\begin{tabular}{l} I. The markets for gasoline and cars are interdependent because the demand for cars affects the \ demand for gasoline, and vice versa. Both markets are given by: \ $$ \qquad $$ Gasoline: $$ Q_{d G}=500-2 P_{G}+0.5 P_{c}, Q_{s G}=100+P_{G} $$ \ $$ \quad $$ Cars: $$ Q_{d c}=300-3 P_{c}-0.2 P_{G}, Q_{s c}=50+2 P_{c}+3 P_{G} $$ \ Find the equilibrium prices and quantities of gasoline and cars. \ II. The markets for rice, lentils, and spices are interdependent because they are complementary goods \ in cooking. The relationships are: \ Rice: $$ Q_{d R}=1000-6 P_{R}+0.4 P_{L}+0.2 P_{S}, Q_{s R}=200+3 P_{R} $$ \ Lentils: $$ Q_{d L}=800-5 P_{L}+6 P_{R}-10 P_{S}, Q_{s L}=150+2 P_{L} $$ \ \hline Spices: $$ Q_{d s}=500-4 P_{S}+5 P_{R}-10 P_{L}, Q_{s S}=100+P_{S} $$\end{tabular}

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Lynch Chambers · Accepted Answer

The equilibrium prices and quantities for gasoline and cars are approximately $$ P_G \approx 126.73 $$, $$ Q_G \approx 266.34 $$, $$ P_c \approx 39.6 $$, $$ Q_c \approx 155.85 $$. For rice, lentils, and spices, the equilibrium values are found by solving a system of equations involving the demand and supply functions for each market.

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