Question

In: Economics

Consider a public good with only two consumers, A and B. The demand function by Customer...

Consider a public good with only two consumers, A and B. The demand function by Customer A is Q = 10 - 0.5P, while the demand function by Customer B is Q = Q = 10 - 0.25P, where Q is quantity demanded and P is price. Construct the market demand curve for the public good. If a company can produce the public good at a constant marginal cost of $30, what is the market equilibrium price and quantity of the public good?

Expert Solution

The demand for customer A is Q₁ = 10 - 0.5 P

Demand for customer B is Q₂ = 10 - 0.25P

The market demand is the sum of individual demand equations of customer A and customer B

Q = Q₁ + Q₂

Q = 10 - 0.5 P + 10 - 0.25P

Q = 20 - 0.75 P

The market demand equation is Q = 20 - 0.75 P

To construct the market demand curve, we have to make a price & demand table

Price (Y)	Quanity demanded (X)
0	20
4	17
8	14
12	11
16	8
20	5
24	2

The firm can produce at a constant marginal cost of $30 , hence its supply curve will be

P = 30Q

Q_s = 0.033 P

The market equilibrium occurs when the quantity demanded equals quantity supplied i.e. Q_d = Q_s

Q_d = 20 - 0.75 P & Q_s = 0.033 P

Equating both the equation

20 - 0.75 P = 0.033 P

Market equilibrium price P = $ 25.5

Market equilibrium quantity = 20 - 0.75 $ 25.5

Market equilibrium quantity = 0.875 1

Market equilibrium quantity = 1 unit

Market equilibrium price = $ 25.5

Rahul Sunny answered 3 hours ago

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