31.

32.

33.

34.

35.

36.

4 D 40200

Explain the importance of mathematical representation of economic models.

The lond run cost function of a firm is C = q° — 8q? + 20g. Prove that MC = AC at the minimum
point of AC.
(6 x 5 = 30 marks)
Part D (Essay Questions)

Answer any two questions.
Each question carries 12 marks.

Given the demand function Qd = 100 — 3P and the supply is Qs = 200 — 87.
(i) Find the equilibrium price and quantity.
(ii) Find the price and quantity sold if a tax of 2.5 Rs per unit is imposed. ۱
(iii) Ifa specific subsidy of Rs 2.5 per unit is given, calculate new equilibrium values.
(iv) What will be the total revenue of the government ?

The utility function of the consumer is given by u = X, x2 —10X, where X, and X, are the quantities
of two commodities consumed. Find the optimal utility value if his income is 116 and product prices
are 2 and 8 respectively.

Solve the following LPP graphically.

Maximize Z = 3x, + 4x

subejct to the costraints

41 + 2x9 <80

2] + 5.2 < 180

ॐ], 2 > 0.

Given the demand curve of the monopolist P = 100 — 4q. His cost function is TC = 50+ 20 q. Find
the profit of the firm at this level of output.

(2 x 12 = 24 marks)