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econ 201 - ps4

# econ 201 - ps4 - 5 Lil Jon(consumer 1 and the East Side...

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1 ECONOMICS 201 SPRING 2012 PROBLEM SET 4 1. Suppose that consumers in the economy may have different preferences, but that good 1 is normal for everyone. That is, 0 ) , , ( 2 1 1 n n n m m P P X for all N n ,..., 1 . Is aggregate demand necessarily decreasing in price? Is 0 ) ,..., , , ( 1 1 2 1 1 P m m P P X N ? 2. Demonstrate that aggregate supply is always increasing in price, i.e. 0 ) , , , ( 1 2 1 2 1 1 P w w P P y . 3. Using the following utility possibility set, explain whether or not giving all resources to consumer 1 is Pareto Optimal. 4. Ernie (consumer 1) and Burt (consumer 2) are the competitive consumers in the economy. Their endowments of smiles (good 1) and laughs (good 2) are ) 5 , 10 ( Ernie e and ) 7 , 2 ( Burt e , respectively. Market prices are 1 1 P , and 2 2 P . What are the total economy-wide endowments of smiles and laughs? Draw the Edgeworth Box and the endowment bundle. What are Ernie and Burt’s budget lines? Write the equations and draw the budget line in the Edgeworth Box.
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Unformatted text preview: 5. Lil Jon (consumer 1) and the East Side Boyz (consumer 2) are the competitive consumers in the economy. Their endowments of Yeah! (good 1) and OK! (good 2) are ) 5 , 10 ( LilJon e and ) 10 , 5 ( EastSide e , respectively. Lil Jon’s demand functions for Yeah! and OK! are 1 1 P m X LilJon LilJon and 2 2 ) 1 ( P m X LilJon LilJon . The East Side Boyz’ demand functions are analogous, 1 1 P m X EastSide EastSide and 2 2 ) 1 ( P m X EastSide EastSide . Show that if 5 . , the equilibrium prices cannot be 2 1 P , and 3 2 P . 6. Given the conditions in Question 5 (using generally), what are the two equations which determine the equilibrium prices in the economy? Now normalize 1 1 P . Solve for the equilibrium prices if 5 . . Solve for the equilibrium prices if 25 . ....
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