Equilibrium: Supply and Demand and Price

Test Version A SEMESTER I EXAMINATIONS Mid-Term Assessment ECON 30110 Microeconomics II Time Allowed: 50 minutes Instructions for Candidates This exam counts for 30% of the Module Grade. All questions carry equal marks. Note there is NO negative marking Correct answer is worth 1 mark. No answer or more than one answer, will both receive a 0 mark. Incorrect answer will receive a 0 mark. Attempt all 20 questions. Shade in the box in the appropriate space with a HB pencil on the RESPONSE SHEET. Write the test version at the top of the RESPONSE SHEET You may use the paper provided to make notes or calculations to help you.

Instructions for Invigilators Foreign language/English dictionaries are permitted. Non-Programmable Calculators are permitted NO MOBILE PHONES ALLOWED 1. If two people in a pure exchange economy have identical utility functions, then they: a) may want to trade if their marginal rates of substitution are different b) will want to trade if they are on the contract curve c) will not want to trade if their consumption bundles are not Pareto-efficient d) will only want to trade if they are not at their endowment e) may want to trade if the price ratio is not equal to one nswer a If MRSA is not equal to MRSB, the two consumers will be able to arrange a mutually beneficial trade. Mutually beneficial trade will not occur only when the allocation of resources among A and B is already efficient. In the case of our two-consumer economy, MRSA=MRSB indicates an efficient allocation of goods (on contract curve). 2. Suppose in a two-good (X and Y) two-person (Ann and Bob) exchange economy, the MRS for person A is YA/XA and the MRS for B is YB/XB. The total amount of X is 40 and the total amount of Y is 40.

Ann has an initial endowment of 10 units of X and 30 of Y, while Bob has the remainder. This implies: a) No trade will take place. b) Ann will give some of Y to Bob in exchange for X. c) Ann will give some of X to Bob in exchange for Y. d) Ann will give some of X and Y to Bob. e) There is no enough information to make any predictions Answer b: MRSA = 30/10 = 3 Ann will give 3Y for 1X (or 1Y for 1/3X) MRSB = 10/30 = 1/3 …. Bob will give 1Y for 3X (or 1X for 1/3Y) Ann will trade Y for X (gives 1Y for min 1/3X and Bob accepts ….. n exchange for 1 Y will give up to 3X) 3. An Edgeworth Box is shown for individuals A and B, along with the contract curve. Which of the allocations b through i can be reached through free trade from “a”, and once they have been reached no further mutually beneficial trade is possible? a) Allocations b, e and f only b) Allocations c, i and f only c) Allocations d, c, i, g and h only d) Allocations c and i only e) None of these Answer: d Given endowment a, only points within the lens shaped area are mutually beneficial, or pareto superior (so points c, i and f).

That is to say, any point outside of this lens would result in at least one of the individuals being worse off compared with point a. However, at only the points on the contract curve illustrate outcomes that are pareto efficient – where the indifference curves are just tangent (MRS of A and B are equal). That is to say, pareto efficiency means that no one can be made better off without someone else being made worse off. So all the gains from trade are exhausted and no further mutually beneficial trade is possible. Point f is not on the contract curve, represents a case where MRS of A and B are different, and hence a case where further mutually beneficial trade is possible. ) 4. An Edgeworth Box is shown for individuals A and B. The endowment point E represents the initial allocation of the goods X and Y. A price line is shown passing through points E, A and B, representing a given price ratio of –PX/PY. At this given price ratio, which of the following statements is True? a) We are at a competitive equilibrium ) To achieve a competitive equilibrium, the price of good Y will rise and/or the price of good X must fall c) To achieve a competitive equilibrium, the price of good X will rise and/or the price of good Y must fall d) To achieve a competitive equilibrium the price of both goods must rise e) We cannot achieve a competitive equilibrium given the initial endowment Answer b At the given price ratio, there is excess demand for Y and excess supply of X. This means that the price of good Y will rise and/or the price of good X must fall.

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Process continues until all excess demand and supply are eliminated, and IC tangent to each other (on the Contract curve) and to the price line (which will now be flatter. So in the competitive equilibrium all markets clear, MRSA = MRSB = PX/PY. (see lecture overheads) 5. Suppose the production possibilities for two countries, A and B, producing two goods, X and Y, are as follows: | A| B| X| 2| 7| Y| 4| 7| They can each produce any linear combination as well. Measuring X on the horizontal axis, the joint production possibility frontier: a) will kink away from the origin at 7 units of X. ) will kink toward the origin at 7 units of X. c) will kink away from the origin at 2 units of X d) will kink toward the origin at 2 units of X e) will not have a kink answer: a jointly the countries can produce either a total of 9X or 11Y. MRT of A is – 4/ 2= -2 MRT of B is – 7/7 = -1 Country B has comparative advantage in X (gives up 1Y for additional 1X … whereas country A needs to give up 2Y for an additional X). Country A has a comparative advantage in production of Y (gives up 1/2 X for additional 1Y …… whereas B must give up 1X for additional Y) Jointly then can produce 9 X and 0 Y …… or 11Y and 0 X.

These define the intercepts of the joint PPF. Kink arises where both countries specialise in good in which have a comparative advantage: so B produces only X (i. e. 7X) and A produces only Y (i. e. 4Y) If jointly produce more than 7X then B produces only X, and A both X and Y (with MRT of -2). If jointly produce more than 4Y then A produces 4Y and B both X and Y (with MRT of -1). Hence answer a 6. Competition results in the efficient product mix because: a) the slope of the production possibility frontier will equal the slope of the contract curve. b) the distribution of the final output is Pareto efficient. ) producers are setting MRT equal to minus the price ratio while consumers are setting MRS equal to minus the price ratio ensuring that MRT will equal MRS. d) consumers are on the contract curve e) none of these answer c ( see self assessment sheet 2, Q1, part iv. 7. One test of whether a firm is a profit-maximizing monopoly is to check whether the firm is operating in the elastic portion of its demand curve. Why is this a relevant test and what would the elasticity be if the firm were maximizing revenue? a) If a firm were operating in the inelastic portion of the demand curve, it could raise its price and increase profit.

Revenue is maximized when elasticity equals – 1. b) If a firm were operating in the inelastic portion of the demand curve, it could raise its price and increase profit. Revenue is maximized when elasticity equals 0. c) If a firm were operating in the elastic portion of the demand curve, it could raise its price and increase profit. Revenue is maximized when elasticity equals – 1. d) If a firm were operating in the elastic portion of the demand curve, it could raise its price and increase profit. Revenue is maximized when elasticity equals 0. e) None of these. Answer a see lecture and also self assessment sheet 3, question 1 part (v) for related question) 8. Consider a firm that is the sole producer of a homogeneous product. It faces a market demand function of Q =100 – P , where P is the price of the good, and Q is the quantity of the good demanded. The firm’s costs of production are given by 40Q. The profit maximising price is then given by: a) P = 100 b) P = 60 c) P = 30 d) P = 70 e) None of these solution d: Monopoly. Profits ? = TR-TC Profit max where MR = MC Q = 100 – P and hence P = 100 – Q So TR = 100Q – Q2 So MR = 100 – 2Q TC = 40Q so MC = 40 MR = MC implies 100 – 2Q = 40

Thus Q = 30 Therefore P = 100 – 30 = 70 9. Consider a firm that is the sole producer of a homogeneous product. It faces a market demand function of Q =100 – P , where P is the price of the good, and Q is the quantity of the good demanded. The firm’s costs of production are given by 40Q. Then the firm’s Lerner index is equal to: a) 1/2 b) 3/4 c) 11/7 d) 1 e) None of these Answer e: none of these From previous question, optimal P = 70 Lerner index = (p-c)/p = (70 – 40)/70 = 30 / 70 = 3/7 10. This figure shows the demand and cost curves facing a monopoly. 80 60 40 20 800 600 400 200 0 The deadweight loss of the monopoly is: a) 48000 ) 4000 c) 2000 d) 32000 e) None of these Answer c: Draw in MR curve – cuts horizontal axis at ? Q of demand function, and has same intercept at the D on the vertical axis. MR cuts horizontal axis at Q = 40 Setting MR = MC allows monopolist to charge P = 600 (and output of Q = 20) (note: alternatively, from picture can see that expression for demand function is P = 800 – 10Q …….. when Q = 0 then P = 800 ….. and slope given by – 800 / 80 = – 10 Hence, TR = 800Q – 10 Q2 and so MR = 800 – 20Q. Set MR = MC we get Q = 20 and substituting into inverse demand we get P = 600) Competitive output occurs where P = MC = 400 and so Q = 40

DWL = area of shaded triangle = ? (600 – 400) * (40 – 20) = 100*20 = 2000 11. Suppose a monopolists price elasticity of demand is –5, and the marginal cost of production equals €80. The monopolist’s profit maximising price is then equal to: a) 75 b) 400 c) 16 d) 100 e) Cannot be computed with the information given Answer d Lerner index = (p-c)/p = 1/e So (p – 80)/p = 1/5 Hence solving for p gives p = 100 12. If the government regulates a natural monopoly by forcing it to set a price equal to Marginal Cost then a) the natural monopoly will still make high profits. b) the natural monopoly will shut down ) the natural monopoly’s marginal cost curve will shift down. d) the natural monopoly’s marginal cost curve will shift up. e) the natural monopoly will earn zero profits answer b. Natural monopoly has MC below AC. So p = MC would mean loss – which would mean exit 13. perfect price discriminating monopolist: a) generates a deadweight loss to society. b) Provides quantity discounts to customers buying larger quantities c) charges each buyer her reservation price. d) charges different prices to each customer based upon different costs of delivery. e) reduces, but does not eliminate, consumer surplus nswer c see lecture. With perfect price discrimination each consumer charged reservation price, which allows monopolist to fully extract consumer surplus (so CS is zero) and maximises total social welfare (so no deadweight loss) 14. A monopoly sells to two countries, and resales between the countries are impossible. The demand functions of the two countries are given as P1 = 100 – Q1 P2 = 120 – 2Q2 The monopolists marginal cost is €30. The profit maximising monopolist will set prices as follows: a) P1 = 65 and P2 = 75 b) P1 = 35 and P2 = 22. 5 c) P1 = 68. 33 = P2 d) P1 = 100 and P2 = 60 ) None of these Solution a: Profit max monop will choose p1 to max profit in country 1, and choose p2 to max profit in country 2. We have two separate demand functions. Hence, this implies MR1 = MC and set MR2 = MC TC = 30Q TR1 = 100Q1 – Q12 MR1 = 100 – 2Q1 = 30 MC Solving: Q1 = 35 And hence P1 = 100 – Q1 = 65 TR2 = 120Q2 – 2Q22 MR2 = 120 – 4Q2 = 30 MC Solving: Q2 = 45/2 = 22 ? And hence P2 = 120 – 2Q2 = 120 – 45 = 75 15. Two firms, A and B, selling identical products face an inverse market demand function given by P = 100 – Q, and each have a constant marginal cost of 40.

The firms simultaneously choose quantities to maximise profit. Firm A’s reaction function can then be written as: f) qA = 30 – qB g) qA = 30 + ? qB h) qA = 60 – qB i) qA = 30 – ? qB j) None of these Answer d: DEMAND : P = 100 – Q Two firms in the industry, so Q = qA + qB Hence we can write P =100 – qA – qB Profit function for firm A: = TR – TC = P qA – C Thus, ? A = 100qA – qA2 – qAqB – 40qA Firm A will choose qA to maximise profit, given the qB set by its rival B ….. First order condition for profit maximisation then is ?? A / ? qA = 100 –2 qA – qB – 40 = 0

Rearranging, we find qA = (60 – qB) / 2 = 30 – ? qB ….. this is firm A’s reaction function …… in order to maximise it’s profit, firm A will choose and output qA that is a best response to qB …… Identical firms, so similarly qB = 30 – ? qA ………. this is firm B’s reaction function …… in order to maximise it’s profit, firm B will choose and output qB that is a best response to qA…… 16. Two firms, A and B, selling identical products face an inverse market demand function given by P = 100 – Q, and each have a constant marginal cost of 40.

The firms simultaneously choose quantities to maximise profit. The equilibrium outcomes are: k) P = 40 and qA = 30 = qB l) P = 60 and qA = 20 = qB m) P = 70 and qA = 15 = qB n) P = 100 and qA = 20 = qB o) None of these Answer b Solving reaction functions: 1) qA = 30 – ? qB 2) qB = 30 – ? qA Substituting equation (2) into equation (1) we can then solve for the optimal qA that A should choose to maximise profits…. qA = 30 – ? (30 – ? qA) qA = 20 Since we have identical firms, we know that similarly we can solve for qB = 20 Market quantity Q = qA+ qA = 40 And we can solve for the market price.

Since P = 100 – Q this implies that P = 60 17. In a Bertrand model with differentiated products p) price is independent of marginal cost. q) firms set price at marginal cost. r) firms set price independently of one another. s) firms can set price above marginal cost. t) price may be either equal to or above marginal cost answer d 18. In a homogeneous good Bertrand model, the equilibrium price u) declines with the number of firms in the market v) is independent of the number of firms in the market w) is independent of marginal cost x) is above marginal cost . ) is the same as the monopoly price answer b (note n = 1 implies a monopoly and not an Oligopoly). for n = 2, p = mc ….. and for all n;2 price = mc so price does depend upon mc, is equal to mc, and is independent of the number of firms in the market 19. In the long run in a monopolistic competitive market, a) Firms will set P ; MC and produce where P = AC b) Firms will set P ; MC and produce where P ; AC c) Firms set P = MC and produce where P = AC d) Firms set P = MC and produce where P ; AC e) Total Social Welfare is maximised Answer a Have market power: set P ; MC …. ut no entry barriers, so in long run all profits are eroded and so P = AC and profits are zero 20. The payoff matrix for two firms, A and B, that must choose between setting a High or Low price strategy is shown as follows: | Firm B| Firm A| | Low| High| | Low| (10 , 10)| (25 , 5)| | High| (5 , 25)| (20,20)| A Nash equilibrium in this game is: a) Both firms set a High price b) Both firms set a Low price c) Firm A sets a Low price and firm B sets a High price d) Firm A sets a High price and firm B sets a Low price e) There is no nash equilibrium in this game Answer b

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