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# International Industrial Organizations ECON 467

UW

GPA 3.6

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This 4 page Class Notes was uploaded by April Jerde on Thursday September 17, 2015. The Class Notes belongs to ECON 467 at University of Wisconsin - Madison taught by Maria Muniagurria in Fall. Since its upload, it has received 41 views. For similar materials see /class/205132/econ-467-university-of-wisconsin-madison in Economcs at University of Wisconsin - Madison.

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Date Created: 09/17/15

Econ 467 Monopolistic Competition Problem Consider the Monopolistic Competition Model studied in class for the following parameter values Fixed costs in labor units F 2 Marginal cost in labor units c 12 Utility Function Parameter cc 12 Notice that in this case the utility function is co uq1 qz Z q 11 1 Calculate the autarky equilibrium for a country that has 10 agents with 8 units of labor each ie the labor endowment is L80 and the number of consumersagents is 10 2 Free trade between two identical countries Home and Foreign Calculate the free trade equilibrium when each country looks like the country in question 1 3 Show that a consumer from either country is happier in free trade than heshe was in autarky you need to compare the home consumer s utility level in both situations 4 Growth in the foreign country Assume now that the foreign country has now 20 agents and therefore labor endowment has doubled ie the total labor endowment in foreign is 160 Everything else is unchanged and the two countries are trading freely Show how this change affects the level of happiness of the consumer in the home country you need to compare the utility level of the home consumer in free trade before and after the change Econ 467 Summer 2006 Oligopoly Theory Strategic Trade third market case I Homogeneous Products 2 Firms Typical Demand function p A b q1 qz Costs identical or not MC1 c1 MC2 c2 1 Firms choose quantities simultaneously We look for the NE in quantities or Cournot equilibrium Step 1 Calculate reaction functions by choosing q to max Hi qj qj assuming q is xed Let Ri qj be rm I s reaction function Step 2 Calculate the NE by nding the intersection of the two reaction functions ie nd the values of q1 and q2 that solve q1 R1 qz and q2 R2 ql 2 Firms choose quantities sequentially assume Firm 1 moves rst We look for the SPNE in quantities or Stackelberg equilibrium Step 1 Calculate Firm 2 s reaction function by choosing q2 to max H2 q1 qz assuming q1 is xed Let R2 ql be rm 2 s reaction function Step 2 Calculate the optimal q1 by max H1 q1 qz assuming q2R2 ql Replacing the optimal q1 into R2 ql we get the value of q2 at the SPNE Remark H1 gt H2 so the rm that goes rst has an advantage 3 Firms choose prices simultaneously We look for the NE in prices or Bertrand equilibrium with homogeneous products i If both rms have the same marginal costs 01 c2 no mathematical calculation needed Just a clear argument to justify the NE prices ii If 01 lt 02 there will be two cases depending on whether 02 is bigger or smaller than the monopoly price for rm 1 II Differentiated Products 2 Firms Typical Demand functions p1abq1cq2 p2 d e q2 g q1 for rms choosing quantity 11 h39 m P1 11 P2 p2 r s p2 11 p1 for rms choosing prices Costs identical or not MC1 c1 MC2 c2 no xed costs 5 Firms choose prices simultaneously We look for the NE in prices or Bertrand with differentiated products Step 1 Calculate reaction functions by choosing pi to max Hi pi pj assuming pj is xed Let Ri pj be rm is reaction function Step 2 Calculate the NE by nding the intersection of the two reaction functions ie nd the values of p1 and p2 that solve p1 R1 p2 and p2 R2 p1 6 Firms choose prices sequentially assume Firm 1 moves rst We look for the SPNE in prices Step 1 Calculate Firm 2 s reaction function by choosing p2 to max H2 p1 p2 assuming p1 is xed Let R2 p1 be rm 2 s reaction function Step 2 Calculate the optimal p1 by max H1 p1 p2 assuming p2R2 p1 Replacing the optimal p1 into R2 p1 we get the value of p2 at the SPNE Remark H1 lt H2 so the rm that goes rst is at a disadvantage Strategic Trade Policy Third Market Sales III Cournot Competition in Output market homogeneous products 7 Brander Spencer argument for an optimal export subsidy Set up Two rms Firm 1 and Firm 2 from countries 1 and 2 respectively choose quantities simultaneously All their output is exported to a third country This is a sequential game where country 1 moves rst choosing an export subsidytax and then the two rms compete as indicated The government s objective is to maximize the country s welfare By choosing a subsidytax level the government is choosing rm l s marginal cost Theoretical Result The optimal policy is an export subsidy With the optimal subsidy rm l s output coincides with the output level of a Stackelberg leader Therefore the subsidy shifts pro ts from rm 2 to rm 1 Country 1 is better off and country 2 worse off than without intervention Steps Calculate NE quantities for an arbitrary level of subsidy Choose the subsidytax that maximizes country l s welfare 8 Both Governments can choose a SubwayTax Set up Two rms Firm 1 and Firm 2 from countries 1 and 2 respectively choose quantities simultaneously All their output is exported to a third country This is a sequential game where in Stage 1 both countries choose a subsidytax simultaneously Stage 2 after the subsidytaxes are known the two rms compete choosing their outputs simultaneously Each government maximizes its social welfare By choosing a subsidytax level governments are choosing their rm s marginal cost Steps Calculate NE quantities for arbitrary levels of subsidiestaxes Calculate the NE in subsidiestaxes assuming that the rms will use their NE quantities in Stage 2 Theoretical Result At the NE both countries subsidize their rms In that equilibrium both countries are worse off than without intervention IV Bertrand Com petition in Output market differentiated products 9 Eaton Grossman result that an export tax is optimal Set up Two rms Firm 1 and Firm 2 from countries 1 and 2 respectively choose prices simultaneously All their output is exported to a third country This is a sequential game where country 1 moves rst choosing an export subsidytax and then the two rms compete as indicated The government s objective is to maximize the country s welfare By choosing a subsidytax level the government is choosing rm 1 s marginal cost Theoretical Result The optimal policy is an export tax With the optimal tax pro ts for Firm 1 are obviously higher than without intervention In this case Firm 2 s pro t also increase Therefore both countries are better off than without intervention Steps Calculate NE prices for an arbitrary level of subsidy Choose the subsidytax that maximizes country 1 s welfare 10 Both Governments choose a SubwayTax Set up Two rms Firm 1 and Firm 2 from countries 1 and 2 respectively choose prices simultaneously All their output is exported to a third country This is a sequential game where in Stage 1 both countries choose a subsidytax simultaneously Stage 2 after the subsidytaxes are known the two rms compete choosing their prices simultaneously Each government maximizes its social welfare By choosing a subsidytax level governments are choosing their rm s marginal cost Steps Calculate NE prices s for arbitrary levels of subsidiestaxes Calculate the NE in subsidiestaxes assuming that the rms will use their NE prices in Stage 2 Theoretical Result At the NE both countries tax their rms In that equilibrium both countries are better off than without intervention

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