QUESTION
ECON30600 Microeconomics III Semester 2
Assessed Coursework
READ THE FOLLOWING INSTRUCTIONS CAREFULLY:
Please answer all parts of the coursework question. There are 33 possible marks and each mark will contribute 1% to the overall semester mark (a 33% contribution in total). Your answers should be typed / word processed in an acceptable format (e.g. Arial or Times, size 12, at least 1.5 spaced, every page numbered). Diagrams may be produced by hand. There is no word limit, however conciseness is desirable.
This piece of coursework is an individual work. Communication or collaboration about this piece of work is not allowed. Do not share your work with others. Plagiarism is a serious academic offence. Be aware of the rules regarding this issue.
You should submit your coursework by the following date:
Wednesday 25th April 2012.
You will be emailed by Leonora Wells before this date with specific time and place instructions regarding submission.
Please put your full name and registration number as a header on each page.
PLEASE TURN OVER TO FIND THE COURSEWORK QUESTION.
ANSWER ALL PARTS.
Question: Answer all parts (a, b, c, d, e & f).
Consider the following insurance market. There are two states of the world, B and G, and two types of consumers, H and L, who have probabilities pH =0.5 and pL =0.25 (high and low risk) respectively of being in state B. They have common endowment e=(eG,eB) = (£900, £100). The individuals have expected utility preferences over state-contingent consumptions c=(cG,cB), with common utility function u(ci)=ln(ci), where i=B,G. Insurance firms are risk-neutral profit maximisers and offer contracts in exchange for the individuals’ endowments.
Suppose the market is competitive.
a) Outline the definition of a competitive equilibrium of this market and explain why every contract, offered by every firm, must earn zero profit in equilibrium. [7 marks]
b) Suppose the information concerning individuals’ types is symmetric, but void. It is commonly known, however, that the proportion of low risk consumers is 0.4. Derive the equilibrium set of contracts. [5 marks]
c) Find the equilibrium set of contracts when information is symmetric and perfect. [5 marks]
Now suppose that information is asymmetric; individuals know their own type but insurance firms cannot distinguish between types. (Note: there does exist an equilibrium set of contracts for this market. You may make use of this fact without proving it).
d) Explain why it must be that, if {cH,cL} is the equilibrium set of contracts, then
cH ≠ cL. [4 marks]
e) Explain and derive the equilibrium contract offered to high risk individuals. [3 marks]
f) Explain and derive the equilibrium contract offered to low risk individuals. [9 marks]
SOLUTION
Question (a) Competitive Equilibrium
Competitive equilibrium of market is a established concept of equilibrium (Callan, Thomas, 2007) of the economy, which is accurate and appropriate for commodity market analysis with lithe prices and several traders. It is also helping as the standard for the effectiveness in the study of the economy. This equilibrium relies basically on the expectation of an aggressive environment, wherein every single trader chooses regarding the quantity that is little enough in comparison with the trading of the total quantity. Here is the practical representation that why and how the company can earn profit in zero equilibrium.
This type of equilibrium is a segment of costs and an allotment that with the prices, several traders raise their goal function to the maximum, pending for the technical prospects and resource limitations schemes to the business into into the part of the planned allotment, and such that the money creates all net businesses companionable with one or the other by comparing average demand and supply of the commodity that are traded.
In the entry of new companies in the expositing market, if the profit goes positive, these firms will enter the industry, and if profits are negative, these companies prefer exiting the market. However, zero profit is the equilibrium state, wherein most of the new companies enter the market with an optimistic approach.
(b) Equilibrium = Ph x Pl / risk
This is the formula of equilibrium which is defined as a condition wherein all competing influences are offset, in a large variety of of context. In this formula, Ph and Pl are the probabilities, where Ph is probability of consumer type H and Pl is the probability of consumer type L. And the third part included in this is risk. Risk is included everywhere, where the assumptions come.
= 0.5 x 0.25/0.4
= 0.5 x 0.625
= 0.3125
This formula explains the basics of equilibrium. First of all, this can be explained with the help of the following diagram:
In this diagram, the point of intersection (in pink) is the point of equilibrium. The model, however referred to by Keynes, did not get its full expansion till the late 1950s and early 1960s. The outcome model is also called as the “neoclassical synthesis.” (Stein1982) Generally, the model expects that there are two relationships amid result and the cost level. Collective demand is basically related to the combined demand for goods and services of customers, companies and the government , however collective supply raises from the costing and the decision of production of the companies. The point of intersection of the two slopes ascertains the level of price and the result. Changes in either collective demand or collective supply can head to short-run changes in results and costs. It is expected that in the long-run, collective supply is vertical, and changes in collective demand only head to variations in prices. Sometimes, an extreme assumption is made that prices are solely inflexible in the short run, so that collective demand activities affect results wholly. Under this expectation, the components of collective demand should drives, and seek the short-run effects of several shocks to results.
(c) When the information regarding the equilibrium (Samuelson, 1947) set of the agreement is symmetric and perfect, then the equilibrium comes to be zero, which shows optimism in the market for the new companies. Under this division, the single period result is extended to a multi-period horizon. This segment is secondary and not important as one-period section. It is not compulsory to first compute the one-period mean-variance analysis to calculate multi-period analysis. One can directly switch to this segment. But, if the requirement is to extend the one-period mean-variance analysis result, both the sections are needed to be related. The point of intersection of the two slopes ascertains the level of price and the result. Changes in either collective demand or collective supply can head to short-run changes in results and costs. It is expected that in the long-run, collective supply is vertical, and changes in collective demand only head to variations in prices. Sometimes, an extreme assumption is made that prices are solely inflexible in the short run, so that collective demand activities affect results wholly. Under this expectation, the components of collective demand should drives, and seek the short-run effects of several shocks to results.
This theory provides a lot of option to investors and gives a better of understanding of risk and expected return, before he or she puts the money in the market. It is considered to be an alternative method to unite unrestricted mean with limited second market to find out the portfolios that are ideal in a sense of mean-variance for average and common conditions of the market. Therefore, this is approach mostly comes out as one of the sensible choices for policy portfolios of institutional investors of long-term.
(d). If C^H C^L is the equilibrium set of the agreement then it is clear that C^H is not equal to C^L. Macroeconomics comprise national, global and area-wise economy. Equilibrium is one of the most general field in economics. This set of equilibrium is the type of economics has indicated methods, including GDP, unemployment rates, and price indexes to get the knowledge about the functioning of the economy as an individual.
This is responsible for developing basics that explains the connection amongst measures like national income, output, unemployment, consumption, inflation, savings, international trade and finance. Therefore we can clearly say that when there is a set of equilibrium is symmetric and perfect, then the equilibrium appears to be not equal.
(e). This segment is secondary and not important as one-period section. It is not compulsory to first compute the one-period mean-variance analysis to calculate multi-period analysis. One can directly switch to this segment. But, if the requirement is to extend the one-period mean-variance analysis result, both the sections are needed to be related. The point of intersection of the two slopes ascertains the level of price and the result. Changes in either collective demand or collective supply can head to short-run changes in results and costs. It is expected that in the long-run, collective supply is vertical, and changes in collective demand only head to variations in prices. Sometimes, an extreme assumption is made that prices are solely inflexible in the short run, so that collective demand activities affect results wholly. Under this expectation, the components of collective demand should drives, and seek the short-run effects of several shocks to results.
It is considered to be an alternative method to unite unrestricted mean with limited second market to find out the portfolios that are ideal in a sense of mean-variance for average and common conditions of the market. Therefore, this is approach mostly comes out as one of the sensible choices for policy portfolios of institutional investors of long-term.
(f) This is responsible for developing models that elaborates the relationship amongst factors such national income, output, unemployment, consumption, inflation, savings, international trade and finance. Therefore we can clearly say that when there is a set of equilibrium is symmetric and perfect, then the equilibrium appears to be not equal.
This segment is secondary and not important as one-period section. It is not compulsory to first compute the one-period mean-variance analysis to calculate multi-period analysis. One can directly switch to this segment. But, if the requirement is to extend the one-period mean-variance analysis result, both the sections are needed to be related. This is the basic section of mean-variance analysis. In this segment, the standard mean-variance is developed for log returns for single period log. In this section, the result cannot be extended to a multi-period environment, even if it is required. To do this, one has to switch over to the next segments of mean-variance analysis. The point of intersection of the two slopes ascertains the level of price and the result. Changes in either collective demand or collective supply can head to short-run changes in results and costs. It is expected that in the long-run, collective supply is vertical, and changes in collective demand only head to variations in prices. Sometimes, an extreme assumption is made that prices are solely inflexible in the short run, so that collective demand activities affect results wholly. Under this expectation, the components of collective demand should drives, and seek the short-run effects of several shocks to results.
Equilibrium also includes Keynesian model. This is the standard model of the economy in the short-run. This model is still existed in the textbooks of undergraduate macroeconomics. This is the other name of Aggregate Demand/Aggregate Supply model. This type of equilibrium is a segment of costs and an allotment that with the prices, several traders raise their goal function to the maximum, pending for the technical prospects and resource limitations schemes to the business into into the part of the planned allotment, and such that the money creates all net businesses companionable with one or the other by comparing average demand and supply of the commodity that are traded.
In the entry of new companies in the expositing market, if the profit goes positive, these firms will enter the industry, and if profits are negative, these companies prefer exiting the market. However, zero profit is the equilibrium state, wherein most of the new companies enter the market with an optimistic approach.
This model was established by John Maynard Keynes and John Hicks in the years of 30s and 40s. The model, however referred to by Keynes, did not get its full expansion till the late 1950s and early 1960s. The outcome model is also called as the “neoclassical synthesis.” Generally, the model expects that there are two relationships amid result and the cost level. Collective demand is basically related to the combined demand for goods and services of customers, companies and the government , however collective supply raises from the costing and the decision of production of the companies.
This theory provides a lot of option to investors and gives a better of understanding of risk and expected return, before he or she puts the money in the market. It is considered to be an alternative method to unite unrestricted mean with limited second market to find out the portfolios that are ideal in a sense of mean-variance for average and common conditions of the market. Therefore, this is approach mostly comes out as one of the sensible choices for policy portfolios of institutional investors of long-term. An when it comes to risk, it is (Franklin, 2001) is the possible form of the pressure that comes in between, when an activity or action. It leads to the loss or an undesirable result for the company. There are many types of risk in the market now a day, such as economic risk, health risk, environment risk, financial risk, information risk, technology risk, information security risk, insurance risk, business risk, management risk societal risk, human risk, factor risk, and many more. These risks normally exist in the market with all the pressures, and the individuals have to face one or the other risk while either investing in the market, the purpose of this topic is to introduce the formal foundation of an understanding of risk. This understanding is conveyed by ‘models’ that are statements of ideas that experience has shown to be logical and useful. Amongst other attributes, these models enable us to define terms formally. These definitions may be different from the colloquial meaning of the terms. The ability to converse about risk using clearly defined terms is one mark of the person who is approaching the subject from a rigorous standpoint.
As mentioned in the introduction to the subject, everyone is to some degree a manager of risk and most of the terms we use have a meaning that is generally understood. By the end of this study, you should be able to distinguish yourself from others by the ability to think more clearly and meaningfully about risk, using these formal meanings. However, in the end you will still need to be able to convey this understanding to the non risk-literate person.
REFERENCES
Callan, S.J & J.M. Thomas, 2007, ‘Modelling the Market Process: A Review of the Basics’, Thompson Southwestern, Mason, OH, USA
Campbell, J.Y., Y.L. Chan, L.M. Viceira, 2003, “A multivariate model of strategic asset allocation”, Journal of Financial Economics
Samuelson, A. Paul, 1947, “Foundations of Economic Analysis”, Harvard University Press, ISBN 0-674-31301-1
Franklin, James 2001, “The Science of Conjecture: Evidence and Probability Before Pascal, Baltimore”, Johns Hopkins University Press, 274
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