Suppose you are given the following supply and demand functions for cell phone b

Question

Suppose you are given the following supply and demand functions for cell phone batteries: Q_B - 60+10P_B = 0 Equation 1 Q_B - 10 P_B = 0 Equation 2 Which is the demand curve? The Supply Curve? Derive the Inverse Demand Curve. Show all steps Find the price and quantity equilibrium using the Inverse Demand and Supply curves. Derive the intercepts and slopes of the Regular Demand and Supply Curves Suppose the government imposes an excise tax of dollar 2, find the new price and quantity equilibrium.

Explanation / Answer

a) The above equation can be written as follows,

1. QB= 60 -10 PB   

2. QB= 10PB   

The first equation is demand curve as price is negatively related to quantity demanded. Notice the negative sign of Price PB.

The second equation is supply curve as we know quantity supplied is positively related to price which is clearly seen the above equation.

b) The inverse demand function expresses price as a function of quantity demanded. The inverse demand function can be found by doing following steps,

QB=60- 10 PB

QB - 60 = -10 PB   

6 -1/10 QB = PB is the inverse demand function.

c) At equilibrium,Quantity demanded = Quantity supplied

Equate the inverse demand curve and supply curve to arrive at equilibrium quantity and prices.

Inverse demand function is 6 -1/10 QB = PB   

Supply function is QB = 10 PB

6 -1/10 QB = QB /10

60 - QB = QB   

60 = 2 QB

QB = 30

By substituting QB= 30 in supply curve we get PB = 3

The equlibrium quantity is 30 and price is 3

d. Let the demand curve be of the form,

Qd = a- bP

where 'a'is the intercept and b is the slope

Qd is the quantity demanded and P is price

Qd + bP =a

a/P - Qd/P = b

  

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