Market demand (D) for x is P=30-Qand market supply (S) for x is P=6+Q.The Government decides...

Market demand (D) for x is P=30-Qand market supply (S) for x is P=6+Q.The Government decides to impose a per-unity of production tax (t = 3) which causes the market supply function to decrease by 3 (shift to the left) or become Sor P= 9+ Q.Graph, in the same diagram, D, S, and S.Compute:(a) Market Gains (MG) before and after the tax;(b) Governmental Revenue (GR);(c) Economic Welfare (EW); and(d) Dead-Weight Loss (DWL); how is the burden of the tax distributed among consumers and producers?

Solutions

Expert Solution

Market Demand P = 30 - Q

Market Supply P = 6 + Q

Market equilibrium will be at that point where Quantity Demanded is Equal to Quantity Supplied

30 - Q = 6 + Q

2Q = 24

Q* = 12 units

P* = $ 18 (=30 -12)

Market gain

Consumer Surplus(Before tax) = (1/2)*(30-18)*12 = $ 72

Producer surplus (before tax) = (1/2)*(18-6)*12 = $ 72

Total surplus (before tax) = CS +PS = $ 144

After tax

Supply curve, P' = 9 + Q

30 - Q = 9 + Q

2Q = 21

Q' = 10.5 units

P' = $ 19.5 per unit

CS(After tax) = (1/2)*(30-19.5)*10.5 = $ 55.125

Producer surplus (after tax) = (1/2)*(16.5-9)*7.5 = $ 28.125

Dead weight loss = (1/2)*(12-10.5)*(19.5 -16.5) = $ 2.25

Govt. Revenue = (19.5-16.5)*10.5 = $ 31.50

Tax burden on consumer = (19.5-18)*10.5 = $ 15.75

Tax burden on seller = (18-16.5)*10.5 = $ 15.75

Refer the attached picture below to understand the concept

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Rahul Sunny answered 1 year ago

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