Microeconomics, IB and IBP

Transcription

1 Microeconomics, IB and IBP Question 1 (25%) RETAKE EXAM, January 2007 Open book, 4 hours Page 1 of What is an externality and how can we correct it? Mention examples from both negative and positive externalities. 1.2 What are the special characteristics of a public good? Does existence of public goods necessiate the existence of a public sector? Question 2 (25%) 2.1 What is the Production Possibility Frontier? Explain in detail the reason for drawing it as a concave function. 2.2 Using the Production Possibility Frontier demonstrate that there are aggregate gains from engaging in international trade. Question 3 (25%) Suppose the demand curve for a product is given by Q =10 2P + P S where P is the price of the product and P S is the price of a substitute good. The price of the substitute good is P S = Suppose P =1. What is the price elasticity of demand? What is the cross-price elasticity of demand? 3.2 Assume now that the supply curve is represented by Q =4P Find the equilibrium quantity (Q) and price (P ), and the corresponding consumer and producer surpluses. What is the price elasticity of demand at that equilibrium? What is the cross-price elactisity of demand at the equilibrium? 1

2 Page 2 of 2 Question 4 (25%) Consider a firm with monopoly power that faces the demand curve, and has the total cost function, P =100 3Q +4A 1 2 TC =4Q 2 +10Q + A where A is the level of advertising expenditures, and P and Q are price and output. 4.1 Find the values of A, Q and P that maximize the firm s profit. 4.2 Calculate the Lerner index LI =(P MC)/P, for this firm at its profit maximizing levels of A, Q and P. 2

3 Microeconomics, IB and IBP Question 1 (25%) Answer Key for RETAKE EXAM, January What is an externality and how can we correct it? Mention examples from both negative and positive externalities. Def: Anything that affects others and which is not taken into account by you! Two main ways to correct it: (i) use of the Coase theorem: negotiation under small transaction costs should lead to efficiency solautions, (ii) government intervention, e.g. standards, taxes, tradable licences etc. The typical (negative) externality example is environment, while a positive externality example is education, number of kids etc. 1.2 What are the special characteristics of a public good? Does existence of public goods necessiate the existence of a public sector? The special characteristics are two: non-excludability and non-rivalry. An explanation of these two notions should follow. One can also divide the producs in generally in Private goods, Public goods, Artificially Scarce goods, and Common resources according to whether they combine these two characteristics (see. p. 648 in the textbook). Public goods can be produced by private markets without the existence of a public sector. The book mentions (i) private donations, (ii) sale of by-products, (iii) new means of excluding nonpayers, (iv) private contracts/economics of clubs. (see p ). Question 2 (25%) 2.1 What is the Production Possibility Frontier? Explain in detail the reason for drawing it as a concave function. The PPF is the locus of points depicted in a production Edgewoth box (where iso-quants tangent each other) put into a figure where the axes depict the amount of the two goods. In that sense, the PPF depicts the frontier of the production possibilities of a country that produces two goods. To be inside the frontier implies that the allocation of input recourses is not optimal and that there exists some inefficiency. 3

4 The concavity of the PPF is based on the fat that there exist decreasing or constant returns to scale (in the case of increasing returns to scale the PPF can be no strictly concave. The best way of explaining what is happening is to start from one of the axes, say the vertical axe, where all recourses are used in the production of one good, say good X. A release of some resources will definitely reduce the production of good X and will increase the production of the other good, say good Y. However, and due to the fact that the marginal product of these recourses is quite low in the production of good X (which is not-scarce) and quite high in the production of good Y (which is scarce), such a release will reduce the production of X by little, while it will increase the production of Y by much (therefore the flat but negative curve). Clearly as we keep removing inputs from good X and transferring them in good Y this relation will change, and at the end we will have the opposite situation, i.e. a further removal of recourses from X will reduce its output by much, while it will increase the production of Y by little (therefore the steep, and negative curve). All in all, such a procedure leads to a concave curve. 2.2 Using the Production Possibility Frontier demonstrate that there are aggregate gains from engaging in international trade. The figure below describes best whjat is happening. Consider a country that has the PPF depicted below. When the country does not trade, all its production has to be consumed internally and the efficiency point is depicted by point P, where the quantities demanded equal the quantities supplied, viz.x 0 and Y 0. The price ratio is then depicted by the AA line, i.e. the line that passes from the tangency of the PPF and of the indifference curve I1 that the representative consumer in the country has. If the country opens up its trade then the relative prices will change, say BB, (it is irrellevant whether the price ratio will be steeper or not). Again it will be tangent to another point of the PPF, here PP, and to a higher indifference curve, here C. Thus, the country will now produce X 000 and Y 000 and will consume at X 00 and Y 00.The difference of these points describe the trade pattern of the coutnry, viz. it will import X 00 X 000 and it will export Y 000 Y 00. The fact that the indifference curve I2 lies above I1 shows that trade is overall beneficial, i.e. that there aggregate gains from trade. 4

5 B X A X'' X' P C I2 I1 X''' PP O Y' Y'' Y''' B A Y In p. 602 of the book a different proof is provided - a proof that is based on overall welfare comparisons as that was shown in p.164 and used in the classes numereous times. Question 3 (25%) Setting P s =2into the demand function given (Q =10 2P + P s ) we have Q =12 2P. If we also set P =1then we have Q =10. We are now ready to answer question Since dq dp = 2 and dq dp s =+1, we can directly write the following ε p = dq P dp Q = ( 2) 1 10 = 1 5 ε ps = dq P s dp s Q =(+1)2 10 = : With the given supply curve, equilibrium is derived by setting demand equal supply, i.e. 12 2P =4P = P =2 This implies that Q =12 4=8. In deriving the CS and PS, one has to pay attention that the inverse demand function is P =6 Q/2. Then, the consumer surplus is the area under that inverse demand function and above the price. Thus, CS = 1 (6 2)8 =

6 while the producer surplus is PS = 1 2 (2) 8 = 8 Finally the ε P =2 2 8 = 1 2 and the ε P S =1 2 8 = 1 4. Question 4 (25%) 4.1: We first write down the profit function for the firm: Π = (100 3Q +4A 1 2 )Q 4Q 2 10Q A To derive the values of Q,A and P that maximize the profits of the firm, we take the first derivative of the profit function with respect to the two choices the firm has, viz. Q and A, and set it equal to zero. Π Q = 0 = 90 14Q +4A 1 2 =0 Π A = 0 = 4Q1 2 A =0 = 2QA 1 2Q 2 =1= =1= 2Q = A 1 2 This is a system with two equations and two unknowns (Q, A). Substituting the latter equation into the former can solve for Q. A Q +4 2Q =0= Q =15 We can then substitute Q into 2Q = A 1 2 sides into the power of 2 gives and get 30 = A 1 2. Raising both A = 900 It remains to solve for P P = = : The Lerner index gives us how much the price is above the marginal cost of producing a unit of output. At equilibrium the firm charges a price equal to 175 and its marginal cost is MC =8Q 10 = = 130. Thus the Lerner Index is LI = P MC P = =0.27 i.e. the price is set 27% higher than the marginal cost. 6