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# note7 - dD dp dp dG 1 = dS dp dp dG dp dG = 1 dS dp-dD dp 1...

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Microeconomic Theory Econ 101A Fall 2008 GSI: Eva Vivalt Section Notes 7: Deadweight Loss and Monopoly 1 Deadweight Loss 1.1 Introduction Deadweight loss occurs when there is some market inefficiency (e.g. tax, price floor/ceiling, monopoly). Deadweight loss can be illustrated graphically as the area of the region that lies between the demand curve, the supply curve, and a vertical line at Q*. To find the DWL, we thus use the formula for the area of a triangle, using - dQ as the length and as the height. DWL = - 1 2 dτdQ = - 1 2 ση σ - η Qdτ p = - 1 2 ( ) 2 ση σ - η Q p Or, expressing DWL as a fraction of revenue, R = pQ , DWL R = - 1 2 p 2 ση σ - η 1.2 Application: Government Purchases Recall the notes on competitive equilibrium and comparative statics. We had an example of a government purchase of a good, G. The equilibrium conditions were: p D = p s = p * D ( p * ) + G = S ( p * ) Using comparative statics, we found that:

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Unformatted text preview: dD dp * dp * dG + 1 = dS dp * dp * dG dp * dG = 1 dS dp-dD dp 1 dQ * S dG = dQ * S dp * dp * dG = dS dp dS dp-dD dp dQ * D dG = dQ * D dp * dp * dG = dD dp dS dp-dD dp And the elasticities: dp * p = 1 σ-η dG Q dQ * S Q = σ σ-η dG Q dQ * D Q = η σ-η dG Q Assuming the government can sell back to the consumer, the deadweight loss of a government purchase is the remaining triangle that lies below the supply curve, above the demand curve, to the right of the original equilibrium point. We can approximate this area as follows: DWL = 1 2 ( p S-p D )( Q * S-Q ) And if we wanted we could get this to be in terms of the elasticities or, more simply, use the elasticities to ﬁnd these changes, as done in problem sets. 2...
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