“Indifference curves of an investor cannot intersect.” Is this statement true? Give reason for your answer.
The statement "Indifference curves of an investor cannot intersect" is generally true according to standard economic theory. Indifference curves represent different combinations of goods or assets that provide the investor with the same level of satisfaction or utility. These curves slope downward to reflect the trade-off _________ ________ __________ _______ _____ ____ __________ ___ _______.
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Formulate the model for which the reproductive function of the cancer cells in the tumor surface is given by 2 1 ; c 1(2 c)2 3 c2 )c( ≠ − − φ = together with initial conditions 5 c = 20×10 at t = .0 Also find the density of the cancer cells in the tumour’s surface area at t = 20 days.
The return distribution on the two securities X and Y are given in the table below:
| Possible Rates of Return | Associated Probability | |
| X | Y | Pxj=Pyj |
| 0.10 | 0.09 | 0.20 |
| 0.11 | 0.11 | 0.22 |
| 0.17 | 0.16 | 0.25 |
| 0.19 | 0.18 | 0.33 |
Find
A simple model including the seasonal change that affects the growth rate of a population is given by where C is a constant. If 0 x is the initial population, solve the equation and determine the maximum and minimum population.
Do the stability analysis of the trivial equilibrium solution of the following competing species model:
where D1 and D2 are diffusion coefficients of the two population densities N1 and N , 2 respectively. 1 a is the growth rate, 1 b is the predation rate, 1 d is the death rate and 1 c is the conversion rate. The initial boundary conditions are
where Ni are the equilibrium solutions of the given system of equations.
Consider the budworm population dynamics governed by the equation
where ,k the carrying capacity, and r, the birth rate of the budworm population, are positive parameters. Find out the steady states and use the perturbation to do the stability analysis of the equation for 0 < r < 1.
Following is the data for number of years students studied a subject and score he/she received in that subject:
Fit the least square line to this data. What is the score of the student who has studied for two years according to this line?
The transportation cost of 600 tons of a certain type of material from four factories B1, B2 , B3 , and B4 to three target stores T1,T2 , and T3 are given in the following table: