Examen de Microeconomía I UPF 2019 · Exámenes parciales tipo test de (Curso 2019-2020)

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

Test 1. Questions 1-11 (April 14, 2020)

a. Betty allocates her budget across two goods: chupa chups ($x_1$) and m&m's ($x_2$). Her budget constraint is $x_2 = 42 - 7x_1$. What is the maximum amount of chupa chups that Betty can purchase?

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Test 1. Questions 1-11 (April 14, 2020)

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

b. Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2). Which consumption bundle $(x_1, x_2)$ provides exactly 2 litres of water?

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Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

Following the previous question, suppose that one 1/3-litre can costs the same as one 1/2-litre bottle, with $p_1 = p_2 = 1\text{€}$. With an income of $5\text{€}$, what is your budget line?

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

Continuing with the water setup, assume you care exclusively about the total volume of water consumed, so goods 1 and 2 are perfect substitutes. Which bundle $(x_1, x_2)$ lies on the highest indifference curve among the affordable options?

Jennifer consumes only gin ($x_1$) and tonic water ($x_2$) to prepare gin & tonics (G&Ts). Each drink strictly requires 2 units of gin and 5 units of tonic. She only derives utility from complete G&Ts.

e. Jennifer consumes only gin ($x_1$) and tonic water ($x_2$) to prepare gin & tonics (G&Ts). Each drink strictly requires 2 units of gin and 5 units of tonic. If she only derives utility from complete G&Ts, which bundle does she prefer most?

Jennifer consumes only gin ($x_1$) and tonic water ($x_2$) to prepare gin & tonics (G&Ts). Each drink strictly requires 2 units of gin and 5 units of tonic. She only derives utility from complete G&Ts.

f. Under Jennifer's preferences from the previous problem, how many units of tonic is she willing to give up to obtain an extra unit of gin at the bundle $(4, 4)$?

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

g. Marta is indifferent between all consumption bundles satisfying $2x_1x_2 = 32$, where $x_1$ denotes kilograms of kiwis and $x_2$ kilograms of strawberries. What is her marginal rate of substitution ($MRS$) at the bundle $(4, 4)$?

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

h. Assume good 1 represents 2€ coins ($x_1$) and good 2 represents 0.50€ coins ($x_2$). Assuming you only care about total monetary value, what is your marginal rate of substitution ($MRS$) at the bundle $(2, 1)$?

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

i. Which pair of axioms on preferences over a choice set defines rational preferences?

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Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

j. Berta's budget constraint is given by $x_2 = 27 - 3x_1$, where $x_1$ is chocolate bars and $x_2$ is biscuits. What is Berta's opportunity cost of one chocolate bar?

Two goods are considered: canned water in containers of 1/3 litre (good 1) and bottled water in containers of 1/2 litre (good 2).

k. (Extra question) Three brothers (Peter, Patrick, Paul) have individual preferences over games $G = \{X, Y, Z\}$:

- Peter: $X \succ Y, Y \succ Z, X \succ Z$

- Patrick: $X \succ Z, Z \succ Y, X \succ Y$

- Paul: $Z \succ X, X \succ Y, Z \succ Y$

Group preferences are formed via unanimity: $A \succ_{\text{group}} B$ if and only if all three brothers prefer $A$ to $B$. Which statement is correct?

Test 2. Questions 1-12 (April 28, 2020)

a. Andy has utility $U_A(x, y) = 25xy$ and endowment bundle $(12, 8)$. Ben has utility $U_B(x, y) = 4x + 4y$ and endowment $(9, 13)$. Which statement is correct?

Test 2. Questions 1-12 (April 28, 2020)

b. Doreen's utility function is $U(x, y) = 10x + 5y$. She currently consumes $(10, 9)$. If her consumption of $x$ decreases to $1$, how many units of $y$ must she consume to remain equally well off?

Test 2. Questions 1-12 (April 28, 2020)

c.

Ken's utility is $U(A, B) = \sqrt{AB}$, where $A$ is apples (horizontal axis) and $B$ is bananas (vertical axis). At the bundle $(4, 16)$, the slope of his indifference curve is:

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Test 2. Questions 1-12 (April 28, 2020)

d. Pedro considers 3 units of good 1 to be a perfect substitute for 1 unit of good 2. Which utility function represents Pedro's preferences?

Test 2. Questions 1-12 (April 28, 2020)

e. Elena's preferences are given by $U(x_1, x_2) = x_1^{1/3} x_2^{2/3}$ for $x_1, x_2 > 0$. Which of the following functions does not represent Elena's preferences?

Test 2. Questions 1-12 (April 28, 2020)

f. If $x_1$ is the number of 5€ bills and $x_2$ is the number of 0.50€ coins, which utility function represents preferences over total money value?

Test 2. Questions 1-12 (April 28, 2020)

g. Toni has utility $U(x_1, x_2) = \min\{3x_1, x_2\}$ for $x_1, x_2 > 0$. Which statement is correct?

Test 2. Questions 1-12 (April 28, 2020)

h. Alicia has utility $u(x_1, x_2) = 8x_1^2 + x_2^2$. Her budget is 60 and prices are $p_1 = 2$ and $p_2 = 1$. What is her optimal consumption choice?

Test 2. Questions 1-12 (April 28, 2020)

i. Joan's utility is $u(x_1, x_2) = x_1 x_2^4$. What is his marginal rate of substitution at $(2, 6)$?

Test 2. Questions 1-12 (April 28, 2020)

j. Yael has utility $u(x_1, x_2) = 4\sqrt{x_1} + x_2$ with income $m = 12$ and prices $p_1 = 1$, $p_2 = 1$. What is her optimal choice?

Test 2. Questions 1-12 (April 28, 2020)

k. In the experiment discussed in Dunn et al. (2014) conducted with toddlers under two years old giving treats to puppets, which finding is correct?

Test 2. Questions 1-12 (April 28, 2020)

l. In the study in Canada and South Africa (Dunn et al., 2014) regarding personal spending vs. prosocial spending (goody bags for sick children in hospital):

Test 3. Questions 1-10 (May 11, 2020)

a. An individual has utility $U(x_1, x_2) = x_1 + 4x_2$ and faces prices $p_1 = 3$ and $p_2 = 1$. What is the opportunity cost of an extra unit of good 1 in units of good 2?

Test 3. Questions 1-10 (May 11, 2020)

b. Alan's utility for food ($x_1$) and clothing ($x_2$) is $U(x_1, x_2) = x_1 x_2^4$, with prices $p_1 = 1$, $p_2 = 1$ and income $m = 100$. What is his optimal bundle?

Test 3. Questions 1-10 (May 11, 2020)

c. Oscar has utility $U(x, y) = (x + 3)(y + 2)$. The prices are $p_x = 1€$ and $p_y = 1€$. When maximizing utility subject to his budget, he consumes positive amounts of both goods. More specifically, Oscar consumes:

Test 3. Questions 1-10 (May 11, 2020)

d. Wanda's utility function is $U(x, y) = x + 4\sqrt{y}$, with income 24€. If the price of $x$ is 1€ and the price of $y$ is 2€, how many units of good $x$ will Wanda demand?

Test 3. Questions 1-10 (May 11, 2020)

e. Ken's utility is $U(A, B) = AB$. The price of apples is 1.50€/kg and the price of bananas is 2€/kg. What must Ken's fruit budget be if his optimal choice involves buying 4 kg of apples?

Test 3. Questions 1-10 (May 11, 2020)

f. Valerie's utility is $U(x, y) = \min\{3x, 12y\}$. The price of $x$ is 6€ and the price of $y$ is 12€. Plotting $x$ on the horizontal axis and $y$ on the vertical axis, Valerie's income offer curve is:

Test 3. Questions 1-10 (May 11, 2020)

g. Bianca has utility $U(x_1, x_2) = 3\ln x_1 + \ln x_2$ with $x_1, x_2 > 0$. Which expression is Bianca's demand function for good 1?

Test 3. Questions 1-10 (May 11, 2020)

h. Chloe's utility function is $u(x_1, x_2) = x_1^2 + x_2^2$. Prices are $p_1 = 2$ and $p_2 = 1$. What can be said about Chloe's income offer curve?

Test 3. Questions 1-10 (May 11, 2020)

i. Daria has utility $u(x_1, x_2) = \min\{x_1, x_2\}$. If prices are $p_1 = 2$ and $p_2 = 3$, what is Daria's Engel curve for good 1?

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Test 3. Questions 1-10 (May 11, 2020)

j. Market analysis indicates demand for good $x$ is $x(p_x, p_y, m) = \frac{m}{1 + p_x/p_y}$ for $p_x, p_y > 0$. Which statement is false?

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Test 4. Questions 1-8 (May 19, 2020)

a. Cindy exhausts her entire income on goods A and B, consuming bundle $(22, 30)$. With prices $p_A = 2$ and $p_B = 4$, what is Cindy's budget line equation?

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Test 4. Questions 1-8 (May 19, 2020)

b. Bea's preferences are represented by $4\sqrt{x} + 2y$. Which equation describes her indifference curve passing through $(4, 4)$?

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Test 4. Questions 1-8 (May 19, 2020)

c. Maia has stable, monotonic, and strictly convex preferences. Available bundles are $A = (3, 1)$, $B = (2, 2)$, and $C = (1, 3)$. At prices $(1, 1)$ she buys $B$; at prices $(2, 1)$ she buys $C$; at prices $(1, 2)$ she buys $A$. What can be concluded regarding revealed preferences?

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Test 4. Questions 1-8 (May 19, 2020)

d.

Ben consumes two goods with utility $U(x_1, x_2) = 12x_1 x_2^3$. Income and $p_2$ remain constant, while $p_1$ decreases. Which statement is correct regarding income and substitution effects?

Test 4. Questions 1-8 (May 19, 2020)

e. Charlie's utility is $U(A, B) = AB$. The price of apples is initially 1€/kg, the price of bananas is 2€/kg, and income is 24€. If the price of apples rises to 6€ while the banana price stays unchanged, the Slutsky substitution effect reduces apple consumption by:

Test 4. Questions 1-8 (May 19, 2020)

f. Ken has utility $U(A, B) = AB$. Initially $p_A = 1$, $p_B = 1$, and income is 60€. If $p_A$ increases to 3€ and $p_B$ remains constant, what is the income $m'$ that keeps Ken's real income unchanged in the sense of Slutsky?

Test 4. Questions 1-8 (May 19, 2020)

g. Jack's preferences are given by $u(x, y) = \min\{2x, 2y\}$. Income is $m = 40$, $p_x = 1$, and $p_y = 1$. If $p_x$ increases to 4, what is the income effect ($\Delta x^I$) on Jack's demand for good $x$ in the sense of Slutsky?

Test 4. Questions 1-8 (May 19, 2020)

h. Regarding the paper "GARP for Kids" (Harbaugh, Krause, Berry, AER 2001):

Part 1: What did the results demonstrate?

Part 2: In the experimental design, what goods were used?

Test 5. Questions 1-8 (June 2, 2020)

a. Yoram has utility $U(x, y) = x + 5y$. Prices are $p_x = 4€$ and $p_y = 25€$. Yoram has a weekly budget of $120€$. A club allows members to buy $y$ at $10€$ per unit in exchange for a weekly membership fee. What is the maximum fee Yoram would pay to join?

Test 5. Questions 1-8 (June 2, 2020)

b. Carmen's utility is $u(x, y) = \min\{3x, y\}$, where $x$ is pairs of earrings and $y$ is money for other goods. With an income of 18€, the price of earrings increases from 6€ to 15€. What is the compensating variation (CV) of this price increase?

Test 5. Questions 1-8 (June 2, 2020)

c. Two consumer groups have inverse demand curves $p_1(x) = 30 - x$ and $p_2(x) = 30 - \frac{x}{3}$. What is the absolute value of the price elasticity $|\varepsilon|$ of their aggregate demand at price $p = 4$?

Test 5. Questions 1-8 (June 2, 2020)

d. Sonia's demand for cereals is $C = \frac{m}{40} - 2p_c$, where $m = 4000€$ and initially $p_c = 20€$. If the cereal price increases to 40€, what is the Slutsky substitution effect on her cereal demand?

Test 5. Questions 1-8 (June 2, 2020)

e. A firm has production function $f(x, y) = 4x^{1/2}y^{1/2}$ and currently uses 16 units of $x$ and 36 units of $y$. What are the marginal product of factor $x$ ($MP_x$) and the technical rate of substitution ($TRS$)?

Test 5. Questions 1-8 (June 2, 2020)

f. Which of the following production functions displays increasing returns to scale?

Test 5. Questions 1-8 (June 2, 2020)

g. Consider the production function $y = 2x_1^{1/4}x_2^{1/2}$. Which equation describes the isoquant for $y = 10$ units of output?

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Test 5. Questions 1-8 (June 2, 2020)

h. A firm has production function $f(x_1, x_2) = x_1^{0.25} x_2^{0.80}$. This technology features:

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Test 6. Questions 1-8 (June 16, 2020)

a. A competitive firm has short-run production function $q = f(x) = 524x - 4x^2$, where $x$ is the variable input. The output price is 3€/unit and the input price is 12€/unit. How many units of $x$ maximize short-run profit?

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Test 6. Questions 1-8 (June 16, 2020)

b. A competitive firm's production function is $f(x_1, x_2) = 12x_1^{1/2} + 4x_2^{1/2}$. Prices are $w_1 = 1€$, $w_2 = 2€$ and the output price is $p = 4€$. What is the profit-maximizing output quantity?

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Test 6. Questions 1-8 (June 16, 2020)

c. A firm has production function $F(L) = 6L^{2/3}$. Labor cost is $w = 2€$ and output price is $p = 4€$. What is the maximum profit the firm can achieve?

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Test 6. Questions 1-8 (June 16, 2020)

d. A firm faces fixed costs of 4000€. Its short-run production function is $y = 4x^{1/2}$. The price of the variable input is 4000€/unit. What is the firm's short-run total cost function $C(y)$?

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Test 6. Questions 1-8 (June 16, 2020)

e. A competitive firm has production function $y = 8x_1^{1/2}x_2^{1/2}$. Factor prices are $w_1 = 1$ and $w_2 = 64$. What can be said about the firm's marginal cost?

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Test 6. Questions 1-8 (June 16, 2020)

f. With production function $f(x_1, x_2, x_3, x_4) = \min\{x_1, x_2\} + \min\{x_3, x_4\}$ and input prices $(w_1, w_2, w_3, w_4) = (2, 1, 5, 3)$ euros, what is the minimum cost to produce 1 unit of output?

Test 6. Questions 1-8 (June 16, 2020)

g. A competitive firm has long-run total cost function $c(y) = 3y^2 + 300$ for $y > 0$ and $c(0) = 0$. What is its long-run supply function?

Test 6. Questions 1-8 (June 16, 2020)

h. Regarding a tax on sugar-sweetened beverages (Ortún, López-Valcárcel, Pinilla, 2016):