Lecture7_note_one_group_summary.pdf - One group summary April 4 2019 I write down here a version of the model with one group constant elasticities no

Lecture7_note_one_group_summary.pdf - One group summary...

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One group summary April 4, 2019 I write down here a version of the model with one group, constant elasticities, no trade frictions, no housing, with the notations of Fajegelbaum and Gaubert (2018). The last section shows that the market allocation is generically not efficient. 1 Simple model with draft notations 1.1 Setup Utility u j = A j L γ A j c j congestion if γ A < 0 Free mobility u i = ¯ u Output Y j = Z j L γ P j L 1 - β j productivity: Z j L γ P j , agglomeration externality if γ P > 0 β 0 measures decresing returns in production Total labor supply summationdisplay L i = 1 Define the elasticities: ε i U,L = U iL L i U i = γ A ε i Y,L = Y iL L i Y i = 1 - β + γ P 1
1.2 Market Allocation The final homogenous good is the numeraire. Define per capita production in the city and average per capita production: y i := Y i L i ¯ y := summationdisplay parenleftbigg Y k L k parenrightbigg L k The market allocation is the set { u, c i L i } such that Workers choose location (assuming all locations are populated): ¯ u = A j L γ A j c j for all j (1) Workers are paid their marginal product: w i = Y i (1 - β ) L i Labor market clears summationdisplay i L i = L

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