(a) What is indirect utility? Point out a difference between direct and indirect utility.
Indirect utility function represents the maximum utility a consumer can attain given a specific level of income and prices of goods.
Difference: Direct utility is a function of the quantities of goods consumed, whereas indirect utility is a function of prices and income
.(b) State two axioms of the revealed preference theory.
(c) What is substitution effect?
The substitution effect is the change in the consumption of a good resulting from a change in its relative price, holding the consumer's utility (or purchasing power) constant
.Allocation of Time: An individual maximizes utility based on leisure and income (consumption). The budget constraint is determined by the wage rate. The equilibrium occurs where the indifference curve between leisure and income is tangent to the wage line.
Effect of Wage Fall: Not necessarily. A fall in wage has two effects:
Labor Supply Curve: The curve can be backward-bending. Initially, as wages rise, work increases (Substitution effect > Income effect). At very high wages, the individual may value leisure more, and labor supply decreases as wages rise further.
| Feature | Ordinary (Marshallian) Demand | Compensated (Hicksian) Demand |
|---|---|---|
| Held Constant | Nominal Income | Utility (Real Income) |
| Effects Included | Income and Substitution effects | Substitution effect only |
Derivation (Hicksian Method): For a normal good, as the price falls, the Marshallian demand curve shows a larger increase in quantity than the Hicksian curve because the Marshallian curve includes the positive income effect, whereas the Hicksian curve reflects only the substitution effect
.(a) What is meant by expansion path?
The expansion path is the locus of points of tangency between the isoquants and the isocost lines as the scale of production increases, given constant factor prices
.(b) Define homogeneous production function and express it in general functional form.
A production function is homogeneous if, when all inputs are multiplied by a constant factor 'k', the output changes by a factor of 'k' raised to the power 'n'
.Q = f(kL, kK) = k^n f(L, K)
(c) Write two properties of homogenous production function.
Distinction: All homogeneous functions are homothetic, but not all homothetic functions are homogeneous. A function is homothetic if it is a monotonic transformation of a homogeneous function. In a homothetic function, the slopes of isoquants (MRTS) are constant along any ray from the origin.
Returns to Scale: In a homogeneous function of degree 'n':
The Cobb-Douglas production function is a specific functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs (particularly physical capital and labor) and the amount of output
.Q = A * L^a * K^b
Properties:
(a) What do you mean by kinked demand curve?
Used in oligopoly (Sweezy model), it describes a situation where a firm believes rivals will match price decreases but not price increases, leading to a "kink" at the prevailing price and a vertical gap in the Marginal Revenue curve
.(b) Write two distinctions between collusive oligopoly and non-collusive oligopoly.
(c) What are the assumptions of Cournot model of oligopoly?
Monopolistic competition is a market structure characterized by many firms selling differentiated products with free entry and exit in the long run
.Long-Run Equilibrium: In the long run, entry of new firms shifts the demand curve (AR) for existing firms to the left until it is tangent to the Long-Run Average Cost (LAC) curve. At this point, firms earn only normal profits where P = LAC and MR = MC.
Given: AC = MC = 2. Demand: P = 14 - Q.
(i) Action-Reaction Functions:
Profit Firm 1 (π1) = (14 - Q1 - Q2)Q1 - 2Q1 = 12Q1 - Q1² - Q1Q2.
dπ1/dQ1 = 12 - 2Q1 - Q2 = 0 => Q1 = 6 - 0.5Q2.
By symmetry, Reaction Function for Firm 2: Q2 = 6 - 0.5Q1.
(ii) Equilibrium Level:
Substitute Q2 into Q1: Q1 = 6 - 0.5(6 - 0.5Q1) = 6 - 3 + 0.25Q1.
0.75Q1 = 3 => Q1 = 4, Q2 = 4.
Total Q = 8. Price P = 14 - 8 = 6.
(iii) Profits:
Profit = (P - AC) * Q = (6 - 2) * 4 = 16 per firm.
(a) Define marginal physical product and marginal revenue product.
(b) Briefly describe demand of a factor.
Factor demand is a derived demand, meaning it depends on the demand for the final product the factor helps produce. It is determined by the factor's productivity and the market price of the output.
(c) Find the value of the marginal product of labour (VMPL). Price = 10.
| Workers | Qty | MPP | VMPL (MPP * 10) |
|---|---|---|---|
| 1 | 20 | 20 | 200 |
| 2 | 28 | 8 | 80 |
| 3 | 34 | 6 | 60 |
Values of VMPL are 200, 80, and 60 respectively
.Theory: Under perfect competition, every factor is paid a price equal to the value of its marginal product (VMP). A firm hires factors up to the point where the cost of the additional factor unit (Wage/Rent) equals its MRP.
Drawbacks:
(a) What is meant by welfare economics?
Welfare economics is a branch of economics that uses microeconomic techniques to evaluate well-being at the aggregate level
.(b) Distinguish between positive economics and welfare economics.
Positive economics deals with "what is" (objective facts), while welfare economics deals with "what ought to be" (normative judgments/social desirability)
.(c) Pigovian conditions for maximization of welfare.
Pareto optimality is a state where no one can be made better off without making someone else worse off
.Conditions: