3. a. The demand functions of two related goods are given by Q1 = 120 – 2P1 + 4P2, Q2 = 200 + 2P1 – 5P2, where P1 and P2 are the corresponding prices of the two goods. i. Analyse whether the two goods act as substitutes or complements in the market. [15% of marks for this question]
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Substitute goods are those that can be used in place of another. If the price of one good increases, the demand for its substitute will increase. This is because consumers will switch to the cheaper substitute. Complement goods are those that are used Show more…
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The demand and supply functions for two interdependent commodities are given by $$ \begin{aligned} &Q_{\mathrm{D}_{1}}=40-5 P_{1}-P_{2} \\ &Q_{\mathrm{D}_{2}}=50-2 P_{1}-4 P_{2} \\ &Q_{\mathrm{s}_{1}}=-3+4 P_{1} \\ &Q_{\mathrm{s}_{2}}=-7+3 P_{2} \end{aligned} $$ where $Q_{D_{i}}, Q_{s,}$ and $P_{i}$ denote the quantity demanded, quantity supplied and price of good $i$ respectively. Determine the equilibrium price and quantity for this two-commodity model. Are these goods substitutable or complementary?
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