Finite and infinite sets
Finite Sets: A finite set is a collection of distinct elements that has a specific count or number of elements. In other words, a set is considered finite if you can count its elements one by one and eventually reach an end. For example, the set {1, 2, 3} is finite because it contains three elements. The cardinality (size) of a finite set is represented by a non-negative integer, and the empty set (a set with no elements) is also considered finite.
Infinite Sets: An infinite set is a set that has an uncountable number of elements. This means that no _______ _____ ________ _________ ________ ________ ______ __________ ___ ________ _____.
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Given a Cobb-Douglas utility function
Where X and y are the two goods that a consumer consumes at per unit prices of Px and
Pyrespectively. 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
From the following pay-off matrix, determine:
(i) The optimal strategy for each individual.
(ii) Value of the game.
| Player 1 | Player 2 | |||||
| Strategies | I | II | III | IV | V | |
| I | 9 | 3 | 1 | 8 | 0 | |
| II | 6 | 5 | 4 | 6 | 7 | |
| III | 2 | 4 | 3 | 3 | 8 | |
| IV | 5 | 6 | 2 | 2 | 1 | |
There are two firms 1 and 2 in an industry, each producing output Q1 and Q2 respectively and facing the industry demand given by P=50-2Q, where P is the market price and Q represents the total industry output, that is Q= Q1 + Q2. Assume that the cost function is C = 10 + 2q. Solve for the Cournot equilibrium in such an industry.
a. A monopolist uses one input X, which she purchases at the fixed price p=5 in order to
produce output q. Her demand and production functions are:
P=85-3q and q= 2x1/2 respectively.
Derive the equilibrium output and equilibrium profit.
b. “In real world, sometimes it is not possible to achieve optimum welfare.” Comment
and discuss the obstacles in attaining Pareto optimum.
Economies of Scale
Different types of price discrimination
Radha has assets worth 10,000 rupees and is facing a loss of 3,600 with a probability of 0.002. She is indifferent between paying G rupees for insurance protection and assuming the risk of loss personally. She values total assets of amount w≥0 according to the utility function u (w) = w1/2. Determine G.