Chapter 3: Chapter 3

Reduce the payoff matrices by dominance. $$ \begin{array}{r} \\\ a & b & c \\ 1 \\ \text { A } 2 \\ 3 & {\left[\begin{array}{rrr} 2 & -4 & -9 \\ -1 & -2 & -3 \\ 5 & 0 & -1 \end{array}\right]} \end{array} $$

You are given a technology matrix \(A\) and an external demand vector \(D .\) Find the corresponding production vector \(X\). $A=\left[\begin{array}{lll}0.2 & 0.2 & 0 \\ 0.2 & 0.4 & 0.2 \\ 0 & 0.2 & 0.2\end{array}\right], D=\left[\begin{array}{r}16,000 \\ 8,000 \\\ 8,000\end{array}\right]$

You are given a technology matrix \(A\) and an external demand vector \(D .\) Find the corresponding production vector \(X\). $A=\left[\begin{array}{lll}0.2 & 0.2 & 0.2 \\ 0.2 & 0.4 & 0.2 \\ 0.2 & 0.2 & 0.2\end{array}\right], D=\left[\begin{array}{r}7,000 \\ 14,000 \\\ 7,000\end{array}\right]$

Solve for \(x, y, z\), and \(w\). $$ \left[\begin{array}{cc} x-y & x-z \\ y-w & w \end{array}\right]=\left[\begin{array}{ll} 0 & 0 \\ 0 & 6 \end{array}\right] $$

$$ \left[\begin{array}{ll} 3 & 0 \\ 0 & \frac{1}{2} \end{array}\right] $$

Compute the products. Some of these may be undefined.Exercises marked I should be done using technology. The others should be done two ways: by hand and by using technology where possible. $\left[\begin{array}{llll}0 & 1 & -1 & 2\end{array}\right]\left[\begin{array}{rrr}1 & -2 & 1 \\ 0 & 1 & 3 \\ 6 & 0 & 2 \\ -1 & -2 & 11\end{array}\right]$

Compute the products. Some of these may be undefined.Exercises marked I should be done using technology. The others should be done two ways: by hand and by using technology where possible. $\left[\begin{array}{rrr}1 & 0 & -1 \\ 1 & 1 & 2\end{array}\right]\left[\begin{array}{rrr}0 & 1 & -1 \\ 1 & 0 & 1 \\ 4 & 8 & 0\end{array}\right]$

Reduce the payoff matrices by dominance. $$ \begin{array}{rrrr} & & \mathbf{B} & \\ & a & b & c \\ p & {\left[\begin{array}{rrr} 1 & -1 & -5 \\ q & 4 & 0 & 2 \\ \mathbf{A} & r & 3 & -3 & 10 \\ 3 & -5 & -4 \end{array}\right]} \end{array} $$

$$ \left[\begin{array}{ll} 1 & 1 \\ 6 & 6 \end{array}\right] $$

Compute the products. Some of these may be undefined.Exercises marked I should be done using technology. The others should be done two ways: by hand and by using technology where possible. $\left[\begin{array}{lll}0 & 1 & -1 \\ 3 & 1 & -1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 4 & 2 \\ 0 & 1\end{array}\right]$