Suppose orange demand function in a small town is given by $P=5-0.002{Q}_{D}$ . Also, supply function is given by $P=2+0.001{Q}_{S}$ . Where P is the price of one pound of orange ($/lb) and Q is the total pounds of orange demanded/supplied in the market (lb). Find the equilibrium price and quantity.

$$5-0.002{Q}_{D}=2+0.001{Q}_{S}$$

$$\text{Atequilibrium}{Q}_{D}={Q}_{S}=Q*$$

$$5-0.002Q*=2+0.001Q*$$

$$0.003Q*=3$$

$$Q*=1000lbs$$

$$P*=5-0.002Q*=5-0.002(1000)=\$3/lb$$

Assume hurricane damages some orange farms this year. Consequently, supply curve is shifted upward. The new supply curve will be $P=2.75+0.001{Q}_{S}$ . Find the equilibrium price and quantity.

$$P=5-0.002{Q}_{D}$$

$$P=2.75+0.001{Q}_{S}$$

$$5-0.002{Q}_{D}=2.75+0.001{Q}_{S}$$

$$\text{Atequilibrium,}{Q}_{D}={Q}_{S}=Q*$$

$$5-0.002Q*=2.75+0.001Q*$$

$$0.003Q*=2.25$$

$$Q*=\frac{2.25}{0.003}=750$$

$$P*=5-0.002Q*=5-0.002\left(750\right)=\$3.5/lb$$

As we can see from the result upward movement of supply shifts the new equilibrium to ($P*=\$3.5/lb,\text{}Q*=750lb$ ). The new equilibrium has higher price and lower quantity.

Following the previous example, we found that if demand and supply functions for a local orange market are $P=5-0.002{Q}_{D}$ and $P=2+0.001{Q}_{S}$ , then market equilibrium will be ($\text{}Q*=1000lb,P*=\$3/lb$ )

Now assume, results of a recently published study shows that eating an orange a day will have significant health benefit. And this causes the demand curve to shift outward (to the right). Assume new demand function will be $PD=9.5-0.002{Q}_{D}$

Find the equilibrium price and quantity

$$P=9.5-0.002{Q}_{D}$$

$$P=2+0.001{Q}_{S}$$

$$9.5-0.002{Q}_{D}=2+0.001{Q}_{S}$$

$$\text{Atequilibrium,}{Q}_{D}={Q}_{S}=Q*$$

$$9.5-0.002Q*=2+0.001Q*$$

$$0.003Q*=7.5$$

$$Q*=2500lbs\text{oforanges}$$

$$P*=9.5-0.002Q*=9.5-0.002\left(2500\right)=\$4.5lbs$$

Then, new equilibrium is $\left(P*=\$4.5/lb,Q*=2500lbs\right)$ , which indicates that outward (to the right) shift of demand curve increase equilibrium price and quantity.

And let’s find the equilibrium considering both supply and demands shifts. Assume hurricane damages some orange farms causing the supply curve to shift upward with new supply curve of $P=2.75+0.001{Q}_{S}$ . Also, the recently published study causes the demand curve to shift outward (to the right) with new demand function of $PD=9.5-0.002{Q}_{D}$ . Find the new equilibrium in the market. What are your expectations on the new equilibrium price and quantity? Higher or lower compared to initial case?

$$P=9.5-0.002{Q}_{D}$$

$$P=2.75+0.001{Q}_{S}$$

$$9.5-0.002{Q}_{D}=2.75+0.001{Q}_{S}$$

$$\text{Atequilibrium}{Q}_{D}={Q}_{S}=Q*$$

$$9.5-0.002Q*=2.75+0.001Q*$$

$$0.003Q*=6.75$$

$$Q*=2250lbs\text{oforange}$$

$P*=9.5-0.002Q*=9.5-0.002\left(2250\right)=\$5/lb$

$$\text{Thenewequilibriumwillbe}\left(Q*=2250lbs,P*=\$5/lb\right)$$