1

Word problem:

If the demand function is Qd = 60 - 2p and the supply function is Qs = 20 + 4p, what is the equilibrium level of quantity and price?

Solution:

To find the equilibrium level of quantity and price, we need to set the demand function equal to the supply function and solve for Q and p:

Qd = Qs

60 - 2p = 20 + 4p

60 - 20 = 6p

40 = 6p

p = 40/6 = 6.67

Now that we have the value of p, we can substitute it into either the demand or supply function to find the equilibrium quantity:

Qd = 60 - 2p = 60 - 2(6.67) = 46.67

Qs = 20 + 4p = 20 + 4(6.67) = 46.68

The equilibrium level of quantity is approximately 46.67 units and the equilibrium price is approximately $6.67 per unit.

2

Given the demand function Qd = 80 - 3p and the supply function Qs = 12 + 5p, what is the equilibrium level of quantity and price?

Solution:

To find the equilibrium level of quantity and price, we need to set the demand function equal to the supply function and solve for Q and p:

Qd = Qs

80 - 3p = 12 + 5p

68 = 8p

p = 8.5

Now that we have the value of p, we can substitute it into either the demand or supply function to find the equilibrium quantity:

Qd = 80 - 3p = 80 - 3(8.5) = 55.5

Qs = 12 + 5p = 12 + 5(8.5) = 53.5

The equilibrium level of quantity is approximately 55.5 units and the equilibrium price is approximately $8.50 per unit.

3

If the demand function is Qd = 36 - 6p and the supply function is Qs = 30 + 2p, what is the equilibrium level of quantity and price?

Solution:

To find the equilibrium level of quantity and price, we need to set the demand function equal to the supply function and solve for Q and p:

Qd = Qs

36 - 6p = 30 + 2p

6p = 6

p = 1

Now that we have the value of p, we can substitute it into either the demand or supply function to find the equilibrium quantity:

Qd = 36 - 6p = 36 - 6(1) = 30

Qs = 30 + 2p = 30 + 2(1) = 32

The equilibrium level of quantity is 30 units and the equilibrium price is $1 per unit.

4

How does an increase in demand affect the equilibrium price and quantity of a product?

An increase in demand causes an increase in both the equilibrium price and quantity of a product.

5

How does a decrease in production cost affect the equilibrium price and quantity of a product?

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