## Indian Economic Services : Revealed Preference Theory, Elasticity of Demand, Simple Games of Complete Information and Concept of Nash Equilbrium, Choice Under Risk and Uncertainty, Labour Leisure Choice and Backward Bending Supply Curve of Labour and Overtime Wages

Revealed Preference Theory (IES 2019)

Topic Discussed

• Revealed Preference Theory
• Assumption
• The principle of Revealed Preference
• Weak Axiom of Revealed Preference

Past Year Questions Discussed

Q 2 (c) IES 2019

An individual buys two goods X and Y at prices Px and Py. Check whether her behavior satisfies the Weak Axiom of Revealed Preference, given the following information:

When (Px , Py) = (1, 2), (X, Y) = (1, 2)

When (Px, Py) = (2, 1), (X, Y) = (2, 1)

Elasticity of Demand and its relation with the Slope of Demand Curve (IES 2011, 2015, 2017, 2019)

Topic Discussed

• Elasticity of Demand and Supply
• Price Elasticity of Demand
• Arc Elasticity
• Problems in using Arc Elasticity
• Point Elasticity of Linear Demand Curve
• Constant Elasticity Demand Curves
• Elasticity of Demand Curves Parallel to each other
• Elasticity of two intersecting Demand Curves
• Elasticity with Different Slopes of Demand Curves

Past Year Questions Discussed

Q 2(a) IES 2017

How can you measure the price elasticity of demand at any point on a straight line demand curve?

Q 2(b) IES 2017

Compare between price elasticity at a given price and also at a given quantity for a set of parallel demand functions.

Q 3 IES 2011/ 1(b) 2015/ 2019

The demand function Q1 = 50- P1 intersects another linear demand function Q2 at P = 10. The elasticity of demand for Q2 is six times larger than that of Q1 at that point. Find the demand function for Q2.

Cross Price Elasticity of Demand, Income Elasticity of Demand, Total Expenditure Method (IES 2011, 2013, 2014, 2016)

Topics Discussed

• Cross Elasticity of Demand
• Substitute Goods
• Complementary Goods
• Income Elasticity of Demand
• Share of Weighted Income Elasticities = 1
• Homogeneous Function
• Euler’s Theorem
• Sum of Own-Price Elasticity, Cross Price Elasticity and Income Elasticity for Marshallian Demand Function = 0
• Elasticity and Revenue
• Elasticity and Marginal Revenue
• Marginal Revenue Curves

Past Year Ques Discussed

Q 1(e) IES 2011

Define cross elasticity of demand. Based on such definition, how can you distinguish between the

substitute goods and the complementary goods?

Q 2 IES 2016

Derive the demand functions from the utility function U = f (q1, q2, ..qn) subject to budget constraint y = p1q1 + p2q2 + …+ pnqn and if the demand function for a commodity i (i = 1, 2, ..n) is homogeneous of degree zero in prices and income, then show that the sum of own and cross price elasticities of demand for the commodity equals its income elasticity of demand with negative sign.

Q 1 (h) IES 2011

Consider a linear demand function q = a – bp, where q = quantity demanded, p = price per unit

and a, b > 0, Find out the average and the marginal revenue and draw the diagram.

Q 1 (a) IES 2013

If the law of demand is x =a e-bP, where p is price and x is quantity demanded. Express price elasticity

of demand, total revenue and marginal revenue as functions of x.

Q11 IES 2013

For statistically estimated demand function for the commodity X,

DX = 1547 Px 0.2 Py 0.3 A 0.4 / Pz 0.5 B 0.3

(where x, y, z are goods, A stands for advertisement outlay, B for budget of the consumer and Px , Py , Pz are prices of goods x, y, z respectively).

(a) How are x, y and z related?

(b) Whether x is an inferior, normal or Giffen type good?

(c) What would be the percentage change in demand for x (i.e. Dx) and in which direction if advertisement outlay increases by 50 percent?

Simple Games of Complete Information and Concept of Nash Equilbrium (IES 2012, 2014, 2016, 2018)

Topic Discussed

• Dominant Strategy Equilibrium
• Nash Equilibrium
• Mixed Strategy Nash Equilibrium
• Problem with Nash Equilibrium
• Sequential Game
• Mixed Strategy and Nash Equilibrium

Past Year Ques Discussed

IES, Q 1 (f) 2014

What is Nash Equilibrium? Do all games have Nash Equilibrium? Can a game have more than one equilibrium?

Q 12, IES , 2012

What is ‘Prisoner’s Dilemma’? Discuss its importance and implications in Game theory.

Q 9 (b) IES, 2016

In a non- cooperative game, find

• Saddle point in a pure strategy game
• Maximum expected pay-off in a mixed strategy game
• Solution of a sequential game in an ‘extensive form’

Q 3,IES 2018

Consider a one shot simultaneous move game with two players, Player 1 and Player 2. Let si, i = 1, 2 designate a pure strategy of player i. Let si ≠ 0 be the pure strategy set of player i, and πi (s1 , s2 ) be the pay-off function for player i, i = 1, 2.

(a) Define a Nash equilibrium in pure strategies for this game. 3

(b) Consider the following game:

Player 2

.

Player 1

Show that the unique pure strategy Nash equilibrium is not Pareto optimal.

Choice Under Risk and Uncertainty (Part 1) : Simple, Compound and Reduced form Lotteries ; Preferences over Risk (Independence Axiom and Continuity Axiom); Expected Utility Function (VNM Expected Utility Function)

Topics Discussed

• Choice under risk and Uncertainty
• Lotteries
• Simple Lottery
• Compound Lottery
• Reduced Lottery
• Preferences over Lotteries
• Expected Utility Theory

Choice Under Risk and Uncertainty (Part 2) : Expected Utility function Unique (IES 2013); Risk Averse, Risk Loving, Risk Neutral; Arrow Pratt Measure of Risk Aversion; Demand for Insurance

Topics Discussed

• Expected Utility Theory and Risk Aversion
• Certainty Equivalent and Risk Premium
• Arrow Pratt Measure of Risk Aversion
• Relative Risk Aversion
• How Absolute Risk Aversion Changes with Wealth
• How Relative Risk Aversion Changes with Wealth
• Risk Aversion and Insurance

Past Year Question Discussed

Q3, IES, 2013

Describe Von Neuman and Morgenstern utility index. Is this index unique? Explain.

Labour Leisure Choice and Backward Bending Supply Curve of Labour and Overtime Wages (IES 2018)

Topic Discussed

• Backward Bending Labour Supply Curve
• Overtime and the Supply of Labour

Question Discussed

Q 5 (b), IES, 2018

How can you get the wage offer curve and the supply curve of labour? In a flourishing economy there is every possibility that the labour supply curve will be backward bending. Do you agree? Justify your answer.