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IGNOU MEC 001 Solved Assignment 2022-23
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Important Note – IGNOU MEC 001 Solved Assignment 2022-23 You may be aware that you need to submit your assignments before you can appear for the Term End Exams. Please remember to keep a copy of your completed assignment, just in case the one you submitted is lost in transit.
Submission Date :
- 31st March 2033 (if enrolled in the July 2033 Session)
- 30th Sept, 2033 (if enrolled in the January 2033 session).
SECTION – A
1. a) Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y) Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y respectively. Assuming utility functions of individuals A and B to be UA=XA YA 2 and UB=XB 2 YB where Xi and Yi for i= {A, B} represent individual i’s consumption of good X and Y respectively, what will be the set of Pareto optimal allocation in this economy?
b) Determine the conditions that need to be fulfilled by an allocation to be termed as Pareto efficient allocation.
2. Consider a Cobb-Douglas utility function
U (X, Y) = Xα Y (1- α)
,
Where X and y are the two goods that a consumer consumes at per unit prices of Px and
Py respectively. Assuming the income of the consumer to be ₹M, determine:
a. Marshallian demand function for goods X and Y.
b. Indirect utility function for such a consumer.
c. The maximum utility attained by the consumer where α =1/2, Px =₹ 2, Py = ₹ 8 and M= ₹ 4000.
d. Derive Roy’s identity.
SECTION – B
3. a.) What is excess capacity and how is it related to the model of monopolistic competition?
b) Demand function and supply function are given as P=25-X2 and P=2X+1 respectively, find out producer surplus and consumer surplus.
4. a.) Define games of complete and incomplete information
b.) From the following pay-off matrix, where the payoffs (the negative values) are the
years of possible imprisonment for individuals A and B, determine:
(i) The optimal strategy for each individual.
(ii) Do individuals A and B face a prisoner’s dilemma?
5. a.) Differentiate between the Cournot and the Bertrand model of Oligopoly.
b.) Consider an industry with two firms 1 and 2, each producing output Q1 and Q2 respectively and facing the industry demand given by P=140-Q, where P is the market price and Q represents the total industry output, that is Q= Q1 + Q2. Assume that each faces a marginal cost of ₹ 20 per unit with no fixed costs. Solve for the Cournot equilibrium in such an industry.
6. a.) Given the Von Neumann-Morgenstern utility function of an individual, U (W) =W ½
, where W stands for amount of money. Comment upon attitude towards risk of such an individual with the help of a diagram.
b) Now suppose this individual possesses a building worth ₹1600. If the building catches fire, its value falls to ₹ 400. Let the probability of building catching fire be ¼. On the basis of the given information, find out whether the individual would be willing to pay a risk premium of ₹ 76 to the insurance company in order to eliminate the risk associated with the factory building.
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IGNOU MEC 001 Solved Assignment 2022-23
7. Write short notes on following:
a) Moral Hazard
Ans. In economics, a moral hazard is a situation where an economic actor has an incentive to increase its exposure to risk because it does not bear the full costs of that risk. For example, when a corporation is insured, it may take on higher risk knowing that its insurance will pay the associated costs. A moral hazard may occur where the actions of the risk-taking party change to the detriment of the cost-bearing party after a financial transaction has taken place.
Moral hazard can occur under a type of information asymmetry where the risk-taking party to a transaction knows more about its intentions than the party paying the consequences of the risk and has a tendency or incentive to take on too much risk from the perspective of the party with less information. One example is a principal–agent problem, where one party, called an agent, acts on behalf of another party, called the principal. If the agent has more information about his or her actions or intentions than the principal then the agent may have an incentive to act too riskily (from the viewpoint of the principal) if the interests of the agent and the principal are not aligned.
According to research by Dembe and Boden, the term dates back to the 17th century and was widely used by English insurance companies by the late 19th century. Early usage of the term carried negative connotations, implying fraud or immoral behavior (usually on the part of an insured party). Dembe and Boden point out, however, that prominent mathematicians who studied decision-making in the 18th century used “moral” to mean “subjective”, which may cloud the true ethical significance in the term. The concept of moral hazard was the subject of renewed study by economists in the 1960s, beginning with economist Ken Arrow, and did not imply immoral behavior or fraud. Economists use this term to describe inefficiencies that can occur when risks are displaced or cannot be fully evaluated, rather than a description of the ethics or morals of the involved parties.
b) Homogeneous and Homothetic production functions
Ans. If the production function is homogeneous (of any degree), the firm’s isoclines including long-run expansion path would be straight lines from the origin. The homothetic production function has the same isoquants as those of its underlying homogeneous function, although, generally, with different quantity indexes.
That is why the firm’s expansion path and its isoclines would be straight lines from the origin also for a homothetic production function, and along any such straight line with a fixed ratio of the inputs, the firm’s MRTS of L for K or the ratio of MPL to MPK would be constant.
This is because for the underlying homogeneous function as also for the monotonic transformations of that function, the MRTS is a function of the ratio of the input quantities. In other words, the ratio of MPL to MPK would depend not upon absolute, but upon relative, input quantities.
Therefore, in Fig. 8.26, the homothetic production function would give us
Slope of IQ1 at A1 = Slope of IQ2 at A2 and
Slope of IQ1 at B1 = Slope of IQ2 at B2.
c) Arrow prat measure of risk averseness
Ans. The Arrow-Pratt measure of risk-aversion is therefore = -u”(x)/u'(x). Risk-aversion measure of what? Arrow and Pratt’s original measure used wealth as the argument in the Bernoulli function, so for wealth w, the Arrow-Pratt measure of risk-aversion is -u”(w)/u'(w).
This has, in fact, become the traditional way in which the measure is used. However, it is not the only way, and the expected utility axioms do not specify whether the argument of the utility function should be wealth (a stock) or income (a flow). William Vickrey (1945) used income as the argument of the utility function, so for income y, the Arrow-Pratt measure of risk-aversion is -u”(y)/u'(y).
In fact, the Arrow-Pratt measure of risk-aversion can be even more flexible than that, due to the nature of the VNM utility function. James Cox and Vjollca Sadiraj (2004, working paper) use both income and wealth as arguments for the VNM utility function. In this case, wealth represents the fixed portion of an individuals assets, while income is the portion which is subject to change. An individual’s Arrow-Pratt measure of risk-aversion is then -uyy(w,y)/uy(w,y). Here, uyy(w,y) refers to the second-order partial derivative of the Bernoulli utility function with respect to income, and uy(w,y) refers to the first-order partial derivative with respect to income.
d) Bergson-Samuelson Social welfare function
Ans. A Bergson–Samuelson social welfare function considers welfare for a given set of individual preferences or welfare rankings. An Arrow social welfare function considers welfare across different possible sets of individual preferences or welfare rankings and seemingly reasonable axioms that constrain the function.
In welfare economics, a social welfare function is a function that ranks social states (alternative complete descriptions of the society) as less desirable, more desirable, or indifferent for every possible pair of social states. Inputs of the function include any variables considered to affect the economic welfare of a society. In using welfare measures of persons in the society as inputs, the social welfare function is individualistic in form. One use of a social welfare function is to represent prospective patterns of collective choice as to alternative social states. The social welfare function provides the government with a simple guideline for achieving the optimal distribution of income.
The social welfare function is analogous to the consumer theory of indifference-curve–budget constraint tangency for an individual, except that the social welfare function is a mapping of individual preferences or judgments of everyone in the society as to collective choices, which apply to all, whatever individual preferences are for (variable) constraints on factors of production. One point of a social welfare function is to determine how close the analogy is to an ordinal utility function for an individual with at least minimal restrictions suggested by welfare economics, including constraints on the number of factors of production.
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