Answer to Question #277279 in Calculus for Grace

Question

At a unit price of 16,000 the demand of a product is 300 units and at a price of 48000 the demand is 100 units.at a unit price of 30000 the supply is 550 units and at a unit price of 50000 the supply is 650 units.determine the equilibrium price and quantity

Answer 1

Demand:

$$p(q)=kq+b$$

$$16000=300k+b$$

$$48000=100k+b$$

$$k=\dfrac{16000-48000}{300-100}=-160$$

$$b=16000-300(-160)=64000$$

$$p(q)=-160q+64000$$

Supply:

$$p(q)=kq+b$$

$$30000=550k+b$$

$$50000=650k+b$$

$$k=\dfrac{50000-30000}{650-550}=200$$

$$b=30000-550(200)=-80000$$

$$p(q)=200q-80000$$

Determine the equilibrium quantity

$$-160q+64000=200q-80000$$

$$q=400$$

Determine the equilibrium price

$$p=200(400)-80000=0$$