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# ARE100B Midterm 2 Study Guide for Whitney ARE 100B

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This 4 page Study Guide was uploaded by Jessica Notetaker on Sunday November 8, 2015. The Study Guide belongs to ARE 100B at University of California - Davis taught by Marilyn Whitney in Summer 2015. Since its upload, it has received 173 views. For similar materials see Intermediate Microeconomics in Agricultural & Resource Econ at University of California - Davis.

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Date Created: 11/08/15

I. Cournot Model A. Concepts -‐ Simultaneous Quantity Setting , holding others’ Q as a constant. -‐ Market price of good falls as number of oligopolists in the market rise. -‐ Given other firm’s production, each firm chooses optimal output . -‐ One weakness of this model is that the quantity setter assumes rivals don’t do anything to their quantities (constant Q) when it increases its output. In fact, rivals could potentially drop their output levels. -‐ Since market price is dependent on the total output, profits of ot her firms are directly affected by the quantity of one firm. B. Solve for 2 firms 1. Find inverse demand function P=f(Q) 2. Assume q2 is fixed and write out the profit function for firm 1 3. Take the derivative of profit function of firm 1 and set it e qual to 0 to get its reaction function 4. Now maximize firm 2’s profit function and find its reaction function. 5. Substitute one reaction function into the other and solve. C. Solve for “N” identical firms 1. Find inverse demand 2. Find each firm’s Cournot MRi by using shortcut (e.g. -1Q -.05Q-.05qi) 3. Equate MRi=MCi 4. You know that Q=N*qi so plug in for Q in MRi. 5. Solve for qi function; if N known solve Q=N*qi, P, and profit P*qi* -TC(qi*) 6. Producer Surplus (PS) = profit1 + profit2 + FC1 + FC2 II. Bertrand Model A. Concepts -‐ Simultaneous price setting, no other firm can profit more by charging different price. -‐ Given other firms’ prices, each firm chooses optimal price. -‐ Result is same as perfect competition in the short -run. -‐ Barriers to entry, such as control or patents, determine number of firms, N, in the long -run. So, number of firms is fixed and more firms can’t enter. -‐ Firms compete by undermining each other’s prices B. Solve for same TC functions 1. Set P=MCi 2. Invert to get qis=f(P) u sing MCi 3. Find Qs by multiplying number of oligopolists by function qis 4. Set Qs=Qd 5. Solve P by plugging in to Qd, qi by plugging in to qis function, Q by N*qi C. Solve for different TC functions 1. Set P=MC1 and P=MC2 2. Invert to get q1s and q 2s using MC1 and MC2 respectively 3. If market price is between the 2 starting prices, only the firm with smaller starting point produces (Qs=qxs where x is the firm number). If market price is above the firm with higher starting price, both will produce ( Qs=q1s+q2s). 4. First assume that both firms produce (if P is less than firm with higher starting price, then other firm’s little q will turn out negative) 5. Set Qs=Qd and solve for market price and each firm’s level of output and market output (q1+q2). III. Stackelberg Model A. Concepts -‐ Leader firm can set its output before its rival follower when leader enters market first. -‐ Leader foretells what follower will do. Before the follower does anything, the leader will deceive him by choosing its output level. -‐ Leader makes more while rivals shrink. B. Solve for 2 firms with same TC function 1. Assume firm 1 is leader and firm 2 is follower 2. Find follower’s reaction function q2=f(q1) (same as Cournot) 3. Profit2 = P(Q)q2 – TC2 (Q=q1+q2) 4. Derive profit2 by setting q1 constant and optimal profit equal to 0 . 5. Get equation q2=f(q1) 6. Do the same for the leader’s problem but plug q2 into firm 1’s profit equation first before deriving 7. You will find that there is a Stackelberg effect when negative becom es positive 8. Derive profit function of firm 1 and set it equal to 0 9. Solve for q1, q2 by plugging in to its reaction function, Q, and P 10. If they have different total cost functions, just change the TCs IV. Monopolistic Competition Competitive Fring e A. Concepts -‐ Other firms copy price of one firm -‐ Large firm acts as monopolist while small firms are price -takers. -‐ Charge prices above marginal cost -‐ Elasticity of residual demand curve gets smaller as monopolistic competitive firms decrease. B. Solve for given amount of firms 1. Find qid by simplifying the function Qd/N 2. Find inverse demand P=f(qid) each firm’s inverse demand 3. Set MRi=MCi 4. Solve for qi, Q (qi*N), P (use each firm’s inverse demand) 5. No firms will enter if profit is greater than 0, so not in long run C. Solve for one large firm and 2 small firms 1. Set P=MCs 2. Find qs = f(P) 3. Multiply 2(qs) to find Qs 4. Find dominant firm’s residual demand QDL = Qd -Qs 5. Find inverse demand PL = f(QL) 6. Proceed as monopolist 7. Set MRL=MCL and solve for QL. 8. Find P* by plugging in Q to QD function 9. Solve for qs* little firms by plugging in P* into the qs function 10. Q*=QL*+Qs* V. Cartel Method A. Concepts - Work together to raise profits - Changes in one firm’s outp ut affects profits of all members in cartel. - Solves like multi-plant monopolist B. Solve for N firms with one TC function 1. Set MR(Q)=MC(qi) where Q is N*qi 2. Solve for qi* 3. Solve for Q* by N*qi 4. Solve for P* by plugging in to inverse dem and function C. Solve for two firms with 2 different TC functions 1. Find inverse demand 2. Set MR(Q)=MC1=MC2 3. Set MC(q1) = MC(q2) 4. Solve for q2=f(q1) 5. Set MR(Q)=MC1 knowing Q=q1+q2 and plug in for q2 6. Solve for q1* 7. Solve for q2* 8. Solve for Q by adding q1* and q2* and P* by plugging in to inverse demand VI. Auctions A. English/American Style - Bids start small and rise by some increment - Bidder with the highest reservation price will win B. Dutch Style - Bids start high and fall by some increment - We don’t know who wins C. Sealed Bid - Bids are pre-determined and are locked in. These bids have to be sent in by a certain deadline. - The highest bidder could either pay highest bid price, “first -bid auction”, or pay the se cond highest bidder’s price, “second -bid auction” D. Electronic Auction - Ex: eBay - There is a deadline -There are problems with auctioning online. 1. Sniping: many people bid at last minute 2. Shilling: there could be false buyers VII. Auction Values A. Unique Value Auction - Bidders have different reservation prices for different items - Ex: art and antiques B. Common Value Auction - All bidders agree on one price and they have to estimate the costs. Over time, changes are actual prices are close to the median. - Winners curse: bidders love the feeling of winning and end up bidding too much and paying more than what it’s really worth. VIII. Asymmetric Information -‐ There could be false advertisements causing buyers to not know true quality of a pr oduct -‐ There could be different available prices that buyers don’t know about -‐ Examples: o Online prices may no longer be consistent o Shops that sell overpriced items to tourists o Company creates different names for same product model so that buyer will not be able to find the item with same name at a different store (can’t comparison shop). IX. Game Theory Firm B Strategy 1 Strategy 2 Strategy 3 Firm A Strategy 1 7, 6 1, 2 -9, -9 Strategy 2 -1, -3 6, -7 5, 11 Strategy 3 3, 5 2, 10 4, 7 How to find if Firm A or B has dominant strategy -‐ For Firm A, look at the first numbers vertically by column o Out of 7, -1, 3 which one is greatest? 7 o Out of 1, 6, 2 which one is greatest? 6 o Out of -9, 5, 4 which one is greatest? 5 There is no dominant strategy since in once of them A chooses strategy 1 and two others A chooses strategy 2 -‐ For Firm B, look at the s econd numbers horizontally by rows o Out of 6, 2, -9 which one is greatest? 6 o Out of -3, -7, 11which one is greatest? 11 o Out of 5, 10, 7 which one is gr eatest? 10 There is no dominant strategy since B chooses strategy 1, 2, and 3 How do you use maxi -min approach? -‐ For Firm A, look at the first numbers horizontally by rows. o Out of 7, 1, -9 which one is the least? -9 o Out of -1, 6, 5 which one is the l east? -1 o Out of 3, 2, 4 which one is the least? 2 The greatest out of the three is 2 -‐ For Firm B, look at the second numbers vertically by column o Out of 6, -3, 5 which one is the least? -3 o Out of 2, -7, 10 which one is the least? -7 o Out of -9, 11, 7 which one is the least? -9 The greatest of the three is -3 -‐ Now, find the initial outcome: Firm A chooses Strategy 3 and Firm B chooses Strategy 1 o Their initial outcome is (S3, S1) with payoffs (3,5) Is this Nash equilibrium? o No, because A wants to switch to S1 because 7>3; B wants to switch to S2 because 10>5 o Now they are at ( S1, S2) with payoffs (1,2) where they are both worse off. o Result: Cycle back and forth Is there any Nash equilibrium at all? o Yes, at (S1, S1) with payoff (7,6) and (S2,S3) with payoff (5,11)

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