Welfare Economics

Topic 3 The Pareto principle and Pareto optimality

Lecture slides, notes & topic handouts for this module are available from:

http://www.staff.city.ac.uk/n.j.devlin

1.  Pareto improvements

·  The weak Pareto criterion

·  The strong Pareto criterion

2.  Ranking states using the Pareto principle

·  Pareto superior

·  Pareto inferior

·  Pareto indifferent

3.  Pareto optimal states

4.  Pareto non-comparability

5.  Demonstrating Pareto optimality in exchange: a 2-consumer, 2-good model

·  Shifts between which states would be an improvement using the weak Pareto criterion?

·  Shifts between which states would be an improvement using the strong Pareto criterion?

·  Which states are Pareto optimal? Why?

·  What is the condition for Pareto optimality in exchange?


6.  Feasible states: the utility possibility curve

·  Shows the highest feasible levels of utility possible for the 2 consumers, given the quantities of the 2 goods to be allocated

·  Point inside the UPC = non Pareto optimal

·  Points on the UPC = Pareto optimal

·  Points outside the UPC = not feasible given the quantities of goods available for consumption


7.  Production and the Pareto principle.

·  Thus far we have focused on applying the Pareto principle to the ‘exchange economy’ i.e. allocations of goods between consumers.

·  In order to demonstrate the relevance of the Pareto principle to the production of goods, we need to develop the theory of production and costs.

8.  Analysis of a profit maximising firm’s production decisions: isoquant & isocost analysis

Iso = ‘same’

Production: The conversion of scarce resources (factors of production) into goods and services.

Production process

Inputs: / Output:
Factors of Production / è / è / Good or service

Factors of production:

·  Land

·  Labour

·  Capital

·  Physical

·  Human


8a. Production function analysis

Production function for a pharmaceutical product

Two inputs are used to produce drugs: labour and capital

X = Production of 500,000 units of drugs per week, by 5 workers using 4 machines


8a (cont). Production function analysis

Isoquant

The slope of the isoquant is the Marginal rate of technical substitution* (MRTS).

MRTS = ∆Y/∆X

·  the increase in one input needed for a one unit decrease in another input, keeping output at the same level.

*Note that in these diagrams the X axis shows ‘machines’ and the Y axis ‘workers’. In the B&B reading, the X axis shows ‘materials’ and the Y axis ‘labour’. In most introductory micro textbooks, the X axis is labelled ‘labour’ and the Y axis ‘capital’. It doesn’t much matter which input is represented on each axis in a 2-input model – but do ensure that the way you define the MRTS (ΔY/ ΔX) in a manner consistent with the way you have labelled your axes.


8a. (cont). Production function analysis

Isoquant map

I1 = 400,000 drugs

I2 = 500,000 drugs

I3 = 600,000 drugs


8a (cont). Production function analysis

Technical efficiency

Production is technically efficient if output cannot be raised without using more of at least one input.

The isoquant summarises all technically efficient points.

Production of 500,000 drugs at X would be technically inefficient.


8a. (cont). Production function analysis

Returns to scale

I2 uses twice as many inputs as I1.

I1 produces 400,000 drugs.

If I2 produces / Returns to scale are
800,000 / constant
> 800,000 / increasing
< 800,000 / decreasing

8b (cont). Cost function analysis

Input possibilities

1 The total amount available to be spent on workers and machines is £1,000 per week.

2 The rental cost of a machine is £100 per week.

3 The weekly wage of a worker is £200.

Therefore, the employer can hire 5 workers and no machines or 10 machines and no workers or some combination of workers and machines.

All possible input possibilities form the isocost line.


8b (cont). Isocost lines at different input prices


8b (cont). Cost function analysis

Isocost lines at different levels of total cost


8c. Minimising cost of production

May produce 500,000 drugs for the cost C1 (e.g. at Y), but this is higher than cost C2.

Cannot produce 500,000 drugs for the lower cost C3.

May produce 500,000 drugs for the lowest cost, C2, at X.


8c. (cont) Minimising cost of production

Economic efficiency

X is the economically efficient (cost-effective) way to produce 500,000 drugs.

Y is a technically efficient way of producing 500,000 drugs, but is not economically efficient.

9. Demonstrating Pareto optimality in exchange: a 2-firm, 2-input model.


10. The production possibility frontier

·  Shows the highest feasible combinations of outputs of the 2 goods, given the quantities of the 2 inputs available for use.

·  Point inside the PPF = non Pareto optimal

·  Points on the PPF = Pareto optimal

·  Points outside the PPF = not feasible given the quantities of inputs & technology