Suppose the market for alcohol can be described by the following equations: Demand: P = 10 - Q, Supply : P = Q + 2, where P is the price in Kina per unit and Q is the quantity.
a) Illustrate the supply and demand curves on a graph. (Show the key features of the graphs)
b) What is the equilibrium price and quantity?
a) To illustrate the supply and demand curves on a graph, we plot the demand and supply equations on a graph where the y-axis represents price (P) and the x-axis represents quantity (Q).
Demand curve: P = 10 - Q
Supply curve: P = Q + 2
To plot the demand curve, we set P = 10 - Q and solve for Q:
10 - Q = Q + 2
10 - 2 = Q + Q
8 = 2Q
Q = 4
So the demand curve intersects the y-axis at a price of 10 and the x-axis at a quantity of 4.
To plot the supply curve, we set P = Q + 2 and solve for Q:
Q + 2 = Q + 2
Q = 0
So the supply curve intersects the y-axis at a price of 2 and the x-axis at a quantity of 0.
b) To determine the equilibrium price and quantity, we set the demand and supply equations equal to each other and solve for Q:
10 - Q = Q + 2
10 - 2 = Q + Q
8 = 2Q
Q = 4
To find the equilibrium price, we plug the equilibrium quantity (Q = 4) into either the demand or supply equation:
P = 10 - Q
P = 10 - 4
P = 6
Therefore, the equilibrium price is 6 Kina per unit and the equilibrium quantity is 4 units.