Question

Consider a market for oranges with the following supply and demand functions:

Pₛ =10+2Qˢ
Pd =90−2Qᵈ
1. Graph the above functions and calculate the equilibrium price (P∗ ) and quantity (Q∗ ) for the above market

Answer 1

The equilibrium price for oranges is $50, and the equilibrium quantity is 20 oranges. This is found by equating the supply and demand functions and solving for the variables, or graphically where the supply and demand curves intersect.

Step-by-step explanation:

To find the equilibrium price (P*) and quantity (Q*) for oranges, we need to equate the supply function Ps = 10 + 2Qs with the demand function Pd = 90 - 2Qd. The equilibrium is reached where the quantity supplied equals the quantity demanded (Qs = Qd). We must solve for the price and quantity at which these two equations are equal.

To do this, set the supply and demand prices equal to each other: 10 + 2Q = 90 - 2Q. Solving for Q gives us Q* = 20. Plugging this back into either the demand or supply function will give us P* = 50. Therefore, the equilibrium price is $50 and the equilibrium quantity is 20 oranges.

If you prefer visual learning, you can graph these functions. For the demand curve, rearrange to get P = 90 - 2Q and for the supply curve, use the given P = 10 + 2Q. The point where these two lines intersect on the graph will give you the equilibrium price and quantity.