Question

These next five problems consider tax incidence. Suppose the market supply and demand for guitars in Happy Valley are given by: Demand: P = 300 – (1/2)Q Supply: P = 100 + (1/3)Q What is the equilibrium price and quantity of the product?

Answer 1

Answer:

The equilibrium price = 180

The equilibrium quantity of the product = 240

Explanation:

Data provided in the question:

Demand: P = 300 – (1/2)Q

Supply: P = 100 + (1/3)Q

Now,

For equilibrium

Demand = Supply

300 – (1 ÷ 2)Q = 100 + (1 ÷ 3)Q

or

300 - 100 =  (1 ÷ 3)Q +  (1 ÷ 2)Q

or

200 = $Q(\frac{1}{3}+\frac{1}{2})$

or

$Q\times\frac{5}{6}$ = 200

or

Q = 200 × (6 ÷ 5)

or

Q = 240

Therefore,

equilibrium price will be

P = 300 – (1/2)(240)

= 300 - 120

or

= 180

Hence,

The equilibrium price = 180

The equilibrium quantity of the product = 240