Answer to Question #249963 in Microeconomics for nic

Question

Graph the supply and demand curves. Be sure to calculate the P and Q intercepts for demand and the P intercept for supply. Calculate and illustrate the equilibrium price and quantity. [Hint: Show your work. [5]

Answer 1

Assuming we have quantity demanded and supplied at the given prices on the table below which is a representation of the rice f gasoline.

A representation of the data on a graph, produces the the demand and supply curve that appears as shown below.

Calculations

Step 1

Determining the demand slope (Since it is a curve we have to establish the gradient)

in this case the gradient points are (500, 1.60) and (800, 1.00)

$=$ $\frac{dQ_2-dQ_1}{dP_2-dP_1}$

$=$ $\frac{500-800}{1.60-1.00}$

$=$ $\frac{-300}{0.60}$ $=$ -500

$b = -500$

Demand equation

$Q_d = a + bP$

Where:

b$-$ is the slope

a $-$ is quantity demanded when price is zero

replacing the equation with numbers from the table above to determine $a$

$800 = a - 500 (1.00)$

$a = 800 + 500$

$a = 1,300$

therefore the demand equation is

$Qd = 1,300 - 500P$

Step 2

Determining the supply slope (Since it is a curve we determine the gradient)

In this case the points of the gradient are (800,2.20) and (500, 1.00)

$=$ $\frac{dQ_2 - dQ_1}{P_2 - P_1}$

$=$ $\frac{800-500}{2.20-1.00}$

$=$ $\frac{300}{1.20}$

$b = 250$

Supply equation

$Q_s = a + bP$

Where:

b$-$ is the slope

a $-$ is quantity supplied when price is zero

replacing the equation with numbers from the table above to determine $a$

$500 = a + 250 (1.00)$

$a = 500 - 250$

$a = -250$

therefore the supply equation is

$Q_s = -250 + 250P$

At equilibrium Supply equals demand

$Q_s = Qd$

$-250 + 250P = 1,300 -500P$

$500P + 250P = 1,300 - 250$

$750P = 1,050$

Therefore the equilibrium price is

$P_e = 1.40$

Determining the equilibrium quantity

$Q_s = Q_d = Q_e = 1,300 - 500 (1.40)$

$Q_e = 1,300 - 700$

$Q_e = 600$