4 4. (a) Indicate the kind of linearity (variables or parameters) the following equations exhibit:1(i) Y = B₁ + B₁X(ii) Y = B₁ + — X(ii) Y = ₁ + X(iii) Y = B₁ + B₁-B₁(iv) Y = B₁ + B₁X + B₁X² + B₁X³1(vii) Y = B+B²-XY = 12/18/12/2+Bo X(v) Y =(vi) Y = Bo + BỉX

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 23EQ: 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...

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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
The demand and supply functions for two interdependent commodities are given by:Qd1 = 205 − 2.5P1 − P2Qs1 = 1.5P1 − 30Qd2 = 147.5 − 0.5P1− 1.5P2Qs2 =P2 − 60Determine the equilibrium price and quantity for this two-commodity model.
If we modify the Lotka–Volterra equations by including a self-limiting term −σ x2 in the prey equation, and then assume constant-effort harvesting, we obtain the equations x′=x(a−σx−αy−E1),y′=y(−c+γx−E2).x′=xa−σx−αy−E1,y′=y−c+γx−E2. In the absence of harvesting, the equilibrium solution of interest is x = c/γ, y = (a/α) − (σ c)/(αγ).How does the equilibrium solution change if the predator is harvested (E2 > 0), but not the prey (E1 = 0)?
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4. (a) Indicate the kind of linearity (variables or parameters) the following equations exhibit: 1 1 (i) Y = B₁ + B₁X (ii) Y = B₁ + X (iii) Y = B₁ + B₁- B₁ X