Suppose that supply and demand functions for a produc are given by: Qd = 500 - 2

Question

Suppose that supply and demand functions for a produc are given by:

Qd = 500 - 2P

Qs = -100 +3

1. Find the equilibrium price and quanityty.

2. If the curent pice of te product is $100, what is the quantity supplied and the quantity demanded? How would you describe this situation, and what would you expect to happen in the market?

3. If the current price of the product is $150, what is te quaniity supplied and the quantity demanded? How would you describe this situation and what would you expect to happen in this market?

4. Suppose tat demand changes to Qd = 600 - 2P.  Find te new equilibrium price and quantity.

Questions 2 and 3 are not new equilibriums, but new pices with market equilibrium that you calculated from question 1.

Explanation / Answer

(1) Qd=500-2P

Qs=-100+3P

At equilibrium,

Qd=Qs

So, 500-2P=-100+3P

Or, 5P=600

Or, P=600/5

Or, P=120

Putting P=120 in equation of Qd,

Qd=500-2(120)

Or, Qd=260

Hence Price=$120 and Quantity=260 units

(2)Current Market Price i.e. P=$100

Putting P=100 in the equation of Qd, we get quantity demanded:

Qd=500-2(100)

Or, Qd=300

Now, putting P=100 in equation of Qs, we get quantity supplied:

Qs=-100+3(100)

Or, Qs=200

Hence quantity demanded=300 units,whereas quantity supplied=200 units

This is the case of EXCESS DEMAND since Qd>Qs

This can be brought to equilibrium by increasing the price. This is because there is an inverse relation between demand and supply, i.e when price increases, demand decreases.

(3)Current Market Price i.e. P=$150

Putting P=150 in the equation of Qd, we get quantity demanded:

Qd=500-2(150)

Or, Qd=200

Now, putting P=150 in equation of Qs, we get quantity supplied:

Qs=-100+3(150)

Or, Qs=350

Hence quantity demanded=200 units,whereas quantity supplied=350 units

This is the case of EXCESS SUPPLY since Qs>Qd

This can be brought to equilibrium by decreasing the price. This is because there is an inverse relation between demand and supply, i.e when price decreases, demand increases. So, we have to reduce Price so that customers buy the product and demand increases

(4)Now, the equations of demand and supply are :

Qd=600-2P

Qs=-100+3P

At equilibrium,

Qd=Qs

So, 600-2P=-100+3P

Or, 5P=700

Or, P=700/5

Or, P=140

Putting P=140 in equation of Qd,

Qd=600-2(140)

Or, Qd=320                                                              

Hence Price=$140 and Quantity=320 units

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