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 -10PB =0

QB-60+10PB=0

3.1 Which is the demand curve? The Supply Curve?
3.2 Derive the Inverse Demand Curve. Show all steps
3.3 Find the price and quantity equilibrium using the Inverse Demand and Supply curves.
3.4 Derive the intercepts and slopes of the Regular Demand and Supply Curves
3.5 Suppose the government imposes an excise tax of $2, find the new price and quantity equilibrium.
3.6 From problem 3.5, how much of the tax is paid by consumers and how much by producers?

Explanation / Answer

3.1 Qb = 10Pb, this is the supply curve depicting direct relation of quantity with price.

QB-60+10PB=0 or Qb = 60 – 10Pb showing inverse relation between quantity and price, it is he demand function

3.2 Qb = 60 – 10Pb or 10Pb = 60 – Qb or Pb =6 – 0.1Qb(Inverse demand function)

3.3 For equilibrium set demand equal to the supply function

10Pb = 60 – 10Pb

20Pb = 60

Or Pb = 3

At Pb = 3, Qb = 10*3 = 30 units

3.4 Slope (Demand) = dQb/dPb = -10, Slope (Supply) = dQb/dPb = 10

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