute the income-elasticity for R=5.5. Comment.
c- Which is the nature of this good?
Exercise 3. We consider a rational agent. The table below contains the demanded quantities of good
Y as a function of the price of good X, for 𝑝𝑦 = 4 and R=200:
Px
Y
5
5
4
15
3
33
2
40
a- Draw the demand curve of X as a function of 𝑝𝑥 . Comment.
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b- Suppose that the revenue increases at 300. Then the demand of good Y as a function of 𝑝𝑥
becomes (𝑝𝑦 = 4):
Px
Y
5
37.5
4
47
3
61.5
2
67.5
How does the demand of X vary with consumer’s revenue? What can you conclude?
Exercise 4. Consider the following utility function: 𝑈(𝑥, 𝑦) = 𝑥 𝑎 𝑦 𝑏 , under the usual budget
constraint.
1- Give the expression of the demand functions of X and Y.
2- Study the shape of these functions (price elasticities, cross-price elasticities and income
elasticities).
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