Riemann Sum
In Quantitative Methods, the Riemann Sum is a fundamental concept used to approximate the area under a curve or the integral of a function over a given interval. It involves dividing the interval into smaller sub-intervals of equal or unequal width, calculating the value of the function at specific points __________ ______ __________ ___ ___ _____ ________ _______ __________.
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Riemann Sum
Given the input matrix and the final demand vector:
A = [[0.10, 0.15, 0.12],
[0.20, 0, 0.30],
[0.25, 0.40, 0.20]]
d = [[100],
[200],
[300]]
a) Explain the economic meaning of the elements 0.30,0 and 200
b) Explain the economic meaning of (if any) of the third column sum
c) Explain the economic meaning of (if any) of the third row sum
d) Write out the specific input-output matrix equation for this model
e) Find the solution output levels of the three industries using Cramer's rule.
xamine the following functions for maxima and minima:
a)
b)
(a) Explain the theorem of second order optimum.
(b) Consider the following utility maximization problem, in which the utility function of the consumer is given by U(x,y)=x^0.7y^0.3. The consumer income is I=200 and p x=3 and py=2. Find the utility maximizing x and y when the budget constraint of the consumer may or may not bind. (Apply Kuhn-Tucker method)
Ram and Rahim play for a prize of Rs. 99. The prize is to be won by the player who first throws a 3 with a single die. Ram throws first and if he fails Rahim throws it and if Rahim fails Ram throws it again and this process continues. Find their respective expectations.
b.) If P (A B
C) = 0, show that P [(A
B)/ C] = P(A/C) + P (B/C)
Maximin or Minimax Principle
Using Simplex method solve the problem:
Maximise z = 4x + 8y + 2k
Subject to:
Also, minimize the same for z