Question

For the following set of demand and supply, equations do the following,

1. Determine which equation is demand equation and which one is supply equation. Explain how?
2. Find the equilibrium price and equilibrium quantity for each set of equations.
3. Draw each set of equations in a clearly labeled graph and show the equilibrium P and Q.
4. Impose a $5 on equation set 1 and find new equilibrium quantity, Price sellers receive, and price buyer pay.
5. $50 on equation set 2 and find new equilibrium quantity, Price sellers receive, and price buyer pay.
6. Draw d and e showing all the points.
7. Calculate price elasticity of demand if the price changes from $30 to $32 and between 22 and 20 for equation set 1.
8. Calculate price elasticity of demand if the price changes from $2600 to $2800 and between 1600 and 1400 for equation set 2.

Show all your workings

P=50-2Q

P=20+0.5Q        Equation set 1

P=5000-0.5Q

P=250+0.5Q      Equation set 2

Answer 1

As per the HomeworkLib policy, asnwering the first 4 parts to the question:

a.

The coefficient of Q , if negative indicates demand equation.

The coefficient of Q, if positive indicates supply equation

Hence, Equation set 1: Demand equation : P = 50-2Q ; Supply equation: P = 20+ 0.5Q

Equation set 2: Demand equation: P = 5000-0.5Q; Supply equation: P = 250+0.5Q

b.

Equilibrium in Equation set 1:

Qd = Qs

50-2Q = 20+0.5Q

2.5Q = 50-20

Q = 30/2.5 = 12

P=50-2*12 = 26

Hence, equilibrium Q=12, P=26

Equilibrium in Equation set 2:

Qd = Qs

5000-0.5Q = 250+0.5Q

Q=5000-250

Q=4750

P=250+0.5*4750

P=2625

Hence, equilibrium Q=4750, P=2625

(c)

The graph with equilibrium is given by intersection of demand and supply equation in each set of equation 1 & 2

(d)

Impose $5 on equation set 1

Demand equation: P = 50 - 2Q + 5

Supply Equation: P=20+0.5Q + 5

The new equilibrium:

Qd = Qs

50 -2Q + 5 = 20 + 0.5Q + 5

55 - 2Q = 25 + 0.5Q

2.5Q = 30

Q = 12

P = 20 + 0.5*12 = 20+ 6 = 26

The equilibrium Q = 12 and P=26