×

Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

Create a StudySoup account

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

or

By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

by: Paul Hickey

74

0

12

Microeconomic Theory 312: Economics 312

Marketplace > Arizona State University > Economcs > Economics 312 > Microeconomic Theory 312
Paul Hickey
ASU

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

Why put in your email? Get access to more of this material and other relevant free materials for your school

Exam 2 & 3 review notes
COURSE
Microeconomics
PROF.
Brian Goegan
TYPE
Study Guide
PAGES
12
WORDS
KARMA
50 ?

Popular in Economcs

This 12 page Study Guide was uploaded by Paul Hickey on Tuesday January 5, 2016. The Study Guide belongs to Economics 312 at Arizona State University taught by Brian Goegan in Summer 2015. Since its upload, it has received 74 views. For similar materials see Microeconomics in Economcs at Arizona State University.

×

Reviews for Microeconomic Theory 312:

×

×

What is Karma?

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

Date Created: 01/05/16
Intermediate Macroeconomics ECN 312 – Summer 2015 Lecture 18: Exam 2 Review We will use the following production function for this review: 1/2 1/4 ???? = ???? ???? 1. Derive the firm’s cost function. The cost function is found by solving the firm’s cost-minimization problem: min???????? + ???????? ????.????. ???? = ???? 1/???? 1/4 Step 1: Substitute the constraint into the cost function. 4 4 ???? =???? → min???????? + ???????? ???? 2 ????2 Step 2: Get the First-Order Condition ???? 2???????? 4 = ???? − 3 = 0 ???????? ???? Step 3: Solve for k. 4 4 1/3 2???????? 3 2???????? 2???? 4/3 ???? = ???? 3 → ???? = ???? → ???? = ( ???? ) ???? Step 4: Get l. ????4 ????4 ???? 2/3 4/3 ???? = 2 = 1/3 2 = ( ) ???? ???? 2???? 4/3 2???? [( ???? ) ???? ] Step 5: Plug back into the cost function and simplify. 1/3 2???? 4/3 ???? 2/3 4/3 ???? ????,????,???? = ????( ???? ) ???? + ????( 2???? ) ???? 2???????? 3 1/3 ???????? 3/2 2/3 ???? ????,????,???? = ( ) ???? 4/3+ ( ) ????4/3 ???? 2???? 2 1/3 4/3 0.5 2/3 4/3 ???? ????,????,???? = 2???????? ) ???? + 0.5???????? ) ???? 2 1/3 0.5 2/3 4/3 ???? ????,????,???? = [ 2???????? ) + 0.5???????? ) ] ???? For ease, let’s assume w and r are set to whatever they need to be to make it: 3 ???? ???? = ???? 4/3 4 2. Break it down into variable costs, fixed costs, average costs, and marginal costs. Variable Costs These are anything with a y in it. Which is all of it. Variable costs are: 3 ???? ???? = ???? 4/3 ???? 4 Fixed Costs These are anything with a y in it. So a +5 or +20 would be fixed costs. Here there are none. However, an excellent challenge to prepare you for the exam would be to try and figure out a production function that would give fixed costs. Cause the one on the exam does. Average Costs Average costs are: ???? ????) 3????4/3 3 ???????? ???? = = 4 = ???? 1/3 ???? ???? 4 Marginal Costs To get these, we take the derivative of the cost function with respect to y. ???????? ????) 1/3 ???????? ???? = ???????? = ???? This also represents the minimum price at which the firm is willing to supply the y unit of a th good. That is, if the firm has made 26 units, and we want them to make a 27 , at a minimum we will have to pay them \$3, because their cost to make the 27 unit is= 3. Of course, that means that ???? = ????3is the inverse supply curve, since supply represents the minimum price at which the seller will sell that many units of the good. Thus, we get the supply curve by rearranging and solving for y. ???? = ???? 3 3. What happens if this industry is dominated by a monopoly? The monopolist’s profit maximization problem takes demand into account. They want to: max???? ???? ???? − ????(????) ???? 1 Step 1: Enter in the inverse demand function and cost function . Let’s say demand is: ???? = 100 − ????. Then: max 100 − ???? ???? − ???? 1 2 ???? 2 Step 2: Get the first-order condition. ???????? = 100 − 2???? − ???? = 0 ???????? If we wave our math wand: ???? ≈ 33.33 Step 3: Get other relevant variables. ???? = 100 − ???? = 100 − 33.33 = 66.67 ???? ???? = ???????? = 33.33 ∗ 66.67 = 2222.22 1 2 ???? ???? = ????2= 555.56 ???? ????) 555.56 ???????? ???? = = = 16.67 ???? 33.33 ???? = ???? ???? − ???? ???? = 2222.22 − 555.56 = 1666.67 Step 4: Graph it. I’ll do this on the board. 1I am switching this up because the math gets needlessly hard. 2Hope you didn’t miss class! 4. Now let’s try Stackelberg! This model has two firms, where firm 1 is the leader, and firm 2 is the follower. Step 1: Set up the follower’s problem. max???? = 100 − ???? − ???? ???? − ???? 1 2 1 2 2 2 2 Step 2: Get the first-order condition and so2ve for y . ???????? ???????? = 100 − ???? 1 2???? −2???? = 2 2 100 − ???? 1 ????2= 3 Step 3: Enter this into the leader’s problem. 100 − ???? 1 max???? = (100 − ???? − 1)???? − ???? 2 1 3 1 2 1 Step 4: Get the first-order condition and solve. ???????? 100 2 ???????? = 100 − 2???? 1 3 − 3 1 ???? =10 1 ???? = 18.18 1 Step 5: Get other variables of interest. 100 − 18.18 ???? 2 = 27.27 3 ???? = 100 − 18.18 − 27.27 = 54.55 1 ????1= 54.55 ∗ 18.18 − 18.18 = 826.46 2 1 ???? = 54.55 ∗ 27.27 − 27.27 = 1115.75 2 2 Neat! The follower is winning in this case! 5. Ready! Set! Cournot! Cournot has both firms choosing output simultaneously. Step 1: Set up the profit function for both firms. ???? = 100 − ???? − ???? ???? − ???? 1 2 1 1 2 1 2 1 1 ????2= 100 − ???? −1???? ???? 2 ????2 2 2 Step 2: Get first-order conditions for both. ???????? 1= 100 − 2???? − ???? − ???? = 0 → ???? = 100 − ???? 2 ???????? 1 1 2 1 1 3 ???????? 2 100 − ????1 = 100 − ???? 1 2???? 2 ???? =10 → ????2= ???????? 2 3 Step 3: Use the system of equations to solve. 100 − ???? 100 − 1 100 100 1 ???? 1 3 = − − ???? 1 3 3 9 9 8 200 200 ???? = → ???? = = 25 9 1 9 1 8 100 − 25 ????2= 3 = 25 Step 4: Get other relevant variables. ???? = 100 − 25 − 25 = 50 1 ????1= 50 ∗ 25 − 25 = 937.5 2 ???? = 50 ∗ 25 − 25 = 937.5 2 2 Huzzah! 6. Yes We Bertrand! Bertrand has each firm setting the price simultaneously, with the promise that they can meet market demand at that price. Competitively, firms set price equal to marginal cost. Step 1: Get Market Supply Each firm will supply ???? = ????, as this is where p is equal to the marginal cost. Market supply adds these together for all firms, so: ???? ???? = ???? 1 ???? =2???? + ???? = 2???? Step 2: Set this equal to market demand and solve. Well, we have inverse market demand, so let’s reverse to inverse market supply: 1 ???? = 2???? → ???? = 2???? Now set it equal to demand: 1 ???? = 100 − ???? 2 ???? = 66.67 Step 3: Get the market price. 1 1 ???? = ???? = 66.67 = 33.33 2 2 Step 4: Get other relevant variables. ????1= ???? = 33.33 ????2= ???? = 33.33 1 ????1= 33.33 ∗ 33.33 − 33.33 = 555.56 2 1 2 ????2= 33.33 ∗ 33.33 − 23.33 = 555.56 Note also that for both firms, the marginal cost is y, which is equal to the price. That’s a confirmation that we are at the competitive equilibrium. 7. Tonight, we dine in CARTEL! Cartels maximize the profits of the industry. Step 1: Set up the industry profit equation. 1 1 ???? = 100 − ???? −1???? 2)???? 1 ???? 2) − ???? − ???? 2 2 1 2 2 Step 2: Take the first-order conditions. ???????? = ???? + ???? )(−1 + 100 − ???? − ???? )1 − ???? = 0 ???????? 1 1 2 1 2 1 100 − 2????2 → ???? 1 3 ???????? = ???? +1???? 2)(−1 + 100 − ???? − 1 2)1 − ???? 2 0 ???????? 2 100 − 2???? → ???? 2 1 3 Step 3: Use the system of equations to solve. 100 − 2 100 − 2????1 ????1= 3 = 20 3 ???? = 100 − 2 ∗ 20= 20 2 3 Step 4: You know the drill. ???? = 100 − 20 − 20 = 60 ???? = 60 ∗ 20 − 20 = 1000 1 2 1 2 ????2= 60 ∗ 20 − 22 = 1000 Note that out monopolist did \$1,666.67 in profits, but this cartel is doing \$2,000. Why? 8. Compare the Models Specifically, calculate the marginal cost of the last unit produced in each model and then compare it to the price charged. Model MC P Diff. Monopolist 33.33 66.67 33.33 Stackelberg 27.27 54.55 27.28 Cournot 25 50 25 Bertrand 33.33 33.33 0 Cartel 20 60 40 Why does this matter? What questions could I possibly ask you where you would need to do this? 9. Some other questions. 1 Try this all again, but use the cost function: 2 ???? = ???? + 100. Solve the Cournot for n firms with this new cost function. Use your solution to the Cournot model with n firms to determine the maximum number of firms this market could sustain.

×

×

BOOM! Enjoy Your Free Notes!

×

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

Bentley McCaw University of Florida

"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!"

Amaris Trozzo George Washington University

"I made \$350 in just two days after posting my first study guide."

Jim McGreen Ohio University

Forbes

"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."

Become an Elite Notetaker and start selling your notes online!
×

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.