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:

QB - 60 + 10PB = 0

QB - 10PB = 0

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 $2, find the new price and quantity equilibrium.

From the problem above, how much of the tax is paid by consumers and how much by producers?

Explanation / Answer

demand curve QB=60-10PB

supply curve QB=10PB

demand curve is a curve which shows the inverse relationship between price and quantity demanded.which is given in the first equation.

supply curve is a curve which sows the positive relationship between price and quantity supplied. as seen in the 2nd equation.

inverse demand curve is mentioned in terms of price

so,since demand curve is given by the function

QB=60-10PB

inverse function will be given as;

-10PB=QB-60

=>10PB=60 - QB

=>PB=6 - 0.1QB

at equilibrium,quantity demanded = quantity supplied

since quantity supplied QB=10PB;substituting the values of QB in inverse demand function,we get

PB=6-0.1(10PB)

=>PB=6-PB

=>2PB=6

=>EQUILIBRIUM PRICE=PB=3

therefore,substituting the values of PB in supply function we get

QB=10PB

=>QB=10*3=30

equilibrium quantity=30

demand curve

intercept=portion of quantity demanded unaffected by price=60

slope=coefficient of price variable= -10

supply curve

intercept=0

slope=10

Excise tax

since the consumers are willing to pay PB for a unit of commodity therefore,demand function will not change.

however,suppliers will get (PB-2) for per unit of commodity

so new supply function is

QB=10(PB-2)=10PB-20

at,equilibrium

QD=QS=QB

60-10PB=10PB-20

=>80=20PB

=>PB=4=equilibrium price

therefore,

equilibrium quantity=10PB-20=40-20=20

therefore,after imposition of taxes,equilibrium price will increase while quantity will decrease.

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