10.14 Total economic output in three years. The n - vector xt denotes the economic output of a country in n different sectors, in yeart. An economist models the economic output using a linear dynamical system model xt+1 = Axt, where A is an n \times n matrix. Assuming her model is correct, find an expression for the total economic output in yeart + 3, in terms of xt and A. (The total economic output is the sum of the economic output in the n sectors.)

Please show how to do b) and c). Quantity beef consumed is the dependent variable. Each of the others are the independent variables

Solve the following system of equations for a and for b: System of Equations: Value of a Value of b 9a + 3b = 30 8a + 4b = 24

Exercise 3: Population growth and technological progress Consider a version of Solow's Model: Y₁ = AKL₁¹-a sYt = Kt+1 — Kt +6Kt Lt = Lo(1 + n)t 1 a) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of labor, i.e. k = K/L; y = Y/L b) What are the values of k and y in a steady state? What are the growth rates of aggregate output and aggregate consumption? Consider this different version of Solow's Model: 1-a Y₁ = AKtº (E₁L₁) ¹-ª sYt Kt+1 - Kt + 8Kt Lt = Lo(1 + n)t Et = Eo(1+x)t c) Rewrite the production function and the equation of capital accummulation using variables normalized by the units of effective labor, i.e. k = K/(EL); y = Y/(EL). d) What are the values of k and y along a balanced growth path? What is the growth rate of aggregate output and aggregate consumption along this BGP?