### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Note for EconS 571 with Professor Gibson at WSU 02

### View Full Document

## 18

## 0

## Popular in Course

## Popular in Department

This 8 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Washington State University taught by a professor in Fall. Since its upload, it has received 18 views.

## Similar to Course at WSU

## Popular in Subject

## Reviews for Note for EconS 571 with Professor Gibson at WSU 02

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

MONOPOLISTIC COMPETITION MODEL Key ingredients 0 Consumer utility log 00 l plog 1 cf taste for variety of differentiated goods 0 Production of differentiated products y j l b maXZj f 0 increasing retumsfixed costs Assume that good 0 the agricultural good is produced with perfect competition and the constant returns to scale production function yozgoa but that there are n manufactured goods that are produced with monopolistic competition and the increasing returns to scale production function specified above The representative consumer solves maX log 00 lplogZlcf s t p000 ZHpjcj S w gt cj0 0 0 u 6 MRS equals price ratio u co p0 pel 9 cl Z1CJ P1 1 60 1 Producer of good 139 solves the consumer s problem to find the indirect demand function p f multiplying by c EPICp p060 60 p 21 3 Zil summing over 139 2110 We 12 p c 11 simplifying p0 CO 2 poo0 w from previous equation and budget constraint w Indirect demand function Pro ts of rm 139 ply wbx wf revenuevariable costs xed costs We suppose that the rm chooses its output y to maximize its pro ts assuming that the outputs of all other rms are constant and that prices will adjust to clear the markets of each good This is the Cournot competition assumption To maximize profits the rm sets MR M C We set C y in the indirect demand function this is the assumption that the price of good 139 adjusts to clear the market for good 139 and plug this function into expression for profits M w 6 y yI wbyI wf p 2 Z n To maximize profits the rms sets the rst derivative of this expression equal to 0 that is MR M C 0 w 21 yj 1ny yf pyf 1 2 ZWY wb0 Set w l as numeraire Since rms are symmetric we know that there is an equilibrium in which y 7 if y gt 0 Znquotm7 39l VP J b 2 W Z pm 1 J b 2 n2 pn 1 y 2n2b Z bn pl 2 p p 2ny 2ny pn l The pro ts of typical firm are 2 pn 1 b py y f 2quot M f We assume that there is free entryexit until pro ts equal zero 2fn2 1 pn p20 The pro ts of typical rm are Y pn 1 b py y f 2quot M f We assume that there is free entryexit until pro ts equal zero 2fn2 1 p7n p70 n 1 pJ1 p22 4p2f 4f Equilibrium An equilibrium of the monopolistic competition model is the number of manufacturing rm ft a price e for the agricultural good a price 7 for each manufacturing rm that operates at a positive level a wage rate vii a consumption plan 80 cl 82ca production plans J30 20 for the agricultural good and f2 2 j for each manufacturing firm that operates at a positive level such that 0 Given 0j71f72f7 and ft the consumer chooses 5081525 to solve maX log 00 1plogZlcf s t ocoz f7jcj SW C 20 pO wso 0if ogt0 0 Given the indirect demand function p 01 c c that comes from solving the representative consumer s utility maximization problem firm j chooses f2 to solve maX pjA1yjj yj fubyj vif jjj fvbjj fSO 0if 3 gt0 where 27 pjylyjyn o y lbmaX2 f 0j12ft Numerical example b1f2 p12 249 n 2 245 42452 42454 Utility log 245210g715m 74960 Homogenous of degree one representation of utility a real income index eXp12log 245210g715 2 eXp1274960 4244 An integral number of firms There is a problem with our concept of equilibrium if the number of firms ft does not turn out to be an integer Suppose for example that b1f2p12 2490 Then when we solve n 245 quot2452 42454 8 a we obtain ft 622342 How do we interpret this solution There are two approaches that we could take 1 We could restrict ft to be an integer and let it be the largest number of rms for which pro ts are nonnegative In this case however there can be positive pro ts in equilibrium These pro ts need to be earned by someone If we give them to the representative consumer then the consumer s budget constraint becomes oco Zlf7jcj S WZH where fl are pro ts Everything becomes a more complicated even in this simple model with only one market with monopolistic competition Things become much more complicated in applied models with many such markets 2 We could think of ft as being an integer up until we compute the number of rms at which we point we simply calculate a real number This is the approach that economists typically use in applying this sort of model Reinterpreting the model as a model of international trade We can reinterpret this model as a model of international trade among countries that are identical except for their sizes as measured by their labor forces Z Consider the numerical example in which b 1 f 2 p 1 2 and there are two countries one in which 21 441 and the other in which 22 49 We can think of these countries as being the United States and Canada respectively In the integrated equilibrium of the world economy poW1 2 nzm W2622342 yszl szwzlmm 2n b 22622342 p71 zzy 4 bquot M20327 2nyquot 2ny pn 1 612342 yo 5 245 2p0 21 To calculate consumption of each variety in each country we just divide the world production of the variety 7 proportionally In country 1 for example 1 El 1E 2f 19367 17430 6 Z 490 We also divide the production and the consumption of the agricultural good proportionally 1441490ft 441490622342 560108 772 49 490 49 490622342 62234 and 3 4414900 441 490245 2205 49490f0 49490245 245 Strictly speaking there is nothing in this model that pins down the location of production of the agricultural good We are calculating a symmetric equilibrium Trade Equilibrium A1 A1 A1 fl p0 p 1 1 60 51 yo 0 7 country1 560108 10 20327 10 2205 17430 2205 2205 19367 39367 country2 62234 10 20327 10 245 01937 245 245 19367 39367 Utility Real income index Notice that not surprisingly the real income in country 1 is 9 times greater than that in country 2 Gains from Trade To calculate the gains from trade we can compute the autarky equilibria for both countries We 121 log 2205 2log6223421743012 142133 122 log 245 2log6223420193712 98190 em 122005 e11 2 13557 have already calculated this equilibrium for country 2 Autarky Equilibrium a 13 i w 6 5 9 2 7 2 country 1 561075 10 20363 10 2205 19300 2205 2205 19300 39300 country 2 70000 10 23333 10 245 15000 245 245 15000 35000 Utility Real income index 121 log 2205 2log5610751930012 141080 122 log 2452log 705 74960 e11 2 115748 em 4244 The smaller country country 2 has the most to gain from trade In country 1 real income goes up by 54 percent 122005115748 10541 In country 2 real income goes up by 2194 percent 135574244 31944

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.