Econ 221 Exam 3- Study Guide
Econ 221 Exam 3- Study Guide ECON 221 003
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This 14 page Study Guide was uploaded by Lauren Vagnoni on Wednesday April 13, 2016. The Study Guide belongs to ECON 221 003 at University of South Carolina taught by John Gordanier in Spring 2016. Since its upload, it has received 25 views. For similar materials see Principles of Microeconomics in Economcs at University of South Carolina.
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Date Created: 04/13/16
Econ 221 Gordanier Study Guide Exam 3 Highlight = Important Principle Highlight = Important Concept Highlight = Key Term Future Value and Present Discounted Value Future Value You have $100 that you have in an account earning 10% each year. How much will you have in the account in 1 year? In one year you will have $110. You will have the $100 and 10% of $100 that you earned in interest V1 = V0 + rV0 = V0(1 + r) 110 = 100 + (0.1) 100 = 100(1.1) What about in year 2? $110, plus 10% of 110 or $11 for a total of $121 V2 = V1 + rV1 = V1(1 + r) 121 = 110(1.1) = 100(1.1)(1.1) = 100(1.1)2 General formula for future value VT = V0(1 + r)^T VT = 100(1.1)^T Rule of 70 The rule of 70 refers to an approximation for the length of time it takes for a value growing at x% to double There are currently 4,000 followers on twitter, if the number of followers is constantly increasing at 5% The number of periods needed to double is 70/5=14. The denominator is 5 and not .05 Present Discounted Value Present Discounted Value can be thought of as solving the reverse of the future value question PDV= (FV)/ (1+r)^T Example: What is the PDV of $5,000 given in 2 years if the interest rate is 4% PDV= (5000)/(1.04)^2 Can also calculate the PDV of a stream of costs/benefits that is infinite PDV= 5/1.1 + 5/1.1^2 + 5/1.1^3 The PDV of a stream of costs/benefits, X, that begins in exactly one year with a rate r is given by PDV= X/r What is the PDV of a financial instrument that pays the holder $10 every year, starting exactly 1 year from now if the interest rate is 4%? PDV= 10/.04=250 Costbenefit Analysis PDV can also be used to perform a cost benefit analysis This allows us to compare the costs that might be spread across many periods and benefits which also might be spread across periods. Costs Types of costs Total costs Total costs are divided into two components: fixed costs and variable costs Fixed costs are those costs that do not vary with output, while variable costs do. Example: Lemonade stand FC are stand, juicer VC lemons, sugar, 5year olds, cups TC all Example: TC=100 + 5q, FC=100, VC=5q, TC= FC+ VC Average Costs Average costs are defined by dividing the relevant cost (total, fixed, variable) and dividing by output Marginal Cost change TC / change Q = change VC / change Q Production and Costs Average Product of Labor The average product of labor is just the total output divided by the number of workers At first increasing the number of workers quickly increases the amount of output; at some point the additional output that occurs from an additional unit of labor begins to decrease Marginal Product of Labor The marginal product is measuring how much an additional worker produces MC varies inversely with MP L and AVC varies inversely with AP L The AVC will have its minimum where it crosses the MC Whenever the underlying production technology is such that the marginal product is at first increasing, but eventually decreasing the cost curves will have their usual “U” shape Finding Total Costs from a graph Given a graph of MC, AVC and ATC we should be able to calculate Fixed Cost, TVC and TC at any quantity TC= ATC*Q, so TC will be a rectangle with ATC on one side and Q on the other FC should be the same regardless of the quantity chosen, need to find a rectangle with AFC on one side and Q on the other. AFC is the distance between ATC and AVC in the graph Perfect Competition Profit Maximizing Output In competitive markets buyers and firms are price takers The firm’s output decision does not affect the price of the good The firm can sell as many units at the market price as it chooses to produce This implies that for an individual producer the demand curve he or she faces is perfectly elastic The market demand curve for ALL soybeans is downward sloping, but the demand curve fo an individual farmer is completely flat Profits Profit is the difference between total revenue and total cost The total revenue for a producer is the price times quantity Profit Maximizing Output Intro Economists assume that firms choose the quantity that maximizes the total profit. This occurs at the quantity where MC is equal to the price Finding the maximum of the profit function can be done by taking the derivative of the profit function with respect to Q, and settings it equal to zero The derivative of TC is MC, profit is maximized when when P=MC Minimum of the AVC is called the shut down point Firm Supply Competitive Equilibrium in the shortrun Using an individual’s supply curve to construct a market supply curve which combined with market demand determines the shortrun equilibrium price Example: We are given the following demand curve and told that there are 30 firms each with an identical cost structure as depicted below In equilibrium we know that quantity supplied must equal quantity demanded We found the individual supply curve for each firm based on the cost structure, to find the market supply we just need to multiply the quantity at each price by the number of firms That is to say Q s = q* N, where q is the output for each firm From this we see that the shortrun equilibrium price is 8. At this price each firm is producing 220 units and profits per firm at (86.75) * 220 Competitive Equilibrium in the Long Run The main distinction we are going to make for the longrun vs. the short run is that we are going to allow firms to choose to either enter the industry or exit the industry (and avoid paying any fixed costs). Recall that the costs include any opportunity costs so that if firms have negative profits it implies that they can do better by exiting the industry If profits are positive then firm will wish to enter the industry If profits are zero, firms have no incentive to leave or enter In the longrun equilibrium there is no longer any incentive for firms to enter or exit the industry The longrun equilibrium must be at a price where every firm is earning zero economic profits We reach the long run equilibrium by the effect of firms entry/exit decisions on the market place Positive Profits: SInce firms will wish to enter the industry when profits are positive, the quantity supplied at each price will now be larger (Since N is increasing), this the market supply curve shifts to the right. As supply shifts to the right, the market price decreases Negative Profits: As firms exit the industry the quantity supplied decreases at each price. The supply curve shifts to the left and the market price rises. The longrun equilibrium must be at a price that achieves zero profits for each firm (when they are producing at the profit maximizing output). The only price that does this is the minimum of the ATC curve Cost Structure If the cost structure is the one above, then the longrun equilibrium (regardless of demand) is at a price of $6.50. Each firm will produce q= 210 units of output. The firm produces where P=MC, but due to market pressure, in the longrun each firm is producing at the minimum possible ATC. This is another dimension in which the market induces efficient behavior LongRun number of firms Since we know the longrun output for each firm in the industry, we can find the longrun number of firms given a demand curve and cost structure To do this we first find the Q D at the longrun price. Since we know that Q D=Qs,we know that QD= q* N Monopolies Profit Maximizing Monopolist Intro Profit maximizing monopolist describes the output decision of a single price monopolist Just as in the argument under perfect competition, the monopolist maximizes its profits by producing at an output level where MR= MC. When thinking about the effect of increasing output by one unit, the additional revenue is captured by MR and the additional cost by MC, if marginal revenue exceeds marginal cost then producing the unit increases profit Marginal Revenue Under perfect competition MR was simply the price of of the good, but under a monopoly the price of the good is not exogenous, but determined by the choice of quantity This means that the MR for a monopolist is a function of its output choice The MR for the monopolist is less than the price There are two factors affecting MR: the price and the revenue lost from reducing the price on the previous units. In this picture we have the shaded the total revenue from outputs Q1 and Q2. When monopolist increases output to Q2 the monopolist gains the dark blue area as they sell more units at P2. However, the monopolist loses the pink area representing the higher price she used to charge times the number of units she used to sell. Output Now that we have derived marginal revenue we can find the profit maximizing output by looking for where MR and MC cross . The quantity is labeled Q^M. The price is the height of the demand curve at this quantity and labeled P^ M We can also determine the profits for the monopolist the way we did in perfect competition, by looking at the quantity being produced for the distance between price (where Q hits demand curve) and ATC and then multiply that profit per unit by the number of units Deadweight Loss The deadweight loss if found between the demand curve and marginal cost on the units between the monopoly output and the efficient output The efficient output level is where demand intersects with marginal cost Regulating a Monopoly Intro Marginal Revenue < Price Lower price to raise Q Produce where MR= MC Efficient Price Regulation Since the monopoly creates DWL without any intervention it is natural to think that an intervention might be able to correct for the market failure. When we saw market failure previously, with the example of externalities, we suggested that a tax could be used to correct negative externalities or a subsidy for positive externalities Lowering the marginal revenue curve for the monopolist lowers the intersection between MR and MC. The tax actually increases the DWL from the monopoly. The more direct approach is to simply set a price ceiling for the monopolist By setting a price ceiling the monopolist no longer has to consider the effect increasing output has on the price. That means that the MR for the regulated monopolist is equal to the price ceiling. A Natural Monopoly A natural monopoly is a firm where the ATC is always decreasing (for the relevant quantities) implying that one firm can always produce a given output cheaper than two firms could In the graph, a single firm would produce 20 units with a total cost of 20*4=80 but if there were two firms that each produced 10, then the cost of production would be 10*5=50 for each firm; a total cost of 100 Unregulated When unregulated that choice is the same for a regular monopoly The optimal output is where MR=MC and then we find the price off of the demand curve at that quantity In picture, Q^M=10 and P^M= 7, we can find the profit and DWL from the monopoly as well. The profit will be the rectangle formed by the distance between price and ATC and quantity 10 and the vertical axis. The DWL will be the area between MC and demand that is formed between Q^M=10 and Q^E=26 Efficient Price Regulation Set the price equal to the height of the demand curve where demand intersects MC. Quantity for the monopoly is then the efficient quantity and DWL= 0 However, when we find the profit at this quantity we see that price is below ATC, thus there is a loss. We can calculate this because the distance between price and ATC is exactly equal to the distance between ATC and AVC. This means that P ATC = ATC AVC = AFC so when we multiply this by quantity the size of the loss is equal to the size of the fixed cost. Since fixed costs are the same at any quantity we can find this by looking at any Q Thus, the loss is equal to the fixed costs =(53)*10=20 Zero Profit Regulation Since the efficient price regulation leaves the firm earning a negative economic profit it is not considered feasible As alternates we consider zeroprofit pricing and an efficient price plus a subsidy Under zero profitpricing the regulator sets price as low as possible without causing the firm to earn negative profits. This is down by looking at the intersection of the ATC and the demand curve Efficient Plus Subsidy This is our attempt to accomplish both goals at the same time; eliminate DWL and leave the firm with at least zero economic profits. To do this we will regulate the firm just as we did under the efficient price, but we will give them a lump sum subsidy equal to their fixed costs. This leaves them with zero economic profits Games Dominant Strategy Dominant strategy: always the unique best response Pasta and wine is the unique pure strategy equilibrium What would happen if my wife got to pick the drink first, then I got to observe her choice and make a selection? She would know that I would observe her choice and then react. So if she brought home beer, I would get pizza, whiskey and I would get steak, wine and I would get pasta. The payoffs to her for beer would be 1, whiskey 4, and wine 2. Thus she would buy whiskey and I would buy steak Game theory Dominant strategy: always a unique best response Nash equilibrium: each player is playing a best response to the other player ** Watch video to explain** Location Competition Customers buy from whoever is closest
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