Question

In: Economics

Suppose the demand and supply curves of a perfectly competitive market are: Supply: Q = P...

Suppose the demand and supply curves of a perfectly competitive market are:

Supply: Q = P - 10
Demand: Q = 90 - P
(1) Solve for the market equilibrium (price and quantity at equilibrium)
(2) Solve for Welfare (Total Surplus).
(3) Suppose a per-unit tax of $10 is imposed in the market. Calculate tax revenue and deadweight loss.

Expert Solution

1) Market equilibrium has Qs = Qd

P - 10 = 90 - P

2P = 100

P = $50 per unit (market price)

Q = 90 - 50 = 40 units (market quantity)

2) Total surplus = CS + PS

= 0.5*(90 - 50)*40 + 0.5*(50 - 10)*40

= $800 + $800

= $1600

3) New demand is Q = 90 - (P + 10) or Q = 80 - P. New market outcome has

80 - P = P - 10

90 = 2P

P = 45 (sellers)

P = 55 (buyers)

Q = 45 - 10 = 35 units

DWL = 0.5*tax*reduction in quantity = 0.5*10*5 = $25

Revenue = tax*quantity = 10*35 = $350

Rahul Sunny answered 2 years ago

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