Graph the supply and demand curves of
Qd=500 - 2P and Qs = -100 + 3P
To graph the supply and demand curves for the given equations Qd = 500 - 2P and Qs = -100 + 3P, you need to plot the price (P) on the x-axis and the quantity demanded (Qd) and quantity supplied (Qs) on the y-axis.
Step 1: Calculate the equilibrium price and quantity:
At equilibrium, the quantity demanded (Qd) is equal to the quantity supplied (Qs). Set the equations Qd = Qs and solve for P:
500 - 2P = -100 + 3P
Step 2: Solve for P:
Add 2P to both sides:
500 = -100 + 5P
Add 100 to both sides:
600 = 5P
Divide by 5:
P = 120
Step 3: Calculate the equilibrium quantity:
Substitute the equilibrium price (P = 120) into either the Qd or Qs equation and solve for Q:
Using Qd: Qd = 500 - 2P
Qd = 500 - 2(120)
Qd = 500 - 240
Qd = 260
At equilibrium, the price (P) is 120 and the quantity (Q) is 260.
Step 4: Graph the supply and demand curves:
Now that you have the equilibrium price and quantity, you can plot the supply and demand curves.
Demand Curve:
Plot the points using the Qd equation Qd = 500 - 2P.
When P = 0, Qd = 500. Plot the point (0, 500).
When P = 120, Qd = 260. Plot the point (120, 260).
Connect the two points with a straight line. This line represents the demand curve.
Supply Curve:
Plot the points using the Qs equation Qs = -100 + 3P.
When P = 0, Qs = -100. Plot the point (0, -100).
When P = 120, Qs = 260. Plot the point (120, 260).
Connect the two points with a straight line. This line represents the supply curve.
Step 5: Label the axes and curves:
Label the x-axis as "Price (P)" and the y-axis as "Quantity (Q)".
Label the demand curve as "Demand" and the supply curve as "Supply".
Step 6: Determine the equilibrium point:
Plot the equilibrium point at P = 120 and Q = 260, where the supply and demand curves intersect.
Your graph should now have a demand curve sloping downward from top left to bottom right, a supply curve sloping upward from bottom left to top right, and an equilibrium point where the two curves intersect.