Free Essay

# Consumer Theory

Submitted By collinsoyindo
Words 2582
Pages 11
XEQ 201: Calculus II

Contents
Course description
References

iv iv Chapter 1. Applications of Diﬀerentiation
1.1. Mean value theorems of diﬀerential calculus
1.2. Using diﬀerentials and derivatives
1.3. Extreme Values

iii

1
1
5
7

Course description
Application of diﬀerentiation. Taylor theorem. Mean Value theorem of diﬀerential calculus. Methods of integration. Applications of integration.
References
1. Calculus: A complete course by Robert A. Adams and Christopher
Essex.
2. Fundamental methods of mathematical economics by Alpha C. Chiang.
3. Schaum’s outline series: Introduction to mathematical economics by Edward T. Dowling

iv

CHAPTER 1

Applications of Diﬀerentiation
1.1. Mean value theorems of diﬀerential calculus
Theorem 1.1.1 (Mean Value Theorem).
Suppose that the function f is continuous on the closed ﬁnite interval [a, b] and that it is diﬀerentiable on the interval (a, b). Then ∃ a point c ∈ (a, b) such that f (b) − f (a)
= f (c) . b−a It means that the slope of the chord joining the points (a, f (a)) and (b, f (b)) is equal to the slope of the tangent line to te curve y = f (x) at the point
(c, f (c)) so that the two lines are parallel.

Fig 2.28
Example 1.1.1.

Verify the conclusion of the mean value theorem for f (x) = x on the interval [a, b], where a ≤ x ≤ b.

Solution. We are to show that ∃ c ∈ (a, b) such that f (b) − f (a)
= f (c) b−a 1

XEQ 201 so long as f is continuous on [a, b] and is diﬀerentiable on (a, b). Now

1
f (x) = 2√x , f (a) = a, f (b) = b.

1
b− a b− a
1
∴ √ =
= √
=√
√ .

b−a
2 c b+ a b− a b+ a
The above equality implies that a < b, we have

a=

a+
2

a

c=

2

<

b+
2

√ b+ a
2

a

so that c =

2

<

b+
2

b

2
b+ a
.
2

Since

2

=b

which implies that c ∈ (a, b).
Example 1.1.2.
Show that sin x < x for all x > 0.
Solution. If x > 2π, then sin x ≤ 1 < 2π < x. If 0 < x ≤ 2π, then by
MVT, ∃ c ∈ (0, 2π) such that sin x sin x − sin 0 d =
= [MVT on [0, x]] = sin x x x−0 dx = cos c < 1 x=c which implies that sin x < x in this case too.

increasing decreasing functions

Definition 1.1.1 (Increasing and decreasing functions). Suppose that the function f is deﬁned on an interval I and that x1 and x2 are two points in I.
(a) If f (x2 ) > f (x1 ) whenever x2 > x1 , we say that f is increasing on
I.
(b) If f (x2 ) < f (x1 ) whenever x2 > x1 , we say that f is decreasing on
I.
(c) If f (x2 ) ≥ f (x1 ) whenever x2 > x1 , we say that f is non-decreasing on I.
(d) If f (x2 ) ≤ f (x1 ) whenever x2 > x1 , we say that f is non-increasing on I.
Diagram Fig 2.31
2

XEQ 201
Theorem 1.1.2.
Let J be an open interval and let I be an interval consisting of all points in J and possibly one or both of the end points of J. Suppose that f is continuous on I and diﬀerentiable on J.
(a)
(b)
(c)
(d)

If
If
If
If

f f f f (x) > 0
(x) < 0
(x) ≥ 0
(x) ≤ 0

for for for for all all all all x ∈ J, x ∈ J, x ∈ J, x ∈ J,

then then then then f f f f is is is is increasing on I. decreasing on I. non-decreasing on I. non-increasing on I.

derivative of increasing and decreasing functions

Example 1.1.3.
On what intervals is the function f (x) = x3 − 12x + 1 increasing? On what intervals is it decreasing?
Solution. f (x) = 3x2 − 12 = 3 (x − 2) (x + 2). It follows that f (x) >
0 when x < −2 or x > 2 and f (x) < 0 when −2 < x < 2. Therefore f is increasing on the intervals (−∞, −2) and (2, ∞) and is decreasing on the interval (−2, 2).
Diagram Fig 2.32

Example 1.1.4.
Show that f (x) = x3 is increasing on any interval.
Solution. Let x1 , x2 be any two real numbers satisfying x1 < x2 . Since f (x) = 3x2 > 0 for all x = 0, we have that f (x1 ) < f (x2 ) if either x1 < x2 ≤ 0 or 0 ≤ x1 < x2 . If x1 < 0 < x2 , then f (x1 ) < 0 < f (x2 ). Thus f is increasing on every interval.
Theorem 1.1.3.
If f is continuous on an interval I and f (x) = 0 at every interior point of
I, then f (x) = C, a constant on I.
3

derivetive of constant function

XEQ 201

derivative at interior extreme point Theorem 1.1.4.
If f is deﬁned on an open interval (a, b) and achieves a maximum (or a minimum) at the point c ∈ (a, b), and if f (c) exists, then f (c) = 0.
Values of x where f (x) = 0 are called critical points of the function f .
Theorem 1.1.5 (Rolle’s Theorem).
Suppose that the function g is continuous on the closed ﬁnite interval [a, b] and if it is diﬀerentiable on the open interval (a, b). If g (a) = g (b), ∃ a point c ∈ (a, b) such that g (c) = 0.
Theorem 1.1.6 (The Generalized Mean Value Theorem).
If functions f and g are both continuous on [a, b] and diﬀerentiable on (a, b), and if g (x) = 0 for every x ∈ (a, b), then ∃ a number c ∈ (a, b) such that f (c) f (b) − f (a)
=
. g (b) − g (a) g (c)
Exercise 1.1.

1. Illustrate the MVT by ﬁnding any points in the open interval (a, b) where the tangent line is parallel to the chord joining (a, f (a)) and
(b, f (b)).
(a) f (x) = x2 on [a, b]; Ans: c = b+a .
2
2
(b) f (x) = x3 − 3x + 1 on [−2, 2]; Ans: c = ± √3 .
2. Show that tan x > x for 0 < x < π .
2
3. Find intervals of increase and decrease of the following functions
2
(a) f (x) = x3 − 4x + 1. Ans: Increasing on −∞, − √3 and
2
√ ,∞
3

2
2
; decreasing on − √3 , √3 .
2

(b) f (x) = x2 − 4 . Ans: Increasing on (−2, 0) and (2, ∞); decreasing on (−∞, −2) and (0, 2).
(c) f (x) = x3 (5 − x)2 . Ans: Increasing on (−∞, 3) and (5, ∞); decreasing on (3, 5).
(d) f (x) = x + sin x. Ans: Increasing on (−∞, ∞).
4

XEQ 201
1.2. Using diﬀerentials and derivatives
Suppose dx is regarded as a new independent variable called the diﬀerential of x we can deﬁne a new dependent variable dy, called the diﬀerentail of y as a function of x and dx by dy dx = f (x) dx. dx For example if y = x2 , then dy = 2xdx means the same thing as dy/dx = 2x.
If f (x) = 1/x, then df (x) = − 1/x2 dx.
If y is a function of x, y = f (x), then denoting a small change in x by dx instead of ∆x, the corresponding small change in y, ∆y is approximated by the diﬀerential dy, i.e. dy =

∆y ≈ dy = f (x) dx.
Diagram Fig 2.25

Example 1.2.1.
Without using a scientiﬁc calculator, determine by a pproximately how much the value of sin x increases as x increases from π/3 to (π/3) + 0.006. To 3 decimal places, what is the value of sin ((π/3) + 0.006)?
Solution. If y = sin x, then dx = 0.006. Therefore

dy dx = cos x. Now x =

π
3

≈ 1.0472 and

dy π 1 dx = cos xdx = cos
· 0.006 = (0.006) = 0.003. dx 3
2
This means that the change in the value of sin x is approximately 0.003. Now dy =

sin

π π + 0.006 ≈ sin
+ 0.003 = · · · = 0.869(3 d. p.).
3
3
5

XEQ 201
Suppose changes in x are measured with respect to the size of x, then

relative change in x =

dx dx and percentage change in x = 100 . x x

Diﬀerentials and point elasticity1
For a demand function Q = f (P ), the elasticity is deﬁned as relative change in Q
∆Q/Q
=
.
∆P/P relative change in P point elasticity

If the change in P is inﬁnitesimal, then the expressions ∆Q and ∆P reduce to the diﬀerentials dP and dQ. In that case the elasticity measure assumes the sense of point elasticity of the demand function which is denoted by εd .
Thus
dQ/Q dQ/dP εd ≡
=
. dP/P Q/P
The numerator in the right hand is the derivative (or marginal2) function of the demand function while the denominator is the average function of the demand function. Thus the point elasticity is a ratio of the two functions.
In general, for any given total function y = f (x), the point elasticity of y
w.r.t. x is dy/dx marginal function εyx =
=
. y/x average function
The absolute value of the point elasticity measure is used in deciding whether the function is elastic at a particular point. In the case of a demand function, 

elastic
|εd | > 1

The demand is of unit elasticity if |εd | = 1

 inelastic |εd | < 1. at a given point.

1Elasticity is the measure of how an economic variable responds to change in another

variable. An elastic variable is one which responds more than proportionally to changes in other variables. An inelastic variable is one which changes less than proportionally in response to changes in other variables.
2Marginal denotes the rate of change of a quantity with respect to a variable on which it depends. 6

XEQ 201
Example 1.2.2.
Find εd for the demand function Q = 100 − 2P . Determine the point elasticity at P = 25.
Solution.

dQ dP = −2 and εd =

Q
P

=

100−2P
.
P

Therefore

−2
P
=
.
(100 − P ) /P
P − 50

Thus
= · · · = −1.

εd
P =25

Therefore the demand is of unit elasticity when P = 25.
Exercise 1.2.
1. Use diﬀerentials to determine approximate change in the values of the given function as its argument changes from the given value to the given amount. What is the approximate value of the function after the change?
(a) y = 1/x as x increases from 2 to 2.01.
(b) h (t) = cos (πt/4) as t increases from 2 to 2 + (1/10π).
2. Find the approximate percentage changes in the given function that will result from an increase of 2% in the value of x.
(a) y = x2

(b) y = 1/x2

3. Given the consumption function C = a + bY (with a > 0; 0 < b <
1);
(a) Find its marginal function and its average function.
(b) Find the income elasticity of consumption εCY , and determine its sign, assuming Y > 0.
(c) Show that the consumption is inelastic at all positive income levels. 1.3. Extreme Values
Maximum and Minimum Values
Definition 1.3.1. Function f has an absolute maximum value f (x0 ) at x0 in its domain if f (x) ≤ f (x0 ) holds for every x in the domain of f .
7

absolute extreme values

XEQ 201
Similarly, f has an absolute minimum value f (x0 ) at x0 in its domain if f (x) ≥ f (x0 ) holds for every x in the domain of f .
Remark 1. extreme value is unique, can occur at several points existence of extreme value not guaranteed

existence of extreme values for closed ﬁnite intervals local extreme values 1. A function will have only one absolute maximum (or minimum) value if it exists. However the value can occur at many points. For example, f (x) = sin x has absolute maximum of 1 but it occurs at every point π + 2nπ, n ∈ Z.
2
2. A function need not have any extreme value. The function f (x) =
1
x becomes arbitrarily large as x approaches 0 from the right, and so has no ﬁnite absolute maximum value.
Theorem 1.3.1.
If the domain of the function f is a closed, ﬁnite interval or a union of ﬁnitely many such intervals, and if f is continuous on that domain, then f must have an absolute maximum value and absolute minimum value.
Definition 1.3.2. Function f has a local maximum value (loc. max.) f (x0 ) at the point x0 in its domain provided ∃ a number h > 0 such that f (x) ≤ f (x0 ) whenever x is in the domain of f and |x − x0 | < h.
Similarly, f has a local minimum value (loc. min.) f (x1 ) at the point x1 in its domain provided ∃ a number h > 0 such that f (x) ≥ f (x1 ) whenever x is in the domain of f and |x − x1 | < h.
Diagram Fig 4.17

From the above ﬁgure we see that local extreme values can occur at any of the following points.
8

XEQ 201 critical, singular or end points

(i) critical points of f ; points x ∈ D (f ) where f (x) = 0.
(ii) singular points of f ; points x ∈ D (f ) where f (x) is not deﬁned.
(iii) endpoints of the domain of f ; points that do belong to D (f ) but are not interior points of D (f ).

In the ﬁgure above, x1 , x3 , x4 are critical points, x2 and x5 are singular points and a and b are endpoints.
Theorem 1.3.2.
If the function f is deﬁned on an interval I and has a local maximum (or local minimum) value at the point x = x0 in I, then x0 must be either a critical point of f , a singular point of f , or and endpoint of I.
Example 1.3.1.
Find the maximum and minimum values of the function g (x) = x3 − 3x2 −
9x + 2 on the interval −2 ≤ x ≤ 2.

Solution. Since g is a polynomial it can never have a singular point.
For critical points we calculate g (x) = 3x2 − 6x − 9 = 3 (x + 1) (x − 3) = 0.
Thus x = −1 or x = 3. But x = 3 is not in the domain of g and so we ignore it. We then investigate the endpoints x = −2 and x = 2 and critical point x = −1. g (−2) = 0, g (−1) = 7, g (2) = −20
The maximum value of g on −2 ≤ x ≤ 2 is at the critical point x = −1, and the minimum value is at the endpoint x = 2.
Diagram Fig 4.19
9

exteme values occur at critical, singular or end points

XEQ 201
Example 1.3.2.
Find the maximum and minimum values of h (x) = 3x2/3 −2x on the interval
[−1, 1].
Solution. The derivative of h is h (x) = 2x−1/3 − 2.
Note that x−1/3 is not deﬁned at x = 0 in D (h), so x = 0 is a singular point of h. Also h (x) = 0 at x−1/3 = 1, that is at x = 1, which also happens to be an endpoint of the domain of h. We therefore examine the values of h at endpoints x = −1 and x = 1 and at the singular point x = 0. h (−1) = 5, h (0) = 0, h (1) = 1
The function h has a maximum value 5 at the endpoint x = −1 and a minimum value 0 at the singular point x = 0.
Diagram Fig 4.20

10

### Similar Documents

#### Value to Marketers About Understanding Consumer Behavior Theories and Concepts

...VALUE TO MARKETERS ABOUT UNDERSTANDING CONSUMER BEHAVIOR THEORIES AND CONCEPTS Modern day’s business is controlled by Consumers. Large variations in consumer needs and strong competition demands market driven business and marketing plans. It’s the response of Consumers that decides the success of Marketing. Most of the marketers not only avoid theories but also consider them to be irrelevant. They believe that huge experience of Managerial facts and direct observation of consumer’s behavior is enough to succeed. What marketers fail to understand is that experience and observation on one hand and theories on the other hand are inter-linked. By understanding consumer behavior, marketers will be able to investigate and learn consumer’s purchase mannerism and make marketing decisions. 1. INTERNAL INFLUENCES: These are the factors that happen within the consumers. 1.1. LEARNING: Learning is the behavioral change occurring due to the outcome of past experience. Based on Consumers gained experience on purchased and consumed product, they learn about the brands they like and dislike and the qualities they prefer the most. With this experience consumers adjust their behavior for the future. For marketers to understand the learning behavior better, two thoughts are developed – The behaviorist and the cognitive. 1.1.1. Behaviorist Learning Theory: This Theory is concerned with observing changes in an individual’s responses as a result of exposure to stimuli.......

Words: 1842 - Pages: 8

#### Consumer

Words: 316 - Pages: 2

Free Essay

#### Consumer

...Consumer Protection Act 1986: After liberalization of economic policy, consumer goods have flooded the market as never before. Both foreign and India companies are introducing new products and brands with glossy and fancy packing as the middle and lower income groups are taking loans to-Companies still do not pay attention to the quality of their products and also do not value customer satisfaction. Very often a customer may get taken in by a misleading advertisement making tall claim as to the high quality and after-sales service. The consumer may discover later that the goods purchased by him are not up to the claims made by the manufacturer. Companies are not willing to invest in efficient after-sales service so long as their sales keep increasing. Newspaper columns can be seen to be full of complaints and many companies do not care to rectify the complaints. To enable the consumer to have his right to a deal, the consumer protection Act was passed in 1986. The Act promises to rectify all that and make accountant both the manufacture; s and providers of service. It provides for toe setting up of quasi-judicial bodies at district, state and national label for quick and inexpensive redressal of consumer grievances. Three groups-the consumer, registered voluntary consumer associations and the central and state government is covered by this facility. In case a group of person is seeking similar redressal, a class action suit can be filed or may be treated as a public interest......

Words: 1266 - Pages: 6

#### Consumer

...If the demographic segmentation is one of the most popular methods in today's market segmentation, is because of certain benefits that make it the first choice for various organizations. The two major advantages of this segmentation strategy are: The organization can categorize the needs of consumers on the basis of factors demographics such as age, gender, etc. Its variables are much easier to obtain and measure, in comparison with other strategies of segmentation variables. One of the disadvantages highlighted in this segmentation strategy of market, which is often cited by critics, is the one-dimensional approach that follows it. In this segmentation strategy, it is generally believed that all individuals who belong to a particular "group" have the same needs - which is not necessarily the case. If an organization is using only demographic segmentation, it is more likely to be vulnerable to competitors. Demographic segmentation helps the Organization to understand customers and their needs. In a market driven by intense competition, market segmentation analysis can be of great help. Basically, the market segmentation is based on the simple fact that you can not please all consumers with a single product, and therefore you have to identify the market pot Definition Description should give advantages and disadvantages of performing market segmentation vs. not performing marketing segmentation in a travel/tourism business, as follows: Advantages * Allows more precise......

Words: 587 - Pages: 3

Free Essay

#### Bounded Rationality and Consumer Choice Theory

...Introduction The theory of bounded rationality is one that been a cause for discussion in economist circles around the world for many years. The theory, originally coined by Hebert Simon surrounded the limitation of humans to process the amount of information available to make a logical, economic decision and the consumer would therefore, settle for something that satisfyingly sufficient, or ‘satisfice’(Simon 1955). Furthermore, the theory expanded over time to also include mans use of heuristics to simplify cognitive effort in the decision making process (Simon and Newell 1972) and it was argued that ‘logical and economic’ decisions were never reached by humans due to emotions and judgement controlling the decision making process and causing a range of biases and errors (Tversky and Kahneman 1986). The theory identified that humans would use these heuristics, such as rule of thumb or an estimation, to find something that is satisfactory to their needs rather than making the ideal economic decision. I agree with the notion that the world is ‘too complex for people to solve problems by employing strict logical rules and comprehensive thought processes’ (Simon 1955) and am also of the belief that humans will rely on heuristics to make the cognitive process more straightforward. Rational Consumer Choice Rational consumer choice theory has been around for many years and stems from the ideal that consumers act in a ‘rational’ fashion when making economic decisions. Not......

Words: 2256 - Pages: 10

#### Consumer

...Theory This chapter presents the theories behind consumer behaviour. It will also discuss online consumer behaviour in order to continue with the identification of the influencing factors. The theories of consumer behaviour will be used in order to be able to find consumer segments that will show whom the identified factors affect. 3.1 Introduction This dissertation aims at finding factors that affect the online consumer’s buying behaviour. By reading literature concerning consumer characteristics and online consumer characteristics we believe to find implications for certain factors that are of importance for the online consumer. The Internet is a worldwide accessible series of computer networks that transmit data by packet switching using the standard Internet Protocol. It is a "network of networks" that consists of millions of smaller domestic, academic, business, and government networks, which together carry various information and services, such as electronic mail, file transfer, the interlinked Web pages and other documents of the World Wide Web. Originally the Internet was mainly used by academics, research scientists and students; however that scenario has changed as commercial organizations have moved to incorporate the World Wide Web into their promotional campaigns, and by offering the facility of online purchasing (Jobber & Fahy, 2003). The Internet has evolved into a worldwide accessible marketplace for information exchange and e-commerce. The......

Words: 1256 - Pages: 6

Free Essay

#### Consumer

Words: 729 - Pages: 3

Free Essay

#### Consumer

...SUGENTHEERAN KOMANNAYAR (28380) GAYTHRI KUPUSAMY (26347) SELF PERCEPTION THEORY Self-perception theory is an account of attitude change developed by psychologist Daryl Bem. It asserts that people develop their attitudes by observing their behaviour and concluding what attitudes must have caused them. The theory is counterintuitive in nature, as the conventional wisdom is that attitudes come prior to behaviours. Furthermore, the theory suggests that a person induces attitudes without accessing internal cognition and mood states. The person reasons their own obvious behaviours rationally in the same way they attempt to explain others’ behaviours. The self perception theories is categories into three parts which is, Foot-In-The-Door technique There is both foot-in-the-door phenomenon and foot-in-the-door technique. As you can guess, the technique is used to get the phenomenon. The phenomenon is the tendency for people to comply with some large request after first agreeing to a small request. As you can then imagine, the technique is used to get compliance from others (to get them to behave in a way you want) in which a small request is made first in order to get compliance for a larger request. For example, someone might want you to give to give 5 hours of your time a week for the three months as a volunteer to a charity (a big request). But to get you to agree to this big request, they first ask you to volunteer for 1 hour one time and one time only. After......

Words: 1685 - Pages: 7

#### Consumer Culture Theory, Consumer Agency and the Importance of Brands

...Consumer Culture Theory, Consumer Agency and the Importance of Brands Summary of the Importance and Relevance of Topic Consumer Culture Theory (CCT) refers to the classification of a certain approach to studying consumers and the way that they consume. It was first coined in 2005 by Arnould and Thompson, and it specifically addresses the sociocultural, symbolic, experiential and ideological facets of consumption. Their work is the culmination of over a quarter century of research that treats consumer behaviour as a phenomenon worth studying. As we have come to develop the field of CCT, so too are we developing our understanding of the consumer, and the broader economy. The work of Arnould and Thompson has provided students of consumer behaviour with the necessary environment to debate, innovate and advance the field of study.1 CCT is important within the scope of consumer behaviour because it places a focus on meaning and identity creation; it delves deeper in the mentality that surrounds consumers in the marketplace, and an understanding of this mentality is useful to all that engage the market (buyers, sellers, producers, etc...). “CCT explores how consumers actively rework and transform symbolic meanings encodes in ads, brands, retail settings, or material goods to manifest their particular personal and social circumstances and lifestyle goals.”2 In understanding CCT, we understand the market in a broad sense, for example, acknowledging that marketing symbols are......

Words: 3745 - Pages: 15

Free Essay

#### Consumer

...modern trade formats and an evolving consumer has also ensured that even emerging categories like body washes and hair conditioners get more buyers. Dove has capitalised on this trend. Apart from distribution in modern format stores, where Dove claims to be one of the leading brands with 11.54% share, the brand has also entered adjacent categories. In body washes, Dove claims to be nearly 19% of the market, while hair conditioners gets the brand sales of around Rs 40 crore. Segmentation Dove is the largest premium brand in the Hindustan Unilever portfolio," says Rajaram Narayanan, vice president, hair care and Lakme, HUL. Now the Dove portfolio delivers Rs 400 crore in sales. Dove has segmented and targeted the market towards urban areas as it is being positioned and repositioned as the premium brand like, mildest soap, trail for result. Globally it is not soap but a cream bar Continuously evolving the campaign Strong emotional touch Continuous innovation It tries to change the psychology of an average looking women that she can look equally beautiful. Targets girls and women of all ages, shapes and sizes. Especially targets the working women as they have busy schedules and cannot take out time for themselves so by using one soap they can get the benefits of soap as well as a moisturizer Maximum moisturizing content. As the add campaign of dove says that use it on half of your face and see the difference. -Consumers perceive high prices as an......

Words: 792 - Pages: 4

#### Consumer Behaviour Theory

...Jeff Bray Consumer Behaviour Theory: Approaches and Models Consumer Behaviour Theory: Approaches and Models...............................................2  1.1 Consumer behaviour & consumer decision making ............................................2  1.2 Theoretical approaches to the study of consumer behaviour..............................3  1.3 Economic Man .....................................................................................................4  1.4 Psychodynamic Approach ...................................................................................4  1.5 Behaviourist Approach ........................................................................................5  1.6 Cognitive Approach .............................................................................................6  1.6.1 Cognitive Models of Consumer Behaviour ..................................................9  1.6.1.1 Analytic Cognitive Models ..................................................................10  1.6.1.2. Prescriptive Cognitive Models............................................................20  1.7 Humanistic Approach ........................................................................................25  1.7.1 Humanistic Models of Consumer Behaviour..............................................25  1.9 Summary ............................................................................................................28  References.................

Words: 10006 - Pages: 41

#### Price Theory Assignment 1 – Consumer Theory

...Price Theory Assignment 1 – Consumer Theory Click Link Below To Buy: http://hwaid.com/shop/price-theory-assignment-1-consumer-theory/ Answers are in Image Format Suppose that Sally’s preferences over baskets containing petrol (good x), and food (good y), are described by the utility function U (x, y) = xy + 100y. The marginal utilities for this function are, MUx = y and MUy = x + 100. Use Px to represent the price of petrol, Py to represent the price of food, and I to represent Sally’s income. Question 1: Find Sally’s petrol demand function, and Sally’s food demand function. (8 Marks) Question 2: From Sally’s perspective, is food a normal good, an inferior good, or neither normal nor inferior? Brieﬂy explain with reference to your answer to question 1. (2 Marks) Question 3: Suppose that the price of petrol is \$2 per litre, the price of food is \$5 per kilogram, and Sally’s income is \$400. What quantities of food and petrol does Sally consume? What level of utility does Sally receive from this consumption basket? (3 Marks) Question 4: Suppose that, as in question 3, the price of petrol is \$2 per litre, the price of food is \$5 per kilogram, and Sally’s income is \$400. Now suppose that the government is considering two alternative policies to improve Sally’s welfare. Policy 1: Place a \$0.4 per litre subsidy on petrol, reducing the price of petrol to \$1.6 per litre. Policy 2: Give Sally a voucher that can be used to purchase food (but not......

Words: 320 - Pages: 2

#### Theory of Consumer Choice

...Student’s Name: Course Name: Instructor’s Name: Institution: Date: Consumer choice theory is a microeconomics branch that tries to relate preferences to both consumer demand curves and consumer expenditures. The theory analyses the way consumers maximize their need to consume which is measured by their preferences against the limited ways on their expenditure. Consumers do this by utility maximization subject to a constraint on their budget. Other times it gets referred to as the theory of consumer behavior. Through the study of this theory, researchers can explain why the consumers would buy more of the product when its price is less as compared to when its price is high. Another elaboration of the theory is that it shows the reason why the households spend their income as they always do (Haugtvedt, Herr, & Kardes, 2008). The greater assumption is that every consumer is rational and aims at maximizing their satisfaction. Some major theories explain the consumer behavior. First is the Cardinalist approach or the marginal utility theory and the second is the ordinalist approach or the analysis of the indifference curves. The former describes extra satisfaction a consumer derives after consuming an extra unit of a commodity while consumption of all other products remains unchanged. The law of diminishing marginal utility gives a thorough elaboration on why the demand curves always have a downward sloping nature. The latter shows the line of combinations (indifference......

Words: 1179 - Pages: 5

#### Consumer

...Consumer Behavior Models in Tourism Analysis Study Muhannad M.A Abdallat, Ph.D. Assistant Professor Hesham El –Sayed El - Emam, Ph.D. Assistant Professor Department of Tourism and Hospitality, Faculty of Tourism and Archeology King Saud University ABSTRACT The theories of consumer decision-making process assume that the consumer’s purchase decision process consists of steps through which the buyer passes in purchasing a product or service. However, this might not be the case. Not every consumer passed through all these stages when making a decision to purchase and in fact, some of the stages can be skipped depending on the type of purchases. The reasons for the study of consumer’s helps firms and organizations improve their marketing strategies by understanding issues such as: • The psychology of how consumers think, feel, reason, and select between different alternatives (e.g., brands, products); • The psychology of how the consumer is influenced by his or her environment (e.g., culture, family, signs, media); • The behavior of consumers while shopping or making other marketing decisions; • Limitations in consumer knowledge or information processing abilities influence decisions and marketing outcome; • How consumers’ motivation and decision strategies differ between products, that differ in their level of importance or interest that they entail for the consumer; and • How marketers can adapt and improve their marketing campaigns and marketing......

Words: 8106 - Pages: 33