Question

Suppose in Flower Land people grow roses, and you have a demand and supply curve for roses, where P is the price for roses and Q is the quantity of roses:

P=120-8Q

P=10+2Q

Please find the equilibrium price and quantity for roses. Please graph supply and demand curves and show the equilibrium price and quantity demanded on the graph. Please also label the axes, intercepts, and curves.

Suppose the government of Flower Land wants to implement price control and decides to fix the price at P=20. Is this a price ceiling or price floor? On the graph in question 2 above, please show how the new graph will impact quantity supplied and quantity demanded. Please calculate this quantity supplied and quantity demanded. Is this a shortage or a surplus? How much?

How will Valentine’s Day or Mother’s Day impact price and quantity of roses in Flower Land? Briefly explain. Draw a diagram that illustrates this effect (hint: what will be effected: supply or demand? In what way?). On the graph, you can depict original supply and demand and equilibrium (from question 2), carefully labeling the axes, intercepts, and curves.

Answer 1

The demand and supply curves are given as and , respectively.

The equilibrium quantity will be where the price of demand and supply curve are equal, ie or . The equilibrium price can be found by putting the equilibrium quantity in either demand or supply function, yielding the same result. The equilibrium price is hence , ie dollars.

As the equilibrium price is $32, a price control of $20 will be price ceiling (as $20 is maximum price that can be charged). The graph is below.

At $20, the quantity demanded will be or units, while quantity supplied is or . hence, there is a shortage, by 12.5 - 5, ie 7.5 units.

Valentine’s Day or Mother’s Day would increase the demand, and hence would shift the demand curve to right/up, and would not affect the supply curve. Increasing the demand would cause increase in price as well as quantity. The graph is as below (The price ceiiling case is a optional).

As can be seen, the new demand curve makes the equilibrium at E', and quantity is increased from Q1 to Q2, while price is increased from P1 to P2.

Optional: If the same price ceiling still exists, the shortage is increased more than any other day, as the quantity demanded at that price is more now, supply being same as before.