1 Topic 1(e): Three normative questions Normative questions of interest are: 1.Which consumers should get to consume these goods? We know that in equilibrium each consumer chooses Q such that P=MB. Under what circumstances is the “right” Q for each consumer (the one that maximizes aggregate benefits from consumption)? 2.What quantity of goods should be produced? We know that in equilibrium Q is where S=D. Under what circumstances is this the “right” Q in total (the one that maximizes NB)? 3.Which firms should produce these goods? We know that in equilibrium each firm produces until P=MC. Under what circumstances is the the “right” Q for each firm (the one that minimizes aggregate production costs)?

2 Topic 1(e): Three normative questions We will answer each of these questions. 1.Which consumers should get to consume these goods? –Suppose we have a given quantity of a good, and we want to figure out who should get to consume the good. –This is the question of how to achieve the efficient allocation of the good across consumers. –Efficiency  maximization of NB  maximization of TB in this context (fixing Q means fixing TC). –So we are looking for an allocation of the good such that no reallocation is possible in which aggregate benefits from consumption can be higher.

3 Topic 1(e): Three normative questions Example: Suppose that we have 10 units of a good to allocate across two consumers, A and B, with demand curves: –D A : Q A = 16 - P. –D B : Q B = 10 - P. Suppose we give each consumer 5 units of the good. 16 QAQA QBQB 10 PP Aggregate benefits from this allocation of the 10 units? TB A = area under D A up to Q=5 = 67.5 TB B = area under D B up to Q=5 = 37.5 So aggregate TB = TB A + TB B = = 105. Question: can we  Q for one,  Q for other so (TB A + TB B )  ? If so, 5 each can’t be efficient.

4 Topic 1(e): Three normative questions 16 QAQA QBQB 10 PP Suppose we  Q A by 1 unit… …and  Q B by 1 unit TB A  by TB A  TB B  by 5.50 TB B  TB A  > TB B   aggregate TB increase by reallocating.  Initial allocation cannot have been efficient (didn’t maximize aggregate TB) Aggregate TB could increase because MB A > MB B, That is, because the height of D A at Q = 5 > height of D B at Q = 5. Is this new allocation Q A = 6, Q B = 4 efficient?

5 Topic 1(e): Three normative questions 16 QAQA QBQB 10 PP Is the new allocation efficient? No. It is still the case that MB A > MB B so that  Q A and  Q B further can further  aggregate TB. Only when MB A = MB B and Q A + Q B = 10 have we exhausted all opportunities to increase aggregate TB. That is, is Q A =6, Q B =4 efficient allocation of the total Q=10? MB A = 10 MB B = 6

6 Topic 1(e): Three normative questions 16 QAQA QBQB 10 PP So the efficient allocation of the 10 units is where MB A = MB B & Q A + Q B =10 Rewriting the demand curves we have: MB A = 16 - Q A So MB A = MB B  16 - Q A = 10 - Q B, where Q B = 10 - Q A  16 - Q A = 10 - (10 - Q A )  16 - Q A = Q A  Q A = 8 & Q B = 2 & MB B = 10 - Q B MB A = MB B = 8

7 Topic 1(e): Three normative questions 16 QAQA QBQB 10 PP When Q A = 8 and Q B = 2, TB A = 96  aggregate TB = = 114. No reallocation can make aggregate TB higher  Q A = 8 and Q B = 2 must be efficient. NB: recall that - because total Q is fixed - maximizing TB is the same as maximizing NB, which is why we can talk about efficiency without reference to costs MB A = MB B = 8 & TB B = 18

8 Topic 1(e): Three normative questions A slightly harder case: Suppose in this example we had just 4 units of the good in total, rather than 10. What would the efficient allocation be? Try the math approach from earlier: We want to try and set MB A = MB B such that Q A + Q B = 4. MB A = MB B  16 - Q A = 10 - Q B, where now Q B = 4 - Q A  16 - Q A = 10 - (4 - Q A )  16 - Q A = 6 + Q A  2Q A = 10  Q A = 5 and Q B = -1. But this makes no sense, how could person B consume negative quantity and how could A consume more units than we have in total? Try a graphical approach to make sense of this.

9 Topic 1(e): Three normative questions 16 QAQA QBQB 10 P P Q A =5 and Q B = -1 is an impossible allocation, even if this is the answer from the math. But the diagram makes clear what the answer is: We should have Q A = 4 and Q B = 0. MB A = 12 at Q A =4 > MB B = 10 at Q B =0. Basically, A values the good so much more than B that we should (given the limited quantity available) give it all to A MB A = MB B = MB A = 12 at Q A = 4 MB B = 10 at Q B = 0

10 Topic 1(e): Three normative questions What’s the bottom line? Decision rule for the efficient allocation of a fixed quantity of a good across consumers: –Suppose we have a fixed Q of a good. If at any allocation it is true that MB A > MB B, then in order to maximize aggregate benefits to consumers then we should reallocate the good such that Q A  and Q B , if indeed such a reallocation is feasible. Basically, we always give more to the consumer that values the good more on the margin, and less to the consumer that values the good less on the margin.

11 Topic 1(e): Three normative questions Recall the normative questions of interest: 1.Which consumers should get to consume these goods? 2.What quantity of goods should be produced? 3.Which firms should produce these goods? Suppose we want a certain quantity of goods produced. –What is the efficient way to allocate responsibility for this production across different firms? For Q1, we ignored the question of who produced the goods (the cost side), so maximizing NB was the same as maximizing TB. For Q3 we will ignore the question of who gets to consume the goods (the benefit side), so maximizing NB will be all about minimizing costs.  Q3 is essentially a question of how to produce a given quantity of goods in a cost minimizing way.

12 Topic 1(e): Three normative questions Example: Suppose that we want to produce a total of 10 units of a good, and there are two firms, A and B, with supply curves: –S A curve: Q A = P - 5. –S B curve: Q B = P - 9. Suppose we let each firm produce 5 units of the good. 10 QAQA QBQB 14 PP Total costs of production given each produces 5? VC A = area under S A up to Q=5 = 37.5 VC B = area under S B up to Q=5 = 57.5 So aggregate VC = VC A + VC B = = 95. Question: can we  Q for one,  Q for other so (VC A + VC B )  ? If so, 5 each can’t be efficient.

13 Topic 1(e): Three normative questions 5 QAQA QBQB 9 PP Suppose we  Q A by 1 unit… …and  Q B by 1 unit VC A  by VC A  VC B  by VC B  VC A  < VC B   in total VC decrease by reallocating.  Initial allocation cannot have been efficient (didn’t minimize costs of total Q=10) Aggregate VC could decrease because MC A < MC B, That is, because the height of S A at Q=5 < height of S B at Q = 5.

14 Topic 1(e): Three normative questions 5 QAQA QBQB 9 PP Is Q A =6, Q B =4 the least cost way to produce total Q=10? That is, is the new allocation of production efficient? MC A = 11 MC B = 13 No. It is still the case that MC A < MC B so that  Q A and  Q B further can further  aggregate costs. Only when MC A = MC B and Q A + Q B = 10 have we exhausted all opportunities to decrease aggregate costs.

15 Topic 1(e): Three normative questions 5 QAQA QBQB 9 PP MC A = MC B = So efficient way to produce the 10 units is such that MC A = MC B & Q A + Q B =10 Rewriting the supply curves we have: MC A = 5 + Q A So MC A = MC B  5 + Q A = 9 + Q B, where Q B = 10 - Q A  5 + Q A = 9 + (10 - Q A )  2Q A = 14 A  Q A = 7 & Q B = 3 & MC B = 9 + Q B

16 Topic 1(e): Three normative questions 5 QAQA QBQB 9 PP 12 MC A = MC B = When Q A = 7 and Q B = 3, VC A = 59.5  total VC = = 91. No reallocation can make cost of production lower  Q A = 7 and Q B = 3 must be efficient. NB: recall that - because total Q is fixed - maximizing TB is the same as minimizing costs, which is why we can talk about efficiency without reference to benefits. & VC B =

17 Topic 1(e): Three normative questions Exercise (a slightly harder case): Suppose that we have two firms with the supply curves as in the previous example. If we wish to produce 3 units efficiently, how much should each firm produce? Draw a diagram to help illustrate your reasoning.