Given the demand & supply Function for product 'x' at california university have been estimated as:

Qd= 5000- 4 (price)+ 0.2 (pop)
Qs=-300 +5 (price)+ 0.5 (wage rate)

i) determine the equilibrium price & quantity of product X.

ii) Derive the demande & supply curves if pop=10,000 & wage rate is = $ 200/week

iii) At what price, the buyers (Sellers )would purchase (sell) zero Unit of X?

iv) What will be the quantity demand & quantity supplied if product X becomes a FREE GOOD?

i) To determine the equilibrium price and quantity of product X, we need to find the price and quantity at which the quantity demanded (Qd) equals the quantity supplied (Qs).

Setting Qd equal to Qs, we have:

5000 - 4(price) + 0.2(pop) = -300 + 5(price) + 0.5(wage rate)

Simplifying the equation:

4(price) + 5(price) = 5000 + 300 + 0.2(pop) - 0.5(wage rate)

9(price) = 5300 + 0.2(pop) - 0.5(wage rate)

Now, let's substitute the given values for pop and wage rate:

pop = 10,000
wage rate = $200/week

9(price) = 5300 + 0.2(10,000) − 0.5(200)

9(price) = 5300 + 2000 − 100

9(price) = 7200

Dividing both sides by 9:

price = 800

Now that we have the equilibrium price, we can substitute this value back into either the demand or supply function to find the equilibrium quantity.

Using the demand function Qd = 5000 - 4(price) + 0.2(pop):

Qd = 5000 - 4(800) + 0.2(pop)

Substituting pop = 10,000:

Qd = 5000 - 3200 + 0.2(10,000)

Qd = 1800 + 2000

Qd = 3800

Therefore, the equilibrium price of product X is $800, and the equilibrium quantity is 3,800 units.

ii) To derive the demand and supply curves when pop = 10,000 and wage rate = $200/week, we can use the given demand and supply functions:

For the demand curve, substitute the values into the demand function Qd = 5000 - 4(price) + 0.2(pop):

Qd = 5000 - 4(price) + 0.2(10,000)

Qd = 5000 - 4(price) + 2000

Qd = 7000 - 4(price)

For the supply curve, substitute the values into the supply function Qs = -300 + 5(price) + 0.5(wage rate):

Qs = -300 + 5(price) + 0.5(200)

Qs = -300 + 5(price) + 100

Qs = -200 + 5(price)

iii) To find the price at which buyers or sellers would purchase or sell zero units of X, we need to set the demand or supply function equal to zero.

For buyers purchasing zero units:

0 = 5000 - 4(price) + 0.2(pop)

For sellers selling zero units:

0 = -300 + 5(price) + 0.5(wage rate)

Solving these equations will give us the price at which zero units will be bought or sold.

iv) If X becomes a free good, it means the price is zero. We can substitute price = 0 into the demand and supply functions to find the quantity demanded and supplied:

For quantity demanded:

Qd = 5000 - 4(0) + 0.2(pop)

For quantity supplied:

Qs = -300 + 5(0) + 0.5(wage rate)

Simplifying these equations will give us the quantity demanded and supplied when X is a free good.