Introduction to Microeconomics: Course Notes P2

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Economics for Management Studies
Michael Krashinsky

18 October 2012 For the exams, ignore the origins of TC/AC/MC etc., they will just assume we know them and work with it. Typical graph of AC, AVC, MC: AFC is a constant divided by quantity, is always going down but starts off extremely high (asymptotic). AVC begins to rise at a certain point because of diminishing marginal productivity. If AC is the sum of AFC + AVC, it starts off high because AFC is very high, then it lowers, but comes back up because of the rising VC. AVC + AC start becoming closer and closer together as AFC asymptotes towards 0. MC goes through the minimum point on the AVC and AC curve – this always must be true. Example: TC = 400 + 5q + q , q>2 AC = 400/q + 5 + q Find minimum of AC, AVC FC = 300, q>2 AFC = 300/q Min AC = 45 at q = 20 2 VC = 100 + 5q + q , q> 2 AVC = 100/q + 5 + q Min AVC = 25 at q = 10 Minimum of the curve is always where the first derivative is equal to 0. AC = 400/Q + 52+ q dAC/dQ = -400/q + 1 = 0 1 = 400/q2 q = 400 q = 20 Plug 20 into the AC curve, so AC (20) = 45 MC = 5 + 2q Min AC = 45 at q = 20 At q = 20 the minimum value of the AC and MC are the same. MC = 5 + 2q = 45 Min AVC = 25 at q = 10 At q = 10 the minimum value of the AVC and MC are the same. MC = 5 + 2q = 25 Notice the relationship of AC, AVC, and MC, this is no accident. AC = TC/q dAC/dq = 0 at min AC dAC/dq = [q(dTC/dq)−TC]/q2 AVC = TVC/q dAVC/dq = 0 at min AVC The only difference between variable cost and total cost is the fixed cost, so the derivative of total cost and total variable cost has got to be the same. Imagine looking at the function of average height of everybody in the room. Everybody is lined in order from short to tall. Then, we add one more person to the room (marginal person), that person’s height would be the marginal height. If the marginal person is taller, the average is pulled up, if the marginal person is shorter, it pulls the average is down. It must always pass through the minimum AC point. What would be sensible rule for firm to use in deciding how much labour to hire? Goal of firm is to maximize profits, this must include all costs: Profit = π = TR − TC Example: Owner runs a video store: Every week: $2500 in rental income, pay out $1000 for rental of space, $800 for new videos, getting an accounting profit of $700. ECONOMIC PROFIT must include ALL COSTS, including costs of any labour by owner, any interest on owner invested capital (more of an issue for large corporations). ACCOUNTING PROFIT > ECONOMIC PROFIT Accounting profit can be positive when economic profit zero or even negative. Keep hiring labour as long as one more worker adds more to revenue than it does to cost. As long as P < L P MP . Since MP is falling, this means produce where P = P MP . Q L L Q L In long run choose optimal amount of capital. Each SAC is associated with one level of capital (generally cost is lower in the long run than in the short run). Graph of every possible SAC you could have for every possible amount of capital: There is an optimal point associated with each level of capital. There are an infinite amount of curves. In the long run, you get to choose which of these curves you get to be on. For each level of output, you choose to be on the best possible curve – the lowest one. LAC = long run average cost curve. The LAC is defined by all the possible SAC, it is the envelop of all the SAC. The general shape of the LAC is U-shaped. The output associated with minimum efficient scale is called qMES. IRTS: Increasing return to scale, the bigger you get means more efficiency (IE: bigger grocery store has more variety). CRTS: Constant return to scale, where the scale does not seem to matter. This is the range where most of the firms are. DRTS: Decreasing return to scale, when firms become too big, things are harder to manage (IE: when enterprise gets so big people no longer know each other). Keep hiring labour as long as one more worker adds more to revenue than it does to cost. As long as P < L PQMP . Lroduce where P (CosL of one more worker) = P MP (ValQe ofLwhat extra worker produces). How much output should you produce? π = TR − TC dπ/dq = dTR/dq − dTC/dq = MR − MC =0 But if TR = PQQ, then dTR/dq = P (Qssuming PQ constant) dTC/dq = MC PQ = MC As long as marginal cost is below the cost of the output, produce it. If it is greater than the cost of the output, do not produce it. This resembles a supply curve. 22 October 2012 Perfect Competition is a particular model of how the economy works. We look at markets in which there are a lot of firms competing with each other. This is more than just an “abstract model,” in fact; perfect competition is the model underlying supply and demand. Assume:  Many firms (atomistic)  PRICE TAKERS  Homogeneous product  Perfect information (everyone knows what price is), no transaction costs  LAW OF ONE PRICE  Free entry and exit in long run q = output of firm Q = output of industry Example: TC = 400 + 5q + q , q>2 Min AC = 45 at q = 20 FC = 300 Min AVC = 25 at q = 10 Suppose P = 51 π = TR – TC = Pq – TC = 51q – (400 + 5q + q ) = -q + 46q – 400 dπ/dq = -2q + 46 = 0 2q = 46 q = 23 Maximize MC = 5 + 2q = 51 q = 23 2q = 46 π = -529 + 1058 – 400 = 129 q = 23 Suppose P = 47 2 2 π = TR – TC = Pq – TC = 47q – (400 + 5q + q ) = -q + 42q – 400 dπ/dq = -2q + 42 2q = 42 q = 21 Maximize MC = 5 + 2q = 47 q = 21 2q = 42 π = q = 21 Suppose P = 45 Suppose P = 35 q = 20 q = 15 π = 0 π = -157 Suppose P = 27 Suppose P = 23 q = 11 q = 9 (WRONG ANSWER)  0 π = -279 π = -319 (WRONG ANSWER)  -300 So the short run P = MC, as long as π > -TFC. (In this case -300. If you are doing better than -300, then produce, but as soon as your losses are greater than -300, shut the firm down). We can do this even more simply: Pq - TC > −TFC Pq - TVC - TFC > -TFC Pq - TVC > 0 Pq > TVC P > AVC LOGIC: “sunk costs” are gone, “don’t throw good money after bad.” As soon as price drops below AVC curve, produce 0. If the price is above the AVC, the supply curve is just the MC. If the price is below the AVC, the firm is going to shut down, and the supply of the firm is on the vertical axis (0). If the price of the firm is equal to the minimum AVC, then you lose your fixed cost whether you produce or not – you really do not care. MC above AVC If P = 25 TR = 250 MC = 5 + 2q = 25 TC = 550 q = 10 π = -300 Example: TC = 36 + 2q + q , q>2 FC = 20 TVC = 16 + 2q + q2 AVC = 16/q + 2 + q 2 dAVC/dq = -16/q + 1 = 0 => q = 4 AVC = 16/q + 2 + q = 10 MC = 2 + 2q q<2 is part where it is not marginal cost and is not defined. 2 0, if economic profits are positive, the firm is covering all of its costs, making a reasonable return on capital and getting reasonable compensation for the efforts (time) of the entrepreneur plus getting something extra (the economic profits). Positive profits make this a very attractive industry for entrepreneurs looking to make money. Buried behind this is the implicit assumption that there are entrepreneurs hunting for exactly these kinds of opportunities. So π > 0 leads these entrepreneurs to enter the industry as new firms. More firms π shift supply curve to the right, ENTRY  SUPPLY SHIFTS  PRICE FALLS PROFITS FALL. This continues until the entry stops, but entry continues as long as π > 0. So entry continues until profits are driven down to zero. They go down towards zero because as long as there is positive, you get more entry. Negative profits make this a very unattractive industry for entrepreneurs, because they are not earning a decent return on their efforts. As soon as they can (that is, in the long run when they can get rid of their capital), they leave the industry to look for better opportunities elsewhere. So π < 0 leads these entrepreneurs to exit the industry. Fewer firms, π shifts supply curve to the left, EXIT  SUPPLY SHIFTS  PRICE RISES  PROFITS RISE. This continues until the exit stops, but exit continues as long as π < 0. So exit continues until profits are driven up to zero. So, in both cases, profits are driven to zero. π = TR - TC = Pq - (AC)q π = q(P - AC) So profits are zero where P = AC We are in the long run, so this means that P must be driven to the minimum point on the LAC. Price must be driven to this point, if it is below this point; everybody is losing money, even in the long run. If it is above this point, somebody is making money so people will enter the industry and push the price down. The only place profits will be 0 in the long run is right at the minimum point on the AC (We assume there is only ONE LAC point to solve problems). P > min LAC  π > 0  entry P down, π up P < min LAC  π < 0  exit  P up, π up In each case, end up at P = min LAC and π = 0 To do “long run problems”, we must know the minimum point of the LAC (given) or will tell you the minimum point, both the value of q and the minimum LAC at that q, or will use a “trick” and tell you that the short run average cost curve touches the LAC at the minimum (that is, the SAC, which you will be given, and the LAC share the same minimum point, so that the minimum of the SAC is the minimum of the LAC). We assume that costs do not change as firms enter or exit called “constant costs.” Return to problem above where we start with 500 firms: TC = 98 + 4q + 2q2 FC = 48 Min AC at q = 7, AC = 32 Suppose that you are told that this also the minimum LAC. Case 1: Demand is P = 40 - .004Q We know that P = 32, because profits must be zero We know that each firm produces q = 7 From the demand curve, we know that 32 = 40 - 0.004Q Thus, Q = 8/0.004 = 2000 We know that Q = Nq  2000 = 7N N = 2000/7 = 286 (approx), so there must be 286 firms in the long run. Case 2: Demand is P = 52 - .004Q We know that P = 32, because profits must be zero We know that each firm produces q = 7 From the demand curve, we know that 32 = 52 - 0.004Q Thus, Q = 20/.004 = 5000 We know that Q = Nq  5000 = 7N So N = 5000/7 = 714 (approx), so there must be 714 firms in the long run. 29 October 2012 An invisible hand mechanism shifts resources around the economy. If consumers want more: Demand increases, price rises in short run, positive profits. In long run, entrepreneurs respond to lure of profits, shift resources into this sector by opening new firms. Production responds automatically to additional demand, at the end, prices return to minimum LAC. DEMAND INCREASES  PRICE INCREASES  SUPPLY INCREASES PRICE FALLS If consumers want less: Demand decreases, price falls in short run, negative profits. In long run, entrepreneurs respond to losses, shift resources out of this sector by closing firms. Production responds automatically to fall in demand, at the end, prices return to minimum LAC. Demand: P = 100 − 0.001Q In long run, given that min LAC occurs at q = 20, LAC = $40 P = $40 q = 20 π = 0 (There is no elaborate computations for these, we know price is going to have to be driven to the minimum point on the LAC $40, and we know each firm is going to have to produce at that point because it is the only breakeven point, and we know profit is 0 because P=AC). Q = 60,000 N = 3000 Now suppose that in LR there is technological change that reduces min LAC so that it occurs at q = 40, LAC = $30 P = $30 LR q = 40 π = 0 30 = 100 – 0.001Q 0.001Q = 70 Q = 70,000 N = Q/q = 70,000/40 = 1750 This is the way you can link it up. Do not make the mistake of putting LAC ON supply and demand diagram (as you can see, the quantity is very different; the only link is the price). Try a variant on the Long Run problem we just looked at (forgetting about technological change). Demand: P = 100 − .001Q In long run, given that min LAC occurs at q = 20, LAC = $40 P = $40 q = 20 π = 0 Q = 60,000 N = 60,000/20 = 3000 Now, suppose short run MC for firm is MC = −20 + 3q Short run supply: P = −20 + 3(q/3000) = −20 + .001Q Suppose demand increases to: P = 160 − .001Q In short run, Q = 90,000 P = $70 So there must be positive profits In long run, Min LAC occurs at q = 20, LAC = $40 P = $40 q = 20 π = 0 Q = 120,000 N = 120,000/20 = 6000 31 October 2012 What happens if demand falls so much that price goes down to shut down price? Demand: P = 100 − .001Q Start in long run and short run equilibrium, given that min LAC occurs at q = 20, LAC = $40 P = $40 q = 20 Q = 60,000 π = 0 N = 60,000/20 = 3000 Suppose short run MC for firm is MC = −20 + 3q Shut down price is 28 So short run supply is P = −20 + 0.001Q, P ≥ 28 Q = 0 P < 28 Suppose that demand falls to P = 64 − .001Q Short run: -20 + 0.001Q = 64 - 0.001Q Q = 42,000 P = 22 The price is not allowed to be below 28; therefore, we have the wrong answer. If the price goes one penny below 28, we have no production at all – excess demand, if the price goes one penny above 28, then all the firms stay open and we have excess supply. The only possible equilibrium is at the price of 28, where some of the firms open and some shut down. So, P = 28, QD = 36,000 100 – 0.001Q = -20 + 0.001Q 0.002Q = 120 28 (Shutdown price) = 64 – 0.001Q Q D 36/0.001 = 36000 36000/16 = 2250 (2250 firms that operate, supply 16 units each) 750 firms shut down. Long run: 40 = 64 – 0.001Q 0.001Q = 24 Q = 24000 N = Q/q = 24000/20 = 1200 Economists like perfect competition. In short run outcome maximizes sum of producer and consumer surplus. CS + PS = what is between supply and demand curve, that maximizes the area. Any additional output would have the cost of production of an extra unit above the benefit to consumers (marginal utility – the value of demand curve), if we produce more or less, people are worse off. It is getting towards the point everyone is unpleasant. In long run, outcome certainly maximizes consumer surplus (and there is no producer surplus). Producing less than Q*, we would be foregoing output. If we stop producing at Q 1 the marginal utility of additional units is greater than the cost of producing them. In the long run, you would not want to accept less than Q*. At Q , the2 value of additional units you are producing is considerably less than the cost of producing those units. The economy should not be spending $40 to produce goods that are worth $20. Perfect competition gets you to Q* - generating the right amount of output. But the process is not gentle; the impersonality of the market makes it essentially amoral. We essentially hammer producers until they give up and go elsewhere. Producers (and those who work for them) do not like this. Often there are big firms, with no free entry. Polar opposite of perfect competition is monopoly where there is a single firm, and no entry. Firm uses market power to push price up, so positive profits. For this to continue there must be something that prevents entry in the long run. The barriers to entry are: legality, cost advantages of size (natural) and advertising (created). Falling LAC, which could be a natural barrier. Issue of Minimum efficient scale: qMES 2 TC = 36 + 2q + q q = 7 FC = 20 P = 23 Demand: P = 30 − q = 30 − Q π = 62 Maximize profits = TR − TC MC = MR dπ/dq = dTR/dq − dTC/dq = 0 2 TR= Pq = (30 − q)q = 30q – q TC = 36 + 2q + q2 MC = 2 + 2q 30 – 2q = 2 + 2q 28 = 4q q = 7 Monopolist does not produce at minimum AC (neither did the perfect competitor in the short run). Demand: 30 – q MR: 30 – 2q These two equations are very similar having the same intercept but twice the slope. This is not an accident. 2 TR = PQ = AB-Q MR = dTR/dQ = A – 2bQ Demand and marginal revenue. Marginal revenue can go into the negative range. 5 November 2012 Monopolist would produce (maximize profits) where MR = MC. Revenue must cover variable costs. Set MR = MC, as long as P ≥ AVC. 2 TC = 36 + 2q + q FC = 20 P = 30 − q = 30 − Q To solve for profit maximization: MC = 2 + 2q MR = 30 − 2Q MR = MC → 2 + 2Q = 30 – 2Q → Q = 7 P = 23 And you get profit the normal way: π = TR – TC = 7x23 – 99 = 62 [Notice: Because profits are positive, we don’t have to worry about the P ≥ AVC issue] MC comes from the derivative of the total cost function. MR is the same intercept but twice the slope of demand curve. It does not matter if we have a q and Q because in monopoly the market and the firm is the same quantity because there is only 1 firm. We set MR = MC and find Q = 7. We plug Q = 7 back into the demand curve to find what the monopolist is going to charge, which is 23. The monopolist makes the decision to what point along the demand curve to sell the goods. Once you have chosen Q, the P is on the demand curve because monopolists control price. Notice that MR = 30 – 2Q while demand is P = 30 – Q. Clearly MR is below (
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