ECO 132 Lecture Notes - Lecture 5: Pareto Efficiency, Competitive Equilibrium, Diminishing Returns

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ivoryhornet946

31 Oct 2016

School

Hofstra University

Department

Economics (ECO)

Course

ECO 132

Professor

Constantine Alexandrakis

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Document Summary

There are three exogenous variables: g, k, z: notation stands for: government spending, quantity of capital, total factor productivity, these variables are taken as given. There are 7 equations, so the model can be solved: (1) (2) (3) (4) (5) (6) Consumer resource constraint resource constraint, which states that the quantity of goods and services bought (spending) must equal. Note: we are missing the national income identity: . This identity is an aggregate trade (nx=0), so the identity should be: . However, notice that we can get this identity from the quantity of goods and services produced (income/real gdp). Here, there is no investment (i=0) or the fact that profit is the difference between revenue and total cost: By using equation dnwy (4) we get that. Gcygyc snwy and by plugging this and equation (3) into (2) we get that.

Related Questions

Country A is located on a small island that is isolated from the outside world. The country
has one representative consumer, whose preference is represented by:
U(c, l) = ln(c) + ln(l)
There is one representative fi rm in the economy which is owned by the consumer, it produces
one type of good that can be used for consumption or government expenditure using capital
and labour as inputs. The fi rm owns the capital it uses and it's production technology is
represented by
F(K;N) = zK^aN^1-a
where z is the total factor productivity, and a is the capital share of income. The fi rm pays
all of its profit back to consumer as dividend.
The government of country A spend a predetermined G amount of goods to provide public
services, and it taxes consumer through a lump-sum tax t to finance the expenditure. the
government's budget is balanced:
G = t
Now, suppose that the firm cannot change its capital stock, or improve its production technology in the short period, such that z and K are given.
(a) When describing this economy as an macroeconomic model, what is the set of exogenous
variables? What is the set of endogenous variables that can be determined given the set
of exogenous variables using the concept of Competitive Equilibrium?
(b) Defi ne the competitive equilibrium for this economy, be specific about what it is, what
conditions have to be satisfied who solves what problem and etc.
(c) List the set of equations that will be used to determine all of the endogenous variables.
Which four of these endogenous variables are essentials, such that once you know these
four, all other endogenous variables can be obtained easily?
(d) Write down the four equations that can be used to solve for these four essential endogenous variables, and describe where do they come from. Describe in details the steps of
how would you solve for the competitive equilibrium (without actually solving for it ).
(e) Setup the Social planner's problem for this economy. What is the marginal condition
that pins down the planner's choices.
(f) Now, describe what would happen to c, l, and w if the firm had more capital, such
that Knew > Kold.

Let us have an economy that lives only for 2 periods. The representative household has a utility function that values consumption goods for any period as follows

u(c) = ln(c).

The valuation throughout both periods can be represented as a total utility function that discounts future utility with a Î² discount parameter as follows,

U(c1, c2) = u(c1) + Î²u(c2) = ln(c1) + Î² ln(c2),

where ct represent consumption good in period t for every period t = 1, 2. The budget constraint for this person in every period is expressed as

(1+Ïtc)ct + xt =(1âÏtI)(wtnt +rtkt), t=1,2.

where xt represent investment in period t, wt the wages earned by hours worked, rt the return of capital in period t, nt the hours worked supplied by the household in every period t, kt the stock of capital that the household has in period t, Ïtc the tax rate imposed by the government in consumption goods in every period t, and ÏtI the tax rate imposed by the government to total household income in every period t. In every period, the total amount of hours that the representative household is of H Ì = 1. Investment in every period can be defined by the following law of motion of capital

kt+1 = xt +(1âÎ´)kt, t=1,2.

Acknowledge that k3 = 0 because there is no period 3 in this economy. The household starts with a given amount of capital k Ì1 > 0. The representative firm produces good by the following production function in every period t,

Y_t =z_tK_tÎ±N_t1âÎ±, t=1,2.

There is a government that covers government expenditures in period 1 and period 2 by taxing capital rent and labor. Hence, their budget can be expressed as

Ïtcct +ÏtI(wtnt +rtkt)=gt, t=1,2.

a) Before writing any competitive equilibrium definition or the Social Planner Problem, can we modify the budget constraint in â¨order to get rid a variable in every period? Explain.

b) Define the Social Planner Problem.

c) Solve the Social Planner Problem. This is, find the Euler equation in terms of exogenous variables and the only endogenous variable k2.

d) Define the tax distorted competitive equilibrium of this economy.

e) Solve the representative household problem.

f) Solve the representative firm problem in period 1 and 2.

g) Find the optimal Euler equation in terms of exogenous variables and the only endogenous variable k2.

h) Imagine that the government can only implement income taxes. This is Ïtc = 0 for every period t = 1, 2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem?

i) Imagine that the government can only implement consumption taxes. This is ÏtI = 0 for every period t = 1,2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem? â¨

Match the definitions or complete the statements in the first part of the quiz with the appropriate terms found in the second part.

Definitions/Statements

1. _____ refers to marketersâ focus on a product rather than on the needs of the market.

2. _____ companies do not try to persuade consumers to buy what the firm has already produced, but rather to produce only products that they know they can sell, thereby satisfying consumersâ needs and turning them into loyal customers.

3. The impact of technology on buyer behavior relates to factors such as ____; the use of technology to engage customers and build relationships; customization of products and promotional messages; and better prices and distribution.

4. In the case of situational influences, this relates to the situation in which or the occasion on which the product will be used, e.g., special occasion or everyday use.

5. In the case of situational influences, this relates to the fact if we are in a store, point-of-purchase displays could influence us to buy something. We could also make unplanned purchases because we remembered something from seeing the brand while we are in the store.

6. This discipline on which consumer researchers draw focuses on society and large groups in society such as family and social class.

7. This discipline on which consumer researchers draw focuses on cultures and differences among cultures.

8. These are temporary circumstances that affect consumer purchase decisions.

9. In the case of situational influences, this refers to the fact that the person and the occasion for which we are buying something influence our purchase decisions.

10. According to the simple model of consumer decision making, reference groups, family, social class, culture, and subculture are among the _____ on buyer behavior.

11. According to the simple model of consumer decision making, motivation, personality trait, perception, and attitudes are among the _____ on buyer behavior.

12. According to the simple model of consumer decision making, advertising, buzz agents, customized messages, social media, and word-of-mouth are examples of ____.

13. This discipline on which consumer researchers draw focuses on behavior in small groups and helps consumer researchers to understand issues such as opinion leadership, diffusion of innovations, and communication.

14. In the case of situational influences, ______ are consumer mood states or physiological state (for example, hunger, thirst) that influence consumer decision-making.

15. The selection of one or more segments by a marketer to serve.

16. Developing a distinct image for a brand in the mind of consumers.

17. This is an effort by a marketer to change the existing perception that consumers have of a brand.

19. ___ segmentation involves segmenting based on variables such as urban, rural, suburb, state, cities, counties, and regions.

20. ____ segmentation is based on variables such as consumersâ lifestyles as indicated by their activities, interests, and opinions.

21. This criterion for effective targeting says that marketers should have some way of deciding which consumers fall into which segments.

22. This criterion for effective targeting says that marketers should be able to reach segments with appropriate media and distribution channels.

23. This is the most popular segmentation system combining lifestyles and values of consumers.

24. This household segmentation model is based on a combination of geographic and demographic information and the principle that âBirds of a feather flock together.â

25. ______ is defined as âsending consumers personalized and prompt offers and promotional messages designed to reach the right consumers and deliver to them highly relevant messages at the right time and more accurately than when using conventional segmentation techniques.â

Terms

A. Positioning

B. Accessibility

C. Anthropology

D. Situational influences

E. Consumption situation

F. Task definition

G. Identification

H. Marketing-oriented

I. Targeting

J. Psychographic

K. Marketing myopia

L. PRIZM

M. Interactive and novel communication channels

N. Sociology

O. Demographic

P. Purchase situation

Q. Behavioral targeting

R. Antecedent states

S. Communication sources

T. Geographic

U. Sociocultural influences

V. VALS

W. Psychological influences

X. Social psychology

Y. Repositioning

ECO 132 Lecture Notes - Lecture 5: Pareto Efficiency, Competitive Equilibrium, Diminishing Returns

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