1. Alabama State University’s Bookstore has determined that the supply function for a certain author’s newest book is p = (1/300)q + 13. The demand function for this book is p = -.03q + 19. Graph both demand and supply functions on the same set of axes. What is the equilibrium quantity and equilibrium price?
To graph the demand and supply functions on the same set of axes, follow these steps:
1. Set up a coordinate system with the quantity, q, on the x-axis and the price, p, on the y-axis.
2. Plot the points for the demand function, p = -0.03q + 19. To do this, choose a few values for q and substitute them into the equation to find the corresponding p-values. For example, when q = 0, p = -0.03(0) + 19 = 19. Plot the point (0, 19). Repeat this process for a few more values of q and plot the corresponding points on the graph.
3. Draw a line through the plotted points for the demand function.
4. Plot the points for the supply function, p = (1/300)q + 13. Again, choose values for q and find the corresponding p-values using the equation. Plot these points on the graph.
5. Draw a line through the plotted points for the supply function.
6. The equilibrium price and quantity occur where the demand and supply curves intersect, representing the point where the quantity supplied equals the quantity demanded.
7. Identify the x-coordinate of the point of intersection as the equilibrium quantity, qeq, and the y-coordinate as the equilibrium price, peq.
To find the equilibrium quantity and price:
8. Set the two equations equal to each other: -0.03q + 19 = (1/300)q + 13.
9. Solve the equation for q to find the equilibrium quantity. In this case, you can multiply both sides of the equation by 300 to eliminate the fractions: -9q + 5700 = q + 3900. Simplify to: 10q = 1800. Divide both sides by 10 to get q = 180.
10. Substitute the equilibrium quantity, qeq = 180, into either the demand or supply function to find the equilibrium price. Using the supply function p = (1/300)q + 13, substitute q = 180 and solve for p: p = (1/300)(180) + 13 = 13.6.
Therefore, the equilibrium quantity is 180 and the equilibrium price is $13.60.