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M.E.C – 003
QUANTITATIVE
METHODS FOR ECONOMIC ANALYSIS MEC 003 Solved Assignment 2022-23
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Assignment I
Answer the following
questions in about 700 words each.
1. The derivatives have wide application
in economics. Explain the following through derivatives:
(i) Average Revenue and Marginal Revenue
(ii) Average Cost and Marginal Cost
(iii) Elasticity of demand
(iv) Constant Elasticity Demand Curve
2. (i) If the second derivative is zero
at a point, the function may have a maximum, a minimum or a point of inflexion.
In the light of this statement, explain a maximum, a minimum and point of
inflexion.
(ii) Find the point of inflexion for the
following functions
(a) f(x) = 3x3 + 4
(b) f(x) = x3 + x2 + x + 1
Assignment - II
Answer the following
questions in about 400 words each.
3. Explain any two economic applications
of Definite Integral. Use examples to illustrate the applications.
4. Under perfect competition, there is a
firm producing two products. Quantity of first product is q1 and quantity of
second product is q2 . Prices of both commodities must be taken as exogenous.
The price of first product is given by p1 = 5 and the price of second product
is given by p2 = 3. The firm’s cost function is assumed to be C = 2q1 2 + 2q2 2
+ q1q2. Find out the following:
a) firm’s revenue function
b) firm’s marginal cost function for
first product
c) firm’s marginal cost function for
second product
d) firm’s profit function
e) the value of q1 and q2 that maximise
the firm’s profits
f) Value of Hessian matrix
5. (i) What is a partial derivative? Find
the partial derivative of: f (x1 , x2 ) = 4x1 + 5x1x2 + 2x2
(ii) What is a cross partial derivative?
Find the cross partial derivative of: f (x1 , x2 ) = 4x3 + x2 4 + 3x1 3x2 4 +
5x1 x2
(iii)What is a total differential? Find
out the total differential of: f (x1 , x2 ) = 10x1 + x2 4 + 2bx1x2 + 5x2
6. What do you understand by constrained
optimisation? Let the utility function be U (X, Y) = X2 + Y. Price of commodity
X is Px = 2 and price of commodity Y is Py = 1. The income is M = 200. Find out
the equilibrium quantities of X and Y, given the constraint M = PxX+ PyY.
7. Write short notes on the following:
(i) Algebraic function and Non-Algebraic
function
(ii) Right-hand limit and left-hand limit
(iii) Probability distribution function
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