Microeconomics - Undergraduate Essays and Revision Notes

Microeconomics

Undergraduate Essays

Bahrum Lamehdasht

© Bahrum Lamehdasht 2012

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical or photocopying, recording, or otherwise without prior permission of the publisher.

Introduction

Microeconomics: Undergraduate Essays contains a collection of micro essays that answer the key questions in all the major microeconomics topics studied at the undergraduate level. This book delivers revision notes on utility curves and an essay on consumer choice theory. Additionally, this book contains revision notes and essays surrounding different types of competition, ranging from perfect competition to monopoly. Market failure, a crucial micro topic at university, is also covered extensively in this book with essays on externalities, public goods and adverse selection. Lastly, this book also covers more advanced undergraduate micro topics such as general equilibrium and Arrow-Pratt Risk-Aversion.

This book is aimed at undergraduate economic students all over the world. This book is mainly written for second and third year undergraduate students. Whether you are starting an essay and want some guidance or you have written an essay and want confirmation that you are on the right track, this book is here to help you. Additionally, Masters and PhD students could also use this book to study or revize a particular topic.

Economic theory can, at the best of times, be difficult to understand. Resultantly, this book explains theory in a step by step approach to help you build your understanding. Moreover, all the relevant diagrams and equations for each topic are presented and explained thoroughly throughout this book.

This book treats each essay in an unbiased manner and comes to a fair conclusion for each topic based on a careful consideration of theory and empirical evidence. Each essay has been researched meticulously and all the references are provided to allow you to follow up this research and explore further readings.

Please note that this book is not intended for you to plagiarise from. This book intends to help you better understand economic theories, show you how to lay out an essay and gives you relevant empirical examples to illustrate economic theory in action.

Consumer Choice

Question: Describe the assumptions which will yield a unique interior solution to the problem of individual consumer choice subject to a budget constraint. How can this model be developed to accommodate ‘corner’ solutions?

Introduction

Microeconomics is dominated by neoclassical theory and, in particular, the idea of optimization. The neoclassical theory of consumer choice assumes that a rational utility maximizing consumer acts in her own self-interest to buy the consumption bundle that gives her the highest utility, subject to her budget constraint. An interior solution to the problem of consumer choice occurs at the point where the indifference curve is tangent to the budget line and positive amounts of goods are consumed. To describe the assumptions which yield a unique interior solution to the problem of consumer choice, this essay starts off by discussing the assumptions on which the neoclassical model of consumer choice hinges on. Afterwards, this essay illustrates how the Lagrange Multiplier can be used in the analysis of constrained optimization. Next, the model of consumer choice is developed to accommodate ‘corner’ solutions. And finally, this essay will discuss the major limitations and critiques of the neoclassical model and assumptions that yield an interior solution.

Utility and Indifference Curves

Before we begin our discussion of an interior solution let us define the terms utility and indifference curves.[1] Utility describes a consumer’s preferences. Let’s say there are two different bundles of goods, bundles A and B, if the consumer prefers A to B then A gives the consumer a higher utility than B. Ordinal utility is the most commonly used measure of utility. For ordinal utility, the magnitude of the utility function does not matter. With ordinal utility we only want to rank different bundles, we do not want to measure how much ‘better’ one bundle is compared to another. Cardinal utility attempts to show that, for example, the consumer likes bundle A twice as much as bundle B. Cardinal utility is unnecessary for our essay though so we will stick to ordinal utility.

An indifference curve shows all the bundles of X and Y that a consumer is indifferent between. In the figure 1 below, the consumer does not care if she is consuming bundle A or B because they give her the same utility.

Figure 1: Indifference Curve

Assumptions Required for Preference Ordering

A set of axioms, discussed below, are required by neoclassical consumer choice theory to represent an individual’s preferences with indifference curves and determine a unique interior solution.

1)                  Completeness

The assumption of completeness states that, given any two bundles of goods (for example, A and B), one of the following will always hold for an individual: (i) A is preferred to B (A > B); (ii) B is preferred to A (B > A); (iii) or, the individual is indifferent between the two bundles ( ). When confronted with a choice between any two bundles of goods, a consumer will choose one bundle over the other or be indifferent between them. This implies that there are no holes in the preference ordering (Gravelle and Rees 2004, p.12).

2)                  Transitivity

Transitivity assumes that if an individual indicates that A > B and B > C then, logically, the individual must indicate that A > C. This assumption ensures that consumers are consistent in their decision-making. Another important implication of this axiom is that indifference curves cannot cross.

Figure 2: Indifference Curves Cannot Cross

According to figure 2 above, since the bundles A and B both lie on the same indifference curve (U1) and similarly because bundles A and C lie on the same indifference curve . But the above diagram reveals that C>B since bundle C contains more of good Y and the same amount of good X when compared with bundle B. So we have: and but C>A, this clearly violates the transitivity assumption. Therefore, as long as the assumption of transitivity holds, no bundle can belong to more than one indifference curve and, as a result, indifference curves cannot cross.

At this point it is key to note that the axioms of completeness and transitivity combined imply that the consumer is rational but further assumptions are required to give indifference curves certain properties that are required for a unique interior solution.

3)                  Reflexivity

This axiom states that any bundle is preferred or indifferent to itself and ensures that every bundle belongs to at least one indifference set, namely that containing itself, if nothing else (Gravelle and Rees 2004, p.13).

4)                  Non-satiation

The non-satiation axiom states that individuals always prefer more to less, that is, individuals prefer the bundle of goods that has more of at least one good and no less of the other goods. The assumption of non-satiation ensures that none of the goods are ‘bads’ and rules out commodities such as aircraft noise which consumers prefer less of. Referring to figure 3 below, at the bliss (or satiation) point, the consumer is consuming the best possible bundle of goods and any movement from their indifference curve can only be towards a lower indifference curve. Any point inside the shaded area in figure 3 below is past the consumer’s bliss point.

Figure 3: Satiation

Figure 4: Non-Satiation

Referring to figure 4 above, given the non-satiation assumption, bundles within area B (including its boundaries but excluding x’) are preferred to x’ and all points within area W (including the boundaries) (Gravelle and Rees 2004, p.14). The consumer prefers to be on an indifference curve in the northeast direction since she prefers more to less. The assumption of non-satiation is required for two reasons. Firstly, it ensures that points on the indifference set of x’ must lie in areas A and C meaning that an indifference curve is negatively sloped (Gravelle and Rees 2004, p.14). Moving along an indifference curve requires the individual to trade some of one good for more of the other. Secondly, it ensures that an indifference curve is not thicker than a single point. If the indifference curve containing x’ was a band then it would contain bundles in area B and W.

5)                  Continuity: implied by assumption of differentiability

The axiom of continuity[2] ensures that an indifference curve is a continuous surface. For an interior optimum, we must also assume differentiability so that our indifference curves are differentiable at every point so that there are no sudden jumps in the slope of our indifference curves. Since differentiability implies continuity, only the assumption of differentiability will be made.

6)                  No access to credit

Assume there is no access to credit. This is a key assumption because if an individual has access to credit then the model would disintegrate.

7)                  Tangency condition

At the optimal bundle, the slope of the indifference curve, which is the marginal rate of substitution (MRS: the rate of exchange of the two goods)[3], is equal to the price ratio of the two goods:

It is important to note that this tangency condition is a necessary but not sufficient condition for an interior solution.

8)                  Strict convexity

Figure 5: Tangency Condition is Insufficient for a Unique Interior Solution (Nicholson 1989, p.106)

In figure 5 above, there are two tangencies at bundles A and C, but only bundle A is the optimal point. Therefore, the tangency condition is necessary but not sufficient for a unique interior solution. In order to make the tangency condition both necessary and sufficient for a unique interior solution we assume strict convexity to restrict the shape of the indifference curve. The assumption of strict convexity states that for any given consumption bundle x’, its better set is strictly convex.[4] The assumption of strict convexity is key for a unique interior solution.[5] This assumption ensures that the consumer’s tastes are represented by strictly quasi-concave indifference curves so that there is a diminishing marginal rate of substitution (DMRS) as we move along the indifference curves. In the two goods case this simply implies that