Examen de Microeconomía II UPF 2016 · Midterm Exam - Microeconomics I (May 2016)

Question 1 (4 points). Proportional shifts in budget constraints

Consider an initial economic scenario where prices are $p_1$ and $p_2$, and Joan has an income of $m$, leading to the budget constraint $m = p_1 x_1 + p_2 x_2$. Suppose that both prices ($p_1$ and $p_2$) as well as her income $m$ double simultaneously. In standard $(x_1, x_2)$-space, what happens to Joan's budget line?

Question 2 (4 points). Demand response to income changes

Suppose an individual's consumption of a particular good decreases whenever their income rises, holding all other variables constant. From an economic perspective, this good is categorized as:

Question 3 (4 points). Equation of an indifference curve

Sandra's preferences over two goods are described by the utility function $U(x_1, x_2) = 16x_1^{1/2}x_2$. Which expression correctly defines the indifference curve associated with a fixed utility level of $\bar{U} = 64$?

Question 4 (4 points). Marginal Rate of Substitution

Bernat evaluates bundles using the utility function $u(x_1, x_2) = (x_1 + 2)x_2$. Determine the marginal rate of substitution (MRS) evaluated at the consumption bundle $(x_1, x_2) = (2, 12)$.

Question 5 (4 points). Boundary consumption from a budget constraint

Berta allocates her income between chocolate bars (good 1) and biscuits (good 2). Her budget line is given by the relation $x_2 = 27 - 3x_1$. What is the maximum number of chocolate bars that Berta can afford?

Question 6 (4 points). Properties of Leontief preferences

Robert's preferences are modeled by the utility function $U(x_1, x_2) = \min\{x_1, 4x_2\}$ for strictly positive consumption levels $x_1, x_2 > 0$. Identify the statement that is not correct:

Question 7 (4 points). Engel curve for perfect substitutes

Ernesto has preferences represented by $u(x_1, x_2) = 3x_1 + x_2$. He faces prices $p_1 = p_2 = 3$ and has an income of $m = 90$. What is his Engel curve for good 1?

Question 8 (4 points). Weak Axiom of Revealed Preference

When price vector is $(p_1, p_2) = (4, 1)$, Pablo purchases bundle $A = (1, 6)$. When price vector shifts to $(p'_1, p'_2) = (2, 1)$, he purchases bundle $B = (4, 1)$. What can be concluded about his consumer behavior?

Question 9 (4 points). Engel curve for Leontief preferences

Jack has preferences characterized by the utility function $u(x, y) = 4\min\{x, y\}$. If his income is $m$ and prices are $p_x = 2$ and $p_y = 3$, what is his Engel curve for good $x$?

Question 10 (4 points). Monotonic transformations of utility

Maria's preferences are represented by $U(x_1, x_2) = x_1^{1/3} x_2^{2/3}$ with $x_1, x_2 > 0$. Which of the following utility functions does not represent the exact same preferences?

Question 11 (4 points). Optimal bundle in Cobb-Douglas utility

Assume Maria has the utility function $U(x_1, x_2) = x_1^{1/3} x_2^{2/3}$ for $x_1, x_2 > 0$. If her income is $m = 120$ and prices are $p_1 = 40$ and $p_2 = 8$, which bundle represents her optimal choice?

Question 12 (4 points). Slutsky compensated income

Suppose that when Maria faces an income of $m = 120$ and prices $p_1 = 40$ and $p_2 = 40$, her optimal consumption bundle is $x^* = (x_1, x_2) = (1, 2)$. If the price of good 1 falls to $p_1' = 20$ while $p_2 = 40$ and initial income remain unchanged, what level of income $m'$ leaves Maria's purchasing power constant in the sense of Slutsky?

Question 13 (4 points). Properties of linear preferences

If an agent's utility function is expressed as $u(x_1, x_2) = 3x_1 + 4x_2$, which of the following assertions holds true?

Question 14 (4 points). Gross complements and substitutes

David has a fixed income of €900. When prices are $p_1 = 90€$ and $p_2 = 9€$, he selects the bundle $(x_1, x_2) = (8, 20)$. When the price of good 2 increases to $p_2 = 10€$ while $p_1$ remains at $90€$, he selects $(x_1, x_2) = (9, 9)$. Based on these observations, for David:

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Question 15 (4 points). Hicks decomposition and good classification

Lucía has an income of 120 to spend on clothing ($x_1$) and other goods ($x_2$). At prices $p_1 = 3$ and $p_2 = 1$, she purchases the bundle $(30, 30)$. When prices change to $p'_1 = 1$ and $p'_2 = 1$, the Hicks substitution effect for good 1 is $\bar{\Delta} x_1^S = +9$ and the Hicks income effect is $\bar{\Delta} x_1^I = -5$. Consequently, we can conclude that for Lucía: