Chapter 5
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Chapter 5

Course Number: ECON 305, Winter 2012

College/University: Ohio

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Chapter 5 The Production Process and Costs Production function shows the relation between the maximum amount of output and inputs. Example: 2 inputs Labor (L) and Capital (K) Inputs called also factors. Production Function: Q=f(L,K) If L and K assume discrete values, then the production function is discrete. If L and K assume continuous values, then the production function is continuous. Short-run versus...

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5 The Chapter Production Process and Costs Production function shows the relation between the maximum amount of output and inputs. Example: 2 inputs Labor (L) and Capital (K) Inputs called also factors. Production Function: Q=f(L,K) If L and K assume discrete values, then the production function is discrete. If L and K assume continuous values, then the production function is continuous. Short-run versus Long-run In the short run, some inputs are fixed. Example: plant size (capital) is fixed in the shortrun; labor is variable in the short run. In the long-run, all inputs are variable. Measures of Productivity Total product (TP) is the maximum amount of output for a given amount of inputs. For example, when K=1 and L=2, then Q=4. Say L=2 workers and K=1 tractor can produce Q=4 holes. Q=4 holes is the maximum output. You can always produce less than 4 holes if, say, the workers slack. When K is fixed, the Total Product function of Labor (TPL) will show how Q changes as L changes while holding K fixed. It is also known as the short-run production function. Mathematically, TPL = Q = f(L/K), i.e. the amount of output as a function of L for a fixed K. An example of a short-run production function (picture below): K (plant size) is fixed at some level. As we vary L, the output (total product) changes according the function below. If L=LA, Q=QA (say, LA=100 workers, QA=200 units of output). If L=LB, Q=QB (say, LB=140, QB=220). If L=LC, Q=QC (say, LC=300, QC=230). We will talk more about the shape of the production function later. 1 Q QC C QB QA O LA TPL B A LB LC L Average Product Average Product of Labor = APL = Q/L (units per worker) Average Product of Capital = APK=Q/K (units per capital) Marginal Product The Marginal Product of Labor, MPL, shows the change in output associated with a one unit change in labor, holding all other factors (inputs) constant. MPL = Q when L is discrete L MPL = dQ when L is continuous dL MPL is units per worker. For example, MPL=5 for the 1st worker, MPL=7 for the second worker, etc. Example: Calculating MPL (K is fixed at some level) L 1 2 3 4 5 6 7 8 9 10 Q 15 31 48 59 68 72 73 72 70 67 MPL 15 16 17 11 9 4 1 -1 -2 -3 2 The Marginal Product of Capital, MPK, shows the change in output associated with a one unit change in capital, holding all other factors (inputs) constant. MPK = Q when K is discrete K MPK = dQ when K is continuous dK The relationship between AP and MP As long as MP is above AP, AP is increasing. If MP is below AP, AP will decrease. Intuition GPA Analogy Example. GPA is your average grade. Individual grade is like a marginal grade. If the grade from a new course is greater than your existing GPA, your GPA will go up. If the new grade is lower than your existing GPA, your GPA will go down. Showing Average and Marginal Graphically Suppose we have the following short-run production function, i.e, Q is a function of L (the amount of K is fixed at some level). Q C O B TPL A L For this short-run production function (or total product function of labor), we derive the APL and MPL functions (curves). 3 Recall, APL=Q/L. Graphically, APL at any point of the production function is the slope of the line connecting the origin (L=0, Q=0) with that point, Q C QA O TPL B A LA L APL at A is QA/LA and is the slope of line (OA). Similarly for any other point. For the above given total product function of labor, the average product of labor is first increasing, then decreasing, i.e. APL as a function of L has an inverted U-shape. APL LB L Recall that MPL= Q . As discussed in class, if L is arbitrarily small, then MPL at any L given level of L can be shown by the slope of the tangent line to the point of function corresponding to L. 4 Q C TPL B A LA LB LC L MPL at A is the slope of tangent line through A. MPL is increasing until A, then starts decreasing. A is the inflection point. Note that at B, MPL = APL. MPL=0 at C and becomes negative after C. If the slope of the tangent line at A is 4, then MPL=4 at LA. Say, LA=13. This means that the marginal product of the 13th worker is 4. MPL LA LC L If MPL>0, then Q is increasing. If MPL<0, then Q is decreasing. The relationship between TPL, MPL and APL is depicted in the following pictures. 5 Q TPL LA LB LC APL, MPL APL L LA LB LC MPL NOTE: In the book (page 160), the TPL, APL and MPL curves are plotted on one picture. It is not a good practice to put variables with different units of measurement on the same axis. TPL is total output, while APL and MPL are output per worker. I believe the book is sloppy in this case (although its scaling is correct). But the same graph in Powerpoint slides for Chapter 5, 7th slide (if you use them) is very misleading and shouldnt be used. In short, it is better to show TPL separately from APL and MPL. When L is between 0 and LA, MPL is both positive and is increasing. We say there is increasing marginal returns to labor in this range. When L is between LA and LC, MPL is positive, but decreasing. We say there is diminishing or decreasing marginal returns to labor in this range. When L is beyond LC, MPL is negative and decreasing. We say there is a negative marginal returns to labor in this range. 6 When there are increasing marginal returns to L (i.e. MPL is increasing), it means output is increasing at an increasing rate as L increases. For example, when 1st worker is hired, output increases from 0 to 5 units; when 2nd worker is hired, output increases from 5 to 11 units; when 3rd worker is hired, output increases from 11 to 18 units; etc. When there are diminishing (decreasing) marginal returns to L (i.e. MPL is positive but decreasing), it means output is increasing at a decreasing rate as L increases. For example, when the 12th worker is hired, output increases from 140 to 155 units; when the 13th worker is hired, output increases from 155 to 168 units; when the 14th worker is hired, output increases from 168 to 178 units; etc. Negative MPL means that output is decreasing as L is increasing. For most technologies, as the usage of an input increases (holding other inputs fixed), marginal product of that input initially increases, then begins to decline and eventually becomes negative. The Law of Diminishing Returns to a Factor Marginal Product of a variable factor (input) must eventually decline as more of the variable factor (input) is combined with other fixed factors (inputs). Example: Labor is the variable factor (input) and capital (plant size) is the fixed factor (input). When there are relatively few workers, the advantages of additional specialization are so great that each worker makes the others more productive. Hence MP of labor is increasing with additional worker. When there are more workers, the disadvantages of additional crowding are so great that each worker makes the others less productive. In the picture above (the short-run production function), MPL is increasing until point A, i.e. in that region we have increasing returns to L. After B, MPL is decreasing, i.e. we have diminishing returns to L. Moreover, after point C MPL becomes negative, i.e. after point C output would increase if we decreased the amount of factor L. MPL eventually will decrease as L increases (keeping K constant). Otherwise, there would be no limit to the usage of L. The Role of the Manager in the Production Process The manager should make sure the firm operates on the production function and the right amount of inputs re used. Produce on the Production Function 7 Q TPL QA O A LA L For example, if the firm employees LA number of workers, the manager should make sure the output is maximum, i.e. QA. The workers should be provided with the right incentives to work hard. Use the Right Level of Inputs Recall, MPL shows the change in output due to a 1 unit change in L. It is a measure of physical productivity of labor. The economic productivity of labor can be measured by the Value Marginal Product of labor, VMPL. VMPL is the value of output (i.e. revenue) generated by the last unit of labor. Let P be the price of output. Then, VMPL = P MPL For example, suppose you have 5 workers. The last, 5th workers marginal product is 4 units of output. Suppose also the price of output is $6 (i.e. you can sell each unit of output for $6). Then, VMPL=4 6=$24 Similarly, we can talk about the Value Marginal Product of Capital (VMPK). It is the value of output (revenue) generated by the last unit of capital. VMPK = P MPK Example: finding the right level (optimal level) of workers 8 Suppose capital is fixed at some level. The relationship between output and labor is given in Table 5.2. One unit of labor costs $400. Price of output is $3. Table 5.2 L 0 1 2 3 4 5 6 7 8 9 10 11 Price of output (P) $3 3 3 3 3 3 3 3 3 3 3 3 MPL 76 172 244 292 316 316 292 244 172 76 -44 VMPL= P $228 516 732 876 948 948 876 732 516 228 -132 MPL Wage (w) $400 400 400 400 400 400 400 400 400 400 400 Note from the table that initially, when labor usage is low (b/w 0 and 5, MPL is increasing, i.e. we have increasing marginal returns to L). When labor usage is b/w 5 and 10, MPL is positive, but decreasing, i.e. we have decreasing (diminishing) marginal returns to L. After L=10, MPL is negative, i.e. we have negative marginal returns to L. What is the right (optimal) number of workers to employ in this example? Use the principle of marginal analysis. Should the first worker be employed? 1st workers VMPL=$228, but he costs the firm $400. The firm loses $400-$288=$172. You might be tempted to say the 1st worker shouldnt be hired. But if we look beyond the 1st worker, given that we already have one worker, if we hire a 2nd worker, VMPL-w=$516-$400=$116. Hence we partially recovered the loss from the 1st worker. If we hire the 3rd worker, then VMPL-w=$732$400=$332. With 3 workers we have profits. But 3 is not the optimal level of L. We should also hire the 4th, 5th, 6th, 7th, 8th and 9th workers. The last worker hired is the 9th worker. Beyond L=9, VMPL<w, so adding additional workers will only reduce our profits. The right (optimal) number of workers to hire in this example is L=9. L=9 is the equilibrium number of workers to hire. The input should be employed up to the point where value of output produced by the last unit of an input (i.e. VMP) equals to the cost of that unit and the input usage is in the range where marginal return to the input decreases (diminishes). In case of Labor, optimal level of L is when VMPL=w and the marginal product of L is decreasing. If we cannot get an exact equality of VMPL and w, we should stop at level of L such that VMPL is the closet to w and VMPL>w. 9 On picture: VMPL, w w1 w0 w2 L L1 L0 L2 L The VMPL curve is bell shaped. VMPL is increasing when MPL is increasing (recall, VMPL= P VMPL) and VMPL is decreasing when MPL is decreasing. The profit maximizing level of L, for given w is the level at which VMPL=w in the range of diminishing (decreasing) marginal product of L (if cannot get exact equality of VMPL and w, stop at L where VMPL is the closest to w and VMPL>w). You can check that L0 is the right (i.e. equilibrium or optimal) level of L. Given w0, the firm has no incentive to deviate from L0. If it goes to the right of L0, the VMPL of each extra worker is less than w, so profits will decrease. If it goes to the left of L0, it saves in w but loses more in VMPL. In contrast, if the firm is at L, it doesnt stay there. The firm will increase L from L since each extra L will bring in more than its cost. If wage increased to w1, the profit maximizing level of L would be L1. If wage was w2, the profit maximizing level of L would be L2. Hence, for any given w, we find the profit maximizing (i.e. optimal or equilibrium or right) level of L from the downward sloping part of VMPL curve. This means that the downward sloping part of VMPL curve is the firms demand curve for labor. Isoquants Iso = Equal Quant=Quantity Isoquant combination of inputs that can be used to efficiently produce a given level of output. Efficiency means the maximum amount of output that the combination of two inputs can produce. (One can also produce less output with this combination, which would be inefficient). Example: The picture below shows two isoquants. Q=10 units can be produced, for example, by input combination A, B or C (or any other combination on that isoquant). 10 Q=17 units can be produced by combination D, E or F (or any other combination on that isoquant). K D E A B F C Q=17 Q=10 L The shape of the isoquant shows the degree of substitutability of inputs. In picture (a), the production process is such that inputs (gas and oil) are perfect substitutes. In picture (b), the production process is such that the inputs (frames and wheels) are perfect complements. In picture (c), the production process is such that the inputs are imperfect substitutes. 11 The isoquants in picture (c) are common. A dress can be made with a relatively small amount of labor (L1) and a large amount of cloth (C1). Or, the same dress can also be made with less cloth (C2) if more labor (L2) is used. To decrease cloth from C1 to C2 , C , requires increasing labor from L1 to L2. However, in order to have another decrease in cloth equal to C , L should increase now significantly more from L2 to L3. Hence, the substitutability of L for C diminishes as L increases. Marginal Rate of Technical Substitution (MRTS) MRTS is the amount of one input that must be substituted for one unit of another input in order to maintain the same level of output. If K and L are the inputs, then MRTSKL = K L MRTSKL = dK dL for discrete case for continuous case MRTSKL shows the amount of input K that must be substituted for 1 unit of input L in order to stay on the same isoquant. MRTSKL is the absolute value of the slope of the isoquant. K A C L At A, MRTSKL is the absolute value of the slope of the tangent through A. At C, it is the absolute value of the slope of the tangent through C. The slope of isoquant is decreasing, i.e. if one input is increasing (decreasing), the other one should decrease to (increase) stay on the same isoquant. MRTS decreases as we move along the isoquant from left to right, i.e. MRTSKL decreases as L increases. the substitutability of L for K decreases as L increases. 12 The Relationship between MRTS and MP Q Q Recall that MPL = L and MPK = K . Then, (Change in output due to change in L) = Q = L MPL (Change in output due to change in K) = Q = K MPk Consider the initial combination of inputs L and K that produce Q amount of output. Now suppose K decreased by K . (Change in output due to change in K) = If we want to stay on the same isoquant, we have to increase L. (Change in output due to change in L) = L MPL K MPk To stay on the same isoquant, (Change in output due to change in K)+ (Change in output due to change in L) =0 Or K MPk + L MPL = 0 After rearranging, MPL K = L MPK Recall also that MRTSKL = K L . Hence, MRTSKL = MPL MPK Thus, in the previous picture, the absolute value of MRTSKL at point C is the ratio of MPL at C and MPK at C. Isocosts Two inputs: K and L. One output: Q. w=price of input L (eg. wage rate) r = price of input K (eg. rental rate of capital) 13 C= money spent on inputs The isocost curve shows the combination of inputs that will cost the same amount of money. C = wL + rK would be the cost of buying L and K at w and r. On picture, K Isocost C r Slope=-w/r C w L C, i.e. the cost, is constant along the isocost curve. Higher isocost curves mean higher costs. The slope of isocost is determined by the relative factor prices: w/r What happens to isocost if w/r increases, i.e. labor becomes relatively more expensive than capital? What happens to isocost if w/r decreases, i.e. capital becomes relatively more expensive? Cost Minimization Given w and r, what is the optimal combination of inputs to produce a given level of output? Optimal combination of inputs means the least-cost combination for producing a given level of output. 14 K A B C Q=100 L Q=100 units of output can be produced using a combination of inputs represented by A, B or C (or any other combination on the isoquant for Q=100). Which combination is the optimal? The optimal combination of inputs for producing Q=100 units is the one that results in the lowest costs, i.e. is on the lowest isocost. K A B C Q=100 L The combination of inputs represented by B is the optimal combination for producing Q=100 units. It is also the point where the slope of the isoquant equals the slope of the isocost, i.e. MRTSkl = w/r Recall that MRTSKL = MPL/MPK, Thus, at optimal combination of inputs, 15 MPL MPK = w r Or MPL MPK = w r MPL/w is the marginal product of labor per dollar spent. MPK/r is the marginal product of capital per dollar spent. For example, suppose w=10 and r=4. A given level of output, say Q, is produced with some (L,K) combination such that MPL= 5 and MPK=20. Is the input combination used optimal? No. MPL/w = 5/10=1/2, i.e. the last dollar spent on labor resulted in 0.5 units of output. MPK/r = 20/4=5, i.e. the last dollar spent on capital resulted in 5 units of output. Then, the firm could reduce the costs of producing Q if it reduces L and increases K. Here is why. Say the firm decreases the amount spent on L by $1 (i.e. buys less L). Output goes down by 0.5 units. But the firm can recover these 0.5 units by spending less than $1 to buy extra capital. Hence, the firm can reduce the cost of producing Q by reducing L and increasing K. The firm is at the optimal input combination if marginal product of labor per dollar spent MPL MPK = is equal to marginal product of capital per dollar spent, i.e. w r. As output expands, the isoquants shift up. Expansion path is the optimal combination of inputs as the scale of output expands. 16 K C3 C2 C1 L Note that optimal input combination is a necessary but not a sufficient condition for profit maximization. For example, in the above picture, combination A is optimal for output level Q1. However, Q1 may not be a profit maximizing output level. Profit maximization requires optimal input combination plus optimal level of output. Optimal Input Substitution A change in the price of an input will lead to a change in the cost-minimizing input combination. Suppose when cost (price) of labor is w0 and cost (price) of capital is r0, the costminimizing input combination for producing Q0 units is (L0, K0). If the firm uses (L0, K0) combination, the cost of producing Q0 is, say, C0. 17 K C0 Slope=-w0/r0 K0 Q0 L0 L Next, say capital became cheaper (price of labor didnt change), i.e. price of capital decreased from r0 to r1. What is the new optimal input combination for producing the same output (Q0)? The slope of isocost has changed (it is now w/r1). Isocost became steeper. If we use the old input combination (L0,K0) to produce Q0 , the new isocost would be line C1 going through (L0,K0) in picture below. C1 is the cost of producing Q0 units using (L0, K0) when price of labor is w0 and price of capital is r1. But it is obvious from the picture that at w0 and r1, (L0,K0) is not the cost-minimizing input combination for producing Q0. (L1, K1) is the cost-minimizing combination. At (L1, K1) we have more capital and less labor than at (L0,K0). Hence, as capital became relatively cheaper, the firm substituted away from labor to capital, i.e. the firm became more capital-intensive. K Slope=-w0/r1 C1 C0 K1 Slope=-w0/r0 K0 C L1 L0 Q0 L More generally, to minimize the cost of producing a given level of output, the firm should use less of an input and more of other inputs when that inputs price rises. 18 The Cost Function For a given level of output, the cost function shows what is the minimum cost of producing that level of output. Short-Run Costs Recall, some inputs are fixed in the short run. Others are variable. (In the long-run, all inputs can be varied). Fixed cost is a short-run concept. These are costs (expenses) that do not vary with output. Variable costs are costs (expenses) that vary with output. All costs are variable in the long-run. The short-run cost function would show the cost of producing a given level of output when variable inputs are employed in the cost-minimizing fashion. In short run, Total Costs = Fixed Costs + Variable Costs Fixed Costs = FC Variable Costs = VC(Q) (i.e. they vary with output) Total Cost = C(Q) (i.e. also varies with output) Total Cost; Variable Cost, Fixed Cost The shape of the Total Cost is determined by the shape of the Variable Cost. At low levels of output, the Variable Cost is increasing at a decreasing rate because the variable 19 factor (input) productivity is increasing. At high levels of output, the Variable Cost is increasing at an increasing rate because the variable factor productivity is decreasing. For example, suppose labor is the variable factor and capital is the fixed factor. Then, the total product curve of labor (TPL) is Q C TPL B A LA LB LC L You see from above picture that at low levels of output, i.e. low levels of L, the marginal product of labor is increasing ( there are increasing marginal returns to labor). This means that to get, say an X% increase in output, labor should increase by less than X%. Which is the same as saying to get an X% increase in output, costs will increase by less than X%. Hence, when labor productivity is increasing (i.e. increasing MPL), costs will increase at a decreasing rate. If labor productivity is decreasing (i.e. decreasing MPL), to have an X% increase in Q, L should increase by more than X%. to have an X% increase in Q, costs will increase by more than X%. Hence, when labor productivity is decreasing (i.e. decreasing MPL), costs will increase at an increasing rate. Average and Marginal Costs Average Fixed Cost = AFC = FC/Q Average Variable Cost = AVC = VC(Q)/Q Average Total Cost =ATC = C(Q)/Q C(Q) = VC(Q)+FC Divide both sides by Q, ATC = AVC+AFC 20 C (Q ) Marginal Cost =MC = Q MC shows the change in total costs due to a unit change in Q. MC is independent of FC. C (Q ) Question: Does it matter if I calculate MC using Q VC (Q ) or Q ? Graphically, Unit Costs ATC, AVC, AFC and MC are also called unit costs. All are dollars per unit of output. Recall, ATC=AVC+AFC. At low levels of output, ATC is very high because both AFC and AVC are high. Initially, AVC is decreasing because of increasing productivity of the variable input. AFC is decreasing because AFC=FC/Q, hence as Q increases, the given amount of fixed costs is distributed over a larger and larger amount of output, so AFC decreases. These decreases in AVC and AFC drive down ATC. However, at higher levels of output, AFC and AVC behave differently. AFC keeps decreasing and gets closer to zero. But AVC starts increasing because the productivity of 21 the variable input starts decreasing. Because at higher levels of output AFC is closer to zero, then ATC gets dominated by AVC and rises. The distance between ATC and AVC becomes smaller and smaller as Q increases. There is no relationship between marginal and average fixed costs. There is an important relationship between the Marginal cost and the Average Variable and, hence, the Average Total Costs. As long as the marginal cost is above the average variable and average total costs, the last two are increasing. When Marginal cost is below the average variable and average total costs, the last two decrease. Changes in Q will result in movements along the cost curves (both total and unit cost curves). Changes in operating conditions (input costs, technology) will shift the cost curves. Fixed and Sunk Costs Sunk cost is a cost that is forever lost once it has been incurred. In other words, sunk costs are irreversible business expenses. Sunk costs are part of Fixed Costs that cannot be recovered. Example: suppose you leased an equipment and paid $10,000. One year later, if you decide you do not need it, you can return it and get a $6,000 refund. $4,000 is the sunk cost. It is irreversible. Sunk costs are irrelevant to present decisions. In the previous example, suppose now the $10,000 payment was non-refundable. Then your sunk cost is $10,000 and is irrelevant. If someone offers you $1000 for the equipment, you should sell it. Long-Run Costs In the long-run, all inputs are variable. For example, the firm can change both the amount of workers and the amount of capital (plant size). Consider two plant sizes (i.e. two short runs): Plant Size K1 and Plant Size K2, K2>K1 Call Plant Capacity the output level at which the corresponding short run average cost is at minimum. The sort run total costs for the two plants are depicted below. 22 TC TC1 TC2 Q Q Q1 Q Plant 2 is larger than Plant 1 and has higher fixed costs. At low levels of output it is cheaper to produce in plant 1 than in plant 2. At Q1, total costs are equal in the two plants. After Q1, it is cheaper to produce in plant 2. Note that the min ATC of plant 1 is at Q and min ATC of plant 2 is at Q. Similarly, there will be some Q2 and plant size K3 (K3>K2) such that it will be cheaper to produce in plant 3 after Q2 (not shown in the above picture). The picture below shows the short-run average total costs for 4 different plant sizes. ATC Plant 1 Plant 4 Plant 2 Plant 3 Q1 Q2 Q* Q3 23 Up to Q1, it is optimal to produce in plant 1 as it has the lowest average total costs. As output approaches the capacity in plant 1, it becomes optimal to increase plant size and produce in plant 2. Q1 to Q2 is produced in plant 2. After Q2, it is optimal to produce in plant 3. As plant size increases, the crowding effect can decrease allowing the firm to take further advantage of specialization and decrease the average costs. However, at some point, increasing plant size further will not decrease the average total costs. For example, as size becomes too large, it might be harder for management to coordinate and monitor operations. Hence ATC will increase ultimately. The envelope of the short-run average cost curves is the Long Run Average Cost (LRAC) curve. The long-run average cost (LRAC) curve shows the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable inputs. 24 Unit Cost LRAC Economies of Scale Diceconomies of Scale Q* Q Hence, if there are economies of scale present, becoming larger can reduce average costs and make the company more efficient. Economies of Scale is used as one argument for mergers of two companies producing similar products. If LRAC is constant as Q changes, then we have Constant Returns to Scale (or no economies of scale). AC Plant 2 Plant 1 Plant 3 LRAC Q 25 A REMINDER: ECONOMIC COSTS VERSUS ACCOUNTING COSTS Recall, Economic Cost = Opportunity Cost. When the firm uses various resources for production, the explicit outlays for these resources would be the Accounting Costs. But, these explicit outlays are not everything the company gives up when using all those resources. Those resources could have been used to produce some other good. The profits that the company could have earned if the resources were utilized in their next best use are implicit outlays and should be included in Economic Costs. The costs we mention here mean economic costs. Multiple-Output Cost Functions So far, the firm was producing 1 output only. It can produce more than one output. Then the firm is multi-product. Economies of Scope Multi-product firms exist because of Economies of Scope. Economies of Scope exists when the total cost of producing two types of outputs together is less than the total cost of producing each type of output separately. Mathematically, economies of scope exist if C(Q1, 0) + C(0, Q2) > C(Q1, Q2) Intuition: McDonalds can produce both hamburgers and French fries at a lower average cost than what it would cost two separate firms to produce the same goods. This is because McDonalds hamburgers and French fries share the use of food storage, preparation facilities, and so forth during production. Knowledge is another reason why it may be optimal to produce and sell related products together. Information about one product can be relevant for another closely related product. 26

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CHAPTER 3Quantitative Demand AnalysisThe Elasticity ConceptIf the price of the product increases, we know by the law of demand that quantity demanded for thatproduct will decreases (holding everything else constant).How much revenue changes depend on
Ohio - ECON - 305
HW#1 ANSWERS1. TRUE OR FALSE? EXPLAIN BRIEFLY!a. If the interest (discount) rate is 10% and cash flows are $440 at the end of year one and $1210at the end of year two, then the present value of these cash flows is $1400.TRUE4401210 400 1000 1400(1
Ohio - ECON - 305
WINTER 2012ME 3051.Instructor: Vahe LskavyanHW#2ANSWERSTRUE or FALSE? EXPLAIN. USE PICTURES unless told otherwise! Label all axisand curves!a. When the price of wheat decreases, demand for rice will increase.FALSE: If rice and wheat are substitut
Ohio - ECON - 305
Winter 2012, ME305Instructor: Vahe LskavyanMid-Term Exam #1Finish by 5PM. Do all problems. Read problems carefully. Provide concise but complete answers.Explanations without answers will lose points. Closed book. Manage time efficiently.1. (6 POINTS)
Ohio - ECON - 305
The Theory of Individual BehaviorChapter 4Consumer choice is based on consumers tastes (preferences) and opportunities (budget constraints).Assume two goods available for consumption: X (e.g. apples) and Y (e.g. oranges).Bundle= (X apples, Y oranges)=
Ohio - ECON - 305
1.CHAPTER 5 PART 1 PROBLEMSANSWERSTRUE or FALSE. Explain! Use graphs if necessary.a. If the last unit of input increases total product we know that the marginal product isnegative.FALSE: The marginal product of an input shows the change in output du
Ohio - ECON - 305
Econ 305Winter 2012Vahe LskavyanHW#3ANSWERS1. TRUE/FALSE. Use pictures and explain briefly you answers.a. If both X and Y are goods, bundles on higher indifference curves are preferred to bundles onlower indifference curves.TRUE: A simple way of s
Ohio - ECON - 305
Econ 305Winter 2012Vahe LskavyanHW#3DUE BY 5 PM, THURSDAY, FEBRUARY 9. SLIDE UNDER MY OFFICE DOOR IF I AMOUT.1. TRUE/FALSE. Use pictures and explain briefly you answers.a. If both X and Y are goods, bundles on higher indifference curves are preferr
Ohio - COMS - 206
Exam 1 COMS 206Chapters 1 - 4Ch 1About CommunicationWhy we communicate- Needs filled by Interpersonal Communication1) Communication meets physical needsa. Stigma: a characteristic that discredits a person, making him or her be seen asabnormal or und
Ohio - COMS - 206
Exam 2 COMS 206Chapters 5 8Ch 5- The Nature of LanguageOnly creatures on planet who use languageUse language as a way to represent and symbolize our thoughts and feelingsLanguage a structured system of symbols used for communicating meaningOur advan
Ohio - COMS - 206
Study Guide Exam 3Chapters 9 12Chapter 9: Interpersonal Communication in Friendships and ProfessionalRelationshipsWhy Social Relationships Matter (pg. 278)1) We Form Relationships Because We Need to Belong:a. Its in our nature to form relationships,
Ohio - COMS - 206
Study Guide Exam 3 COMS 206Professor ShubertChapters 9 12Some Information about this Study GuideThis study guide includes all the definitions from the book plus other crucial detialsI have listed page numbers frequently throughout the study guide so
Ohio - COMS - 206
Ohio - COMS - 206
Ohio - COMS - 206
Ohio - COMS - 206
One of these was wrong.
Ohio - COMS - 206
One of these is wrong
Ohio - COMS - 206
Models of communication in order from oldest to newest:1) Action2) Interaction model3) Transactional model
Ohio - COMS - 206
Cultures differ in how much they emphasize individuals rather than groups
Ohio - COMS - 206
Ohio - COMS - 206
Ohio - P SC - 100D
Magnetosphere requires: 1) a magnetic field; 2) an atmosphere; Earth &amp; all Jovian planets have it; magnetosphere shields planet from charged particles in solar wind; deflected awayfrom Earth or trapped in the Van Allen Belts; particles escape toward pole
Ohio - P SC - 100D
Cosmic address: Earth, Solar System. Milky Way Galaxy, Local Group, Virgo Supercluster, UniverseScientific method: Observation, Ask a Question, Hypothesis (a proposed explanation which might explain what want to understand); Testable predictions (bothve
Ohio - P SC - 100D
Reflecting v. Refracting Telescope: use curved mirrors to focus light; can support primary mirror on back, so can be made much larger v. use lenses to focus light;problem b/c can only support lens on sides, so deform if too bigBigger Telescope: greater
Ohio - P SC - 100D
Kathryn HudderP SC 100DExtra CreditOne claim used as evidence for the Moon landings being faked is that there were no starsin the pictures taken by the astronauts from the Moon. However, this is not valid evidenceagainst the Moon landings because if
Ohio - P SC - 100D
P SC 100D: Exam 1 Study Guide1. Know our cosmic address: put the following in correct order from smallestto largest (Universe, Local Group, Local Supercluster, Earth, Milky Way, SolarSystem). Know the definitions of each.Earth, Solar System. Milky Way
Ohio - P SC - 100D
PSc 100D: study guide for Exam #2Start at lecture 141. What is the difference between a reflecting and refracting telescope?a. Reflecting telescope: use curved mirrors to focus light; can support the primarymirror on the back, so can be made much larg
Ohio - P SC - 100D
Final Exam Study Guide P Sc 100DProfessor MagerSome Information About This Study Guide/Final ExamThe Final Exam is on Wednesday, March 14 at 12:20 pmThings youre allowed to bring to this exam: a calculator, pencil, and three sheets ofpaper with notes
Ohio - P SC - 100D
Ohio - P SC - 100D
360/28= 12.8 = 13Acceleration can be negative when velocity is decreasingNot sure about second part
Ohio - P SC - 100D
Ohio - P SC - 100D
Ohio - P SC - 100D
Pg. 407; solar wind stops at 100 AU at the interstellar medium (the gas and dust that lie betweenthe stars in a galaxy and that surround the sun)400 trillion solar neutrinos pass through Earth each secondSolar neutrino problem: found only about a third
Ohio - P SC - 100D
Cloud rotation may thwart the collapse of the cloud toward its axis of rotation, but there isnothing to prevent collapse taking place parallel to the axis of rotation.Divide mass of mars by total planetary mass.107/446.657.00024.024 %
Ohio - P SC - 100D
Ohio - P SC - 100D
1)If you are below sea level, then you should be higher than 1,000 millibars; Earths atmosphericpressure at sea level is 1 bar = 1,000 millibars; if you go below sea level atmospheric pressurewould increaseGlobal warming and the ozone hole cause probl
Ohio - P SC - 100D
1)2)3)4)5)6)7)8)9)10)11)12)
Ohio - P SC - 100D
Homework 101)2)3)4)P2 = a3P= orbital period in yearsa = semi major axis of the orbit(76)2 = a3a = 17.95)6)7)P2 = a3P= orbital period in yearsa = semi major axis of the orbitConvert days to years: 3.524/365(.0096548)2 = a3.0453 = a.0 doe
Monash - AFF - 1000
AFF/W 1000Principles of Accounting andFinanceTopic 3Revisiting the recording process-Trading firmsReference: Principles of Accounting and Finance (Second edition)(Carey 2010), Chapter 3Lecture Overview Revising the recording process Trading firm
Monash - AFF - 1000
AFW 1000Principles of Accounting and FinanceTopic 4Adjusting the AccountsReference: Principles of Accounting and Finance (Second edition)(Carey 2010). Chapter 4Review of previous week Revising the recording process Trading firms Recording purchas
Monash - AFF - 1000
AFF 1000Principles of Accounting andFinanceTopic 5Preparing the financial statementsReference: Principles of Accounting and Finance (second edition).(Carey 2010). Chapter 51Department of Accounting and FinanceReview of previous week1.2.3.4.5
Monash - AFF - 1000
AFW 1000Principles of Accounting andFinanceTopic 6Financial Statement AnalysisReference: Principles of Accounting and Finance (second edition).(Carey 2010). Chapter 6Review of previous week1.2.3.4.5.6.Prepare a worksheet;Explain the process
Monash - AFF - 1000
COMMONWEALTH OF AUSTRALIACopyright Regulations 1969WARNING This material has been reproduced andcommunicated to you by or on behalf ofMonash University pursuant to Part VA &amp; VB ofthe Copyright Act 1968 (the Act). The material in this communication
Monash - AFF - 1000
AFW 1000Principles of Accounting andFinanceTopic 10Introduction to FinanceReference: Principles of Accounting and Finance (second edition).(Carey 2010). Chapter 10 Did you do the weekly practice quiz onBlackboard?Department of Accounting and Fina
Monash - AFF - 1000
AFF/W 1000Principles of Accounting andFinanceTopic 12InvestmentsReference: Principles of Accounting and Finance (second edition).(Carey 2010). Chapter 12Learning objectivesExplain what an investment isExplain why people investExplain why investi
Monash - AFF - 1000
COMMONWEALTH OF AUSTRALIACopyright Regulations 1969WARNING This material has been reproduced andcommunicated to you by or on behalf ofMonash University pursuant to Part VA &amp; VB ofthe Copyright Act 1968 (the Act). The material in this communication
Monash - AFF - 1000
Week 9Strategic Management AccountingBudgeting &amp; ResponsibilityaccountingProfessor Paul Collierwww.monash.edu.auStrategic management accounting (ch. 8)Looks beyond the financial year to the longer term,particularly in relation to the product/servi
Monash - AFF - 1000
Welcome to AFW 1000Principles of Accounting and FinancexxxxxLecturer: Jon PhillipsPh:9904 4174 (Peninsula) 9904 7249 (Berwick)Office:D3.19 (Peninsula) 901/130D (Berwick)Email:jon.phillips@buseco.monash.edu.auConsulting Hours: Monday 4.00pm -
Monash - AFF - 1000
AFW 1000Principles of Accounting &amp;FinanceLecture 2The Recording ProcessRequired Reading: Chapter 21Cash Vs Accrual AccountingCash AccountingAccrual AccountingProfit vs Cash FlowGAAP2Disadvantages of cashbasis accountingCan distort financial
Monash - AFF - 1000
Week 11Introduction to Financial MathematicsReadings: Chapter 11, Carey(2010)1Learning objectivesCalculate the future and present value of single-sumand mixed-stream cash flows using both simple andcompound interestPlot cash flows on a timelineE
Monash - BTF - 2220
Business and EconomicsBTF2220 Corporations Law andTrustsLecture Stream 1 Monday 2-4pm B215 Phillip LiptonLecture Stream 2 Friday 1-3pm K321 Tabatha PettittPrescribed books and Other Resources Understanding Company Law 15th ed (LHW) Corporations Leg