If aggregate demand for a product is Qd = 600 – 20P and supplys Qs = 304 + 12P, what would be (1) the equilibrium price and (2) the equilibrium quantity? Also (3) prepare a well calibrated graph illustrating Qd and Qs. Placeprice on the vertical axis and quality on the horizonal axis.
To find the equilibrium price and quantity, we need to set the demand (Qd) equal to the supply (Qs) and solve for the price.
1) Equilibrium Price:
Setting Qd equal to Qs:
600 - 20P = 304 + 12P
To solve for P, we can rearrange the equation:
600 - 304 = 12P + 20P
296 = 32P
Dividing both sides by 32:
P = 296/32
P = 9.25
So, the equilibrium price is $9.25.
2) Equilibrium Quantity:
Now we can substitute the equilibrium price (P = 9.25) into either the demand or supply equation to find the equilibrium quantity.
Using the demand equation (Qd = 600 - 20P):
Qd = 600 - 20(9.25)
Qd = 600 - 185
Qd = 415
Thus, the equilibrium quantity is 415 units.
3) Graph:
To display the equilibrium on a graph, plot the demand (Qd) and supply (Qs) equations on a graph with price on the vertical axis and quantity on the horizontal axis.
On the horizontal axis (x-axis), label it as Quantity, and on the vertical axis (y-axis), label it as Price. Set the scales accordingly.
For the demand curve (Qd = 600 - 20P):
- Start from the point where Qd intersects the price axis, which is (0,600) and plot this point.
- To determine the second point, set P = 0 and solve for Qd:
Qd = 600 - 20(0)
Qd = 600
So, plot the point (600, 0).
- Connect these two points to form a downward-sloping straight line.
For the supply curve (Qs = 304 + 12P):
- Start from the point where Qs intersects the price axis, which is (0,304) and plot this point.
- To determine the second point, set P = 0 and solve for Qs:
Qs = 304 + 12(0)
Qs = 304
So, plot the point (304, 0).
- Connect these two points to form an upward-sloping straight line.
The equilibrium point is where these two curves intersect. Mark this point on the graph (9.25, 415).
Now, you have a well-calibrated graph illustrating Qd and Qs, with price on the vertical axis and quantity on the horizontal axis.