what
is the deadweight loss after the tax? I know 24 is the optimal
tax.The optimal tax will be that level of tax which is equal to marginal damage occurs at the socially optimal level of output.
Private optimal output level will be that point where private marginal benefit or demand is equal to marginal private cost i.e supply. It will be equal to P = 240 - 9Qd = 3Qs. Therefore 240 - 9Q = 3Q , or 12Q = 240, or Q = 240/12 =20. Therefore P = 3*Q = 3*12 =36.
Private equilibrium Q= 12, P=$36
Now if we add the marginal damage with supply then it will be social marginal cost. Social marginal cost function will be MD + P = 24 + 3Qs. Therefore SMC = 24+3Qs.
Equalising SMC and demand we get, 24 + 3Qs = 240 - 9Qd , or 24 + 3Q = 240 - 9Q , or 12Q = 240 -24 =216 , or Q = 216/12 = 18. P = 240 - 9Q = 240 - 9*18 = 240 - 162 = $78.
Therefore social optimal quantity is Q=18, price = $78.
Difference between social optimal quantity and private quantity is 20 -18 =2.
Difference in optimal tax i.e $24 and private equilibrium price is $36 - $24 = $12.
Therefore dead weight loss = 1/2*12*2 = $12. Therefore dead weight loss =12. Here 12 is the base and 2 is the height of triangle.
what is the deadweight loss after the tax? I know 24 is the optimal tax. Question...
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Deadweight Loss of Monopoly Question: Please provide work to
help me understand, thanks!
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