Market Dynamics Examples

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.

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

$At equilibrium Q_{D} = Q_{S} = Q *$

$5 - 0.002 Q * = 2 + 0.001 Q *$
$0.003 Q * = 3$
$Q * = 1000 l b s$
$P * = 5 - 0.002 Q * = 5 - 0.002 (1000) = $ 3 / l b$

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.

$P = 5 - 0.002 Q_{D}$
$P = 2.75 + 0.001 Q_{S}$

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

$At equilibrium, Q_{D} = Q_{S} = Q *$

$5 - 0.002 Q * = 2.75 + 0.001 Q *$
$0.003 Q * = 2.25$
$Q * = \frac{2.25}{0.003} = 750$
$P * = 5 - 0.002 Q * = 5 - 0.002 (750) = $ 3.5 / l b$

As we can see from the result upward movement of supply shifts the new equilibrium to ( $P * = $ 3.5 / l b, Q * = 750 l b$ ). 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 ( $Q * = 1000 l b, P * = $ 3 / l b$ )

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 $P D = 9.5 - 0.002 Q_{D}$

Find the equilibrium price and quantity

$P = 9.5 - 0.002 Q_{D}$
$P = 2 + 0.001 Q_{S}$
$9.5 - 0.002 Q_{D} = 2 + 0.001 Q_{S}$

$At equilibrium, Q_{D} = Q_{S} = Q *$

$9.5 - 0.002 Q * = 2 + 0.001 Q *$
$0.003 Q * = 7.5$
$Q * = 2500 l b s of oranges$
$P * = 9.5 - 0.002 Q * = 9.5 - 0.002 (2500) = $ 4.5 l b s$

Then, new equilibrium is $(P * = $ 4.5 / l b, Q * = 2500 l b s)$ , 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 $P D = 9.5 - 0.002 Q_{D}$ . 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?

$P = 9.5 - 0.002 Q_{D}$
$P = 2.75 + 0.001 Q_{S}$

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

$At equilibrium Q_{D} = Q_{S} = Q *$

$9.5 - 0.002 Q * = 2.75 + 0.001 Q *$
$0.003 Q * = 6.75$
$Q * = 2250 l b s of orange$
$P * = 9.5 - 0.002 Q * = 9.5 - 0.002 (2250) = $ 5 / l b$

$The new equilibrium will be (Q * = 2250 l b s, P * = $ 5 / l b)$

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