1. Demand and supply functions of two firms are following
\[
\begin{array}{ll}
\mathrm{Q}_{\mathrm{d} 1}=45-(15 / 2) \mathrm{P}_{1}+(5 / 2) \mathrm{P}_{2}, & \mathrm{Q}_{\mathrm{d} 2}=30+\mathrm{P}_{1}-5 \mathrm{P}_{2} \\
\mathrm{Q}_{\mathrm{s} 1}=-5+10 \mathrm{P}_{1} & \mathrm{Q}_{\mathrm{s} 2}=-5 \quad+(15 / 2) \mathrm{P}_{2}
\end{array}
\]
In which, \( Q_{\mathrm{at}}, Q_{\mathrm{d} 2}, \mathrm{Q}_{31}, \mathrm{Q}_{32} \) are quantities of demand and supply of firm 1 vĂ 2. \( P_{1} \), and \( P_{2} \) are price of firm 1 vĂ 2 .
a. Explain the coefficients of \( \mathrm{P}_{1} \) and \( \mathrm{P}_{2} \) in supply and demand functions.
b. Are two firms complement or competition? What is your answer if the signs of these coefficients are changed?
c. Find the market balance (price, quantity) of two firms.
2. Suppose demand and supply functions of three goods as following:
\[
\begin{array}{l}
\mathrm{Q}_{\mathrm{2} 1}=-5+3 \mathrm{P}_{1}-\mathrm{P}_{2}-\mathrm{P}_{3} \\
\mathrm{Q}_{\mathrm{d} 1}=8-2 \mathrm{P}_{1}+\mathrm{P}_{2}+\mathrm{P}_{3} \\
\mathrm{Q}_{33}=-1-\mathrm{P}_{1}-\mathrm{P}_{2}+3 \mathrm{P}_{3} \\
\mathrm{Q}_{\mathrm{d3}}=12+\mathrm{P}_{1}+\mathrm{P}_{2}-2 \mathrm{P}_{3}
\end{array}
\]
\[
\begin{array}{l}
\mathrm{Q}_{22}=-2-\mathrm{P}_{1}+3 \mathrm{P}_{2}-\mathrm{P}_{3} \\
\mathrm{Q}_{82}=11+\mathrm{P}_{1}-2 \mathrm{P}_{2}+\mathrm{P}_{3}
\end{array}
\]