QuestionAugust 25, 2025

h. Given that the demand function is p=D(q)=32-1.25q and that the supply function is p=S(q)=0.75q find the equilibrium quantity and the equilibrium price. The equilibrium quantity is square watches.

h. Given that the demand function is p=D(q)=32-1.25q and that the supply function is p=S(q)=0.75q find the equilibrium quantity and the equilibrium price. The equilibrium quantity is square watches.
h. Given that the demand function is p=D(q)=32-1.25q and that the supply function is p=S(q)=0.75q find the equilibrium quantity and the equilibrium price. The equilibrium quantity is square watches.

Solution
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Answer

The equilibrium quantity is 16 watches, and the equilibrium price is 12. Explanation 1. Set Demand Equal to Supply At equilibrium, demand equals supply: D(q) = S(q). 2. Substitute and Solve for q Substitute the given functions: 32 - 1.25q = 0.75q. Combine like terms: 32 = 2q. Solve for q: q = \frac{32}{2} = 16. 3. Find Equilibrium Price Substitute q = 16 into either function (e.g., p = 0.75q): p = 0.75 \times 16 = 12.

Explanation

1. Set Demand Equal to Supply<br /> At equilibrium, demand equals supply: $D(q) = S(q)$.<br /><br />2. Substitute and Solve for $q$<br /> Substitute the given functions: $32 - 1.25q = 0.75q$.<br /> Combine like terms: $32 = 2q$.<br /> Solve for $q$: $q = \frac{32}{2} = 16$.<br /><br />3. Find Equilibrium Price<br /> Substitute $q = 16$ into either function (e.g., $p = 0.75q$): $p = 0.75 \times 16 = 12$.
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