Microeconomics II Exam - Part 1
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Questions and Answers

If A ~ B, then the individual is indifferent regarding the two consumption bundles A and B.

True (A)

If A ~ B, then it must also be that U(A) = U(B).

True (A)

The indifference curves of the individual are strictly convex.

True (A)

The preferences of the individual can also be represented by the utility function U(X,Y) = 2XY.

<p>True (A)</p> Signup and view all the answers

Good X and good Y are perfect complements.

<p>False (B)</p> Signup and view all the answers

The income expansion path is a straight line.

<p>False (B)</p> Signup and view all the answers

In the utility maximum the individual obtains the utility U* = 5.

<p>False (B)</p> Signup and view all the answers

If the price of good X doubles, then the total effect of the price change is equal to the income effect of the price change.

<p>False (B)</p> Signup and view all the answers

The production function has increasing returns to scale.

<p>True (A)</p> Signup and view all the answers

The conditional factor demand for labor is L(Q) = Q.

<p>True (A)</p> Signup and view all the answers

The marginal costs of the firm are increasing in Q.

<p>False (B)</p> Signup and view all the answers

Suppose the firm has to produce Q = 81. Then the total costs of the firm are TC = 6.

<p>False (B)</p> Signup and view all the answers

At a price P* the profit maximizing firm should leave the market immediately.

<p>False (B)</p> Signup and view all the answers

The producer surplus of the firm corresponds to the area ABE.

<p>True (A)</p> Signup and view all the answers

The average fixed costs of producing Q* correspond to the area ABCD.

<p>True (A)</p> Signup and view all the answers

The long-run supply curve of the firm is equal to the marginal cost curve from point F onward.

<p>True (A)</p> Signup and view all the answers

The fixed costs of the two firms are equal to zero.

<p>True (A)</p> Signup and view all the answers

If the two firms form a collusive monopoly, then the industry profit is π₁ + π₂ = 202.50.

<p>True (A)</p> Signup and view all the answers

If the two firms compete in quantity, then the market price in the Cournot-Nash equilibrium is P = 35.

<p>True (A)</p> Signup and view all the answers

If the two firms compete in prices, then the produced industry quantity in the Bertrand-Nash equilibrium is Q = q₁ + q₂ = 18.

<p>True (A)</p> Signup and view all the answers

The individual is risk-loving.

<p>True (A)</p> Signup and view all the answers

The expected utility of the lottery is 90p.

<p>True (A)</p> Signup and view all the answers

If p = 1/2, then the utility of the expected payoff is 54.

<p>False (B)</p> Signup and view all the answers

If p = 1/2, then the certainty equivalent of the lottery is 4√5.

<p>True (A)</p> Signup and view all the answers

If v < p + z(κ; λ), then the consumer always refrains from consuming the product.

<p>True (A)</p> Signup and view all the answers

For z(κ; λ) = κλ, the conditional indirect utility u(к, р; 1) with consumption decreases with an increase in the intensity of climate concerns λ, all other things being equal.

<p>True (A)</p> Signup and view all the answers

The greater the 'loss' E from the climate externality caused by other consumers, the more consumers refrain from consuming the product.

<p>True (A)</p> Signup and view all the answers

Stronger climate concerns λ always lead to a higher profit maximizing price p of the product if the supplier's marginal cost c(κ) decrease with an increasing product carbon footprint κ.

<p>False (B)</p> Signup and view all the answers

Determine the number of subgames. (Select all that apply)

<p>2 (B), 3 (C)</p> Signup and view all the answers

How many pure-strategy combinations survive the iterated elimination of strictly dominated strategies (IESDS) for x = 5? (Select all that apply)

<p>4 (B)</p> Signup and view all the answers

For which values of x does the game have exactly one Nash equilibrium in pure strategies? (Select all that apply)

<p>x &gt; 3 (D)</p> Signup and view all the answers

For x = 0 determine the probability p with which player 1 plays the pure strategy L in the unique Nash equilibrium in mixed strategies. (Select all that apply)

<p>p = 1/6 (C)</p> Signup and view all the answers

Calculate the offer curve of individual A. (Select all that apply)

<p>OCA(p) = (3p₁/(2p₂), 2p₁/(3p₂)) (B)</p> Signup and view all the answers

Indicate the price ratio in the Walrasian equilibrium. (Select all that apply)

<p>p₁/p₂ = 3/4 (B)</p> Signup and view all the answers

What are the quantities that are consumed by individual B in the Walrasian equilibrium? (Select all that apply)

<p>None of the above (E)</p> Signup and view all the answers

Suppose that the country signs a free-trade agreement with the utility maximizing individual C that also consumes the goods l = 1,2 only. The utility function of individual C is given by Uc(x1, x2) = (x1)(x2). The initial endowment of individual C is given by wc = (0,1). The price ratio in the Walrasian equilibrium with free trade is = 3. Which of the following statements is correct? (Select all that apply)

<p>In equilibrium, individual B is better off under free trade than under autarky. (C)</p> Signup and view all the answers

Flashcards

Indifference Curve

In economics, the indifference curve is a graphical representation of all the combinations of two goods that provide a consumer with the same level of utility.

Marginal Rate of Substitution (MRS)

The marginal rate of substitution (MRS) is the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility.

Strictly Convex Indifference Curve

A strictly convex indifference curve implies that the consumer prefers a balanced consumption of both goods rather than consuming only one good excessively.

Production Function

A production function describes the relationship between the quantity of inputs used in production and the quantity of output produced.

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Increasing Returns to Scale

Increasing returns to scale occur when a proportional increase in all inputs leads to a greater than proportional increase in output.

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Conditional Factor Demand for Labor

The conditional factor demand for labor is the amount of labor that a firm will hire to produce a given level of output, given the prices of all inputs.

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Marginal Cost

Marginal cost is the additional cost incurred by a firm for producing one more unit of output.

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Producer Surplus

The producer surplus is the difference between the total revenue a firm receives from selling its output and the total variable cost of producing that output.

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Average Fixed Costs

Average fixed costs are the fixed costs of production divided by the quantity of output produced.

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Long-Run Supply Curve

The long-run supply curve is a curve showing the relationship between the price of a good and the quantity supplied by firms in a perfectly competitive market in the long run.

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Fixed Costs

Fixed costs are costs that do not vary with the level of output produced.

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Variable Costs

Variable costs are costs that vary with the level of output produced.

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Collusive Monopoly

A collusive monopoly is a situation where two or more firms in an industry act together as if they were a single firm.

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Cournot-Nash Equilibrium

The Cournot-Nash equilibrium is a situation where each firm in an oligopoly chooses its output level, taking as given the output levels of the other firms.

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Bertrand-Nash Equilibrium

The Bertrand-Nash equilibrium is a situation where each firm in an oligopoly chooses its price, taking as given the prices of the other firms.

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Risk-loving

Risk-loving individuals prefer a lottery with a higher variance in outcomes, even if the expected value of the lottery is lower.

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Expected Utility

Expected utility is the weighted average of the utility of each possible outcome of a lottery, where the weights are the probabilities of each outcome.

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Certainty Equivalent

The certainty equivalent is the amount of money that an individual would be willing to accept with certainty in exchange for a risky lottery.

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Climate Concerns

Climate concerns, usually quantified as

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Utility Function

The utility function can be used to represent an individual's preferences over different consumption bundles.

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Subgame

A subgame is a part of a sequential game that starts at a particular node and includes all subsequent moves

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Pure Strategy Combination

A pure strategy combination is a set of strategies, one for each player in a game, where each player chooses a specific action with certainty.

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Iterated Elimination of Strictly Dominated Strategies (IESDS)

Iterated elimination of strictly dominated strategies (IESDS) is a process of eliminating strategies that are strictly dominated by other strategies, starting with the first round and repeating the process until all strategies are either dominated or undominated, leaving only the rational strategies.

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Nash Equilibrium

A Nash equilibrium is a state where no player can improve their outcome by unilaterally changing their strategy, given the strategies of the other players.

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Offer Curve

An offer curve shows the combinations of goods that an individual is willing to trade at different price ratios.

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Walrasian Equilibrium

The Walrasian equilibrium is a state where all markets clear, meaning that the quantity supplied of each good is equal to the quantity demanded.

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Pareto Improvement

A Pareto improvement is a change that makes at least one person better off without making anyone worse off.

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Study Notes

Microeconomics II Exam - Part 1

  • Problem 1: Consumer Behavior
    • Preferences of an individual are characterized by the utility function U(X, Y) = XY.
    • If two consumption bundles (A and B) are indifferent (A~B), the utility derived from each bundle is equal (U(A) = U(B))
    • Indifference curves are strictly convex.
    • Preferences can also be represented by U(X,Y) = 2XY.

Problem 2: Individual and Market Demand

  • A utility maximizing individual with the utility function U(X, Y) = max{2X, Y} spends all of their income (I = 15) on X and Y. Prices are PX = 3 and PY = 5.
  • Goods X and Y are perfect complements.
  • The income expansion path is a straight line.
  • Utility in the utility maximum is U* = 5.
  • If price of X doubles, the total effect of the price change is equal to the income effect of the price change.

Problem 3: Production and Cost

  • Production function: Q(K, L) = 16K²L² (Q = output, K = capital, L = labor)
  • Price of capital (R) = 4
  • Price of labor (W) = 1
  • Potential increasing returns to scale.
  • Conditional factor demand for labor (L(Q)) = Q.
  • Marginal costs increase with output (Q).
  • At Q = 81, total costs (TC) = 6.

Problem 4: Perfect Competition and Monopoly

  • Firm operates in a market with free entry and exit.
  • Market price (P*) and profit maximizing quantity (Q*) are defined.
  • Producer surplus is area ABE.
  • Average fixed costs correspond to area ABCD.
  • Long-run supply curve is equal to marginal cost curve from point F onwards.

Problem 5: Imperfect Competition

  • Inverse demand: P(Q) = 50 – Q (Q = quantity, P = price).
  • Market served by two firms (Q = Q1 + Q2).
  • Constant marginal and average total costs (C1 and C2).
  • Fixed costs are zero for the two firms in the given problem.
  • Industry profit (π1 + π2) = 202.50 if two firms form a collusive monopoly.
  • Market price in Cournot-Nash equilibrium (P) = 35 if two firms compete in quantity.

Problem 6: Investment, Time, & Insurance

  • An individual participates in a lottery with a payoff (x) with probabilities (p) of success (x = 10) and failure (x = 0).
  • Utility function: U(x) = x² - 10 (risk-loving individual).
  • Expected utility of the lottery = 90p.
  • Certainty equivalent of the lottery (if p = 1/2) = 4√5.

Problem 7: Monopoly and Climate Protection

  • Consumer's conditional indirect utility is u(κ, p; λ) = v - p - z(κ; λ) - E.
  • If v < p + z(κ; λ), the consumer refrains from consuming the product.
  • Conditional indirect utility decreases with increasing λ if z(κ; λ) = κλ.
  • Increased "loss"(E) from climate externality causes more consumption restraint.
  • Marginal costs (c(k)) decreasing with increasing product carbon footprint (к) leads to a higher profit-maximising price (p) under stronger climate concerns (λ).

Problem 8: Game Theory (Part 2)

  • Sequential game with choices between L, M, and R for player 1 and l, r for player 2.
  • Number of subgames = 1 (in the game structure shown)
  • Number of pure-strategy combinations surviving IESDS (x = 5) = 1
  • Values of x for a game with one NE in pure strategies = x > 3.
  • Probability of strategy L in Nash equilibrium (x = 0) = 1/3.

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Description

This quiz covers key concepts in Microeconomics II, focusing on consumer behavior, demand, and production costs. You will analyze utility functions, indifference curves, and the impact of price changes on demand. Prepare to apply economic theories to practical scenarios.

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