Questions: Question 16 Given: (q is number of items) Demand function: d(q)=630-0.2q^2 Supply function: s(q)=0.5q^2 Find the equilibrium quantity: items Find the equilibrium price:

Question 16 Given: (q is number of items) Demand function: d(q)=630-0.2q^2 Supply function: s(q)=0.5q^2 Find the equilibrium quantity: items Find the equilibrium price:
Transcript text: Question 16 Given: ( $q$ is number of items) Demand function: $d(q)=630-0.2 q^{2}$ Supply function: $s(q)=0.5 q^{2}$ Find the equilibrium quantity: $\square$ items Find the equilibrium price: $\$$ $\square$ Submit Question
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Solution

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Solution Steps

Step 1: Finding the Equilibrium Quantity

To find the equilibrium quantity $q_e$, we set the demand function equal to the supply function: $$A - Bq^2 = Cq^2$$ Solving for $q$, we get: $$A = (B+C)q^2$$ $$q_e = \sqrt{\frac{A}{B+C}} = \sqrt{\frac{630}{0.2+0.5}} = 30$$

Step 2: Finding the Equilibrium Price

Substituting $q_e$ back into the demand function to find the equilibrium price $P_e$: $$P_e = A - Bq_e^2 = 630 - 0.2 \times (30)^2 = 450$$

Final Answer:

The equilibrium quantity is $q_e = 30$ units, and the equilibrium price is $P_e = 450$.

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