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Q: What is the shape of marginal revenue curve if the total revenue curve have concave shape?

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The demand curve is a tremendously useful illustration for those who can read it. We have seen that the downward slope tells us that there is an inverse relationship between price and quantity. One can also view the demand curve as separating a region in which sellers can operate from a region forbidden to them. But there is more, especially when one considers what an area on the graph represents. If people will buy 100 units of a product when its price is $10.00, as the picture below illustrates, total revenue for sellers will be $1000. Simple geometry tells us that the area of the rectangle formed under the demand curve in the picture is found by multiplying the height of the rectangle by its width. Because the height is price and the width is quantity, and since price multiplied by quantity is total revenue, the area is total revenue. The fact that area on supply and demand graphs measures total revenue (or total expenditure by buyers, which is the same thing from another viewpoint) is a key idea used repeatedly in microeconomics. From the demand curve, we can obtain total revenue. From total revenue, we can obtain another key concept: marginal revenue. Marginal revenue is the additional revenue added by an additional unit of output, or in terms of a formula: Marginal Revenue = (Change in total revenue) divided by (Change in sales) According to the picture, people will not buy more than 100 units at a price of $10.00. To sell more, price must drop. Suppose that to sell the 101st unit, the price must drop to $9.95. What will the marginal revenue of the 101st unit be? Or, in other words, by how much will total revenue increase when the 101st unit is sold? There is a temptation to answer this question by replying, "$9.95." A little arithmetic shows that this answer is incorrect. Total revenue when 100 are sold is $1000. When 101 are sold, total revenue is (101) x ($9.95) = $1004.95. The marginal revenue of the 101st unit is only $4.95. To see why the marginal revenue is less than price, one must understand the importance of the downward-sloping demand curve. To sell another unit, sellers must lower price on all units. They received an extra $9.95 for the 101st unit, but they lost $.05 on the 100 that they were previously selling. So the net increase in revenue was the $9.95 minus the $5.00, or $4.95. There is a another way to see why marginal revenue will be less than price when a demand curve slopes downward. Price is average revenue. If the firm sells 100 for $10.00, the average revenue for each unit is $10.00. But as sellers sell more, the average revenue (or price) drops, and this can only happen if the marginal revenue is below price, pulling the average down. The reasoning of why marginal will be below average if average is dropping can perhaps be better seen in another example. Suppose that the average age of 20 people in a room is 25 years, and that another person enters the room. If the average age of the people rises as a result, the extra person must be older than 25. If the average age drops, the extra person must be younger than 25. If the added person is exactly 25, then the average age will not change. Whenever an average is rising, its marginal must be above the average, and whenever an average is falling, its marginal must be below the average. If one knows marginal revenue, one can tell what happens to total revenue if sales change. If selling another unit increases total revenue, the marginal revenue must be greater than zero. If marginal revenue is less than zero, then selling another unit takes away from total revenue. If marginal revenue is zero, than selling another does not change total revenue. This relationship exists because marginal revenue measures the slope of the total revenue curve. The picture above illustrates the relationship between total revenue and marginal revenue. The total revenue curve will be zero when nothing is sold and zero again when a great deal is sold at a zero price. Thus, it has the shape of an inverted U. The slope of any curve is defined as the rise over the run. The rise for the total revenue curve is the change in total revenue, and the run is the change in output. Therefore, Slope of Total Revenue Curve = (Change in total revenue) / (Change in amount sold) But this definition of slope is identical to the definition of marginal revenue, which demonstrates that marginal revenue is the slope of the total revenue curve.

I have never heard that the demand curve must be concave. In fact, it is most often modeled as either linear or convex. Common convex specifications include log-linear and constant-elasticity demand functions. A number of empirical papers attempt to estimate the shape of the demand curve for specific products but I am not familiar with anyone concluding that demand is concave generally.

Overall because of diminishing marginal returns. The marginal cost curve, MC, decreases until diminishing marginal returns set in and and it begins to increase. When the MC is below the AVC, the AVC must fall. When the MC is above the AVC, the AVC must rise. In otherwords, if the marginal cost is decreasing the average cost must be decreasing as well and vice versa.

Scarcity, on a PPC (PPF) is implied by the bowed (concave-down) shape of the curve, since there is a restriction on how much can be produced and, to get more of something, one must give away something else.

what will be the shape of indifference curve if one of the two goods is a free commodity

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it will be parallel to horizantal axis

The demand curve is a tremendously useful illustration for those who can read it. We have seen that the downward slope tells us that there is an inverse relationship between price and quantity. One can also view the demand curve as separating a region in which sellers can operate from a region forbidden to them. But there is more, especially when one considers what an area on the graph represents. If people will buy 100 units of a product when its price is $10.00, as the picture below illustrates, total revenue for sellers will be $1000. Simple geometry tells us that the area of the rectangle formed under the demand curve in the picture is found by multiplying the height of the rectangle by its width. Because the height is price and the width is quantity, and since price multiplied by quantity is total revenue, the area is total revenue. The fact that area on supply and demand graphs measures total revenue (or total expenditure by buyers, which is the same thing from another viewpoint) is a key idea used repeatedly in microeconomics. From the demand curve, we can obtain total revenue. From total revenue, we can obtain another key concept: marginal revenue. Marginal revenue is the additional revenue added by an additional unit of output, or in terms of a formula: Marginal Revenue = (Change in total revenue) divided by (Change in sales) According to the picture, people will not buy more than 100 units at a price of $10.00. To sell more, price must drop. Suppose that to sell the 101st unit, the price must drop to $9.95. What will the marginal revenue of the 101st unit be? Or, in other words, by how much will total revenue increase when the 101st unit is sold? There is a temptation to answer this question by replying, "$9.95." A little arithmetic shows that this answer is incorrect. Total revenue when 100 are sold is $1000. When 101 are sold, total revenue is (101) x ($9.95) = $1004.95. The marginal revenue of the 101st unit is only $4.95. To see why the marginal revenue is less than price, one must understand the importance of the downward-sloping demand curve. To sell another unit, sellers must lower price on all units. They received an extra $9.95 for the 101st unit, but they lost $.05 on the 100 that they were previously selling. So the net increase in revenue was the $9.95 minus the $5.00, or $4.95. There is a another way to see why marginal revenue will be less than price when a demand curve slopes downward. Price is average revenue. If the firm sells 100 for $10.00, the average revenue for each unit is $10.00. But as sellers sell more, the average revenue (or price) drops, and this can only happen if the marginal revenue is below price, pulling the average down. The reasoning of why marginal will be below average if average is dropping can perhaps be better seen in another example. Suppose that the average age of 20 people in a room is 25 years, and that another person enters the room. If the average age of the people rises as a result, the extra person must be older than 25. If the average age drops, the extra person must be younger than 25. If the added person is exactly 25, then the average age will not change. Whenever an average is rising, its marginal must be above the average, and whenever an average is falling, its marginal must be below the average. If one knows marginal revenue, one can tell what happens to total revenue if sales change. If selling another unit increases total revenue, the marginal revenue must be greater than zero. If marginal revenue is less than zero, then selling another unit takes away from total revenue. If marginal revenue is zero, than selling another does not change total revenue. This relationship exists because marginal revenue measures the slope of the total revenue curve. The picture above illustrates the relationship between total revenue and marginal revenue. The total revenue curve will be zero when nothing is sold and zero again when a great deal is sold at a zero price. Thus, it has the shape of an inverted U. The slope of any curve is defined as the rise over the run. The rise for the total revenue curve is the change in total revenue, and the run is the change in output. Therefore, Slope of Total Revenue Curve = (Change in total revenue) / (Change in amount sold) But this definition of slope is identical to the definition of marginal revenue, which demonstrates that marginal revenue is the slope of the total revenue curve.

no concave mirror is in shape of concave mirror

There is no shift in the PPC.Only a dot is marked within the curve(Not on the curve) in the exact center of the two axes.The shape of the PPC is concave to the origin.

I have never heard that the demand curve must be concave. In fact, it is most often modeled as either linear or convex. Common convex specifications include log-linear and constant-elasticity demand functions. A number of empirical papers attempt to estimate the shape of the demand curve for specific products but I am not familiar with anyone concluding that demand is concave generally.

The production possibility curve is not always linear, in fact, it is usually concave down (bowed-in). The shape of the curve depends on the substutability of the goods described by the curve in the question. When goods are perfectly substitutable in production, the PPP (or PPF) is linear.

Overall because of diminishing marginal returns. The marginal cost curve, MC, decreases until diminishing marginal returns set in and and it begins to increase. When the MC is below the AVC, the AVC must fall. When the MC is above the AVC, the AVC must rise. In otherwords, if the marginal cost is decreasing the average cost must be decreasing as well and vice versa.

BECAUSE YOUR EYES ARE SHAPED CONVEX LIKE MEANING THEY CURVE OUTWARD BUT IF THEY WERE TO BE CONCAVE YOUR VISION WOULD BE BLURRED AND WOULD DAMAGE EVERYTHING IN YOUR EYES LIKE THE PUPIL AN CORNEA

The PPF is bowed outwards (concave to the origin) as tradeoffs between the production of any two goods are constant.

No

Scarcity, on a PPC (PPF) is implied by the bowed (concave-down) shape of the curve, since there is a restriction on how much can be produced and, to get more of something, one must give away something else.

the fact that total profit reaches its maximum point where marginal revenue equals marginal cost.Contents[show] 1 Basic definitions2 Total revenue - total cost perspective3 Marginal revenue-marginal cost perspective4 Case in which maximizing revenue is equivalent5 Changes in total costs and profit maximization6 Markup pricing7 Marginal product of labor, marginal revenue product of labor, and profit maximization8 See also9 Notes10 References11 External linksBasic definitionsAny costs incurred by a firm may be classed into two groups: fixed costs and variable costs. Fixed costs, which occur only in the short run, are incurred by the business at any level of output, including zero output. These may include equipment maintenance, rent, wages of employees whose numbers cannot be increased or decreased in the short run, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category, which also includes the wages of employees who can be hired and laid off in the span of time (long run or short run) under consideration. Fixed cost and variable cost, combined, equal total cost. Revenue is the amount of money that a company receives from its normal business activities, usually from the sale of goods and services (as opposed to monies from security sales such as equity shares or debt issuances).Marginal cost and revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced, or the derivative of cost or revenue with respect to the quantity of output. For instance, taking the first definition, if it costs a firm 400 USD to produce 5 units and 480 USD to produce 6, the marginal cost of the sixth unit is 80 dollars.Total revenue - total cost perspectiveProfit Maximization - The Totals Approach To obtain the profit maximising output quantity, we start by recognizing that profit is equal to total revenue (TR) minus total cost (TC). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph. The profit-maximizing output is the one at which this difference reaches its maximum. In the accompanying diagram, the linear total revenue curve represents the case in which the firm is a perfect competitor in the goods market, and thus cannot set its own selling price. The profit-maximizing output level is represented as the one at which total revenue is the height of C and total cost is the height of B; the maximal profit is measured as CB. This output level is also the one at which the total profit curve is at its maximum.If, contrary to what is assumed in the graph, the firm is not a perfect competitor in the output market, the price to sell the product at can be read off the demand curve at the firm's optimal quantity of output.Marginal revenue-marginal cost perspectiveProfit maximization using the marginal approach An alternative perspective relies on the relationship that, for each unit sold, marginal profit (Mπ) equals marginal revenue (MR) minus marginal cost (MC). Then, if marginal revenue is greater than marginal cost at some level of output, marginal profit is positive and thus a greater quantity should be produced, and if marginal revenue is less than marginal cost, marginal profit is negative and a lesser quantity should be produced. At the output level at which marginal revenue equals marginal cost, marginal profit is zero and this quantity is the one that maximizes profit.[1] Since total profit increases when marginal profit is positive and total profit decreases when marginal profit is negative, it must reach a maximum where marginal profit is zero - or where marginal cost equals marginal revenue - and where lower or higher output levels give lower profit levels.[1] In calculus terms, the correct intersection of MC and MR will occur when:[1]The intersection of MR and MC is shown in the next diagram as point A. If the industry is perfectly competitive (as is assumed in the diagram), the firm faces a demand curve (D) that is identical to its marginal revenue curve (MR), and this is a horizontal line at a price determined by industry supply and demand. Average total costs are represented by curve ATC. Total economic profit are represented by the area of the rectangle PABC. The optimum quantity (Q) is the same as the optimum quantity in the first diagram.If the firm is operating in a non-competitive market, changes would have to be made to the diagrams. For example, the marginal revenue curve would have a negative gradient, due to the overall market demand curve. In a non-competitive environment, more complicated profit maximization solutions involve the use of game theory.Case in which maximizing revenue is equivalentIn some cases a firm's demand and cost conditions are such that marginal profits are greater than zero for all levels of production up to a certain maximum.[2] In this case marginal profit plunges to zero immediately after that maximum is reached; hence the Mπ = 0 rule implies that output should be produced at the maximum level, which also happens to be the level that maximizes revenue.[2] In other words the profit maximizing quantity and price can be determined by setting marginal revenue equal to zero, which occurs at the maximal level of output. Marginal revenue equals zero when the total revenue curve has reached its maximum value. An example would be a scheduled airline flight. The marginal costs of flying one more passenger on the flight are negligible until all the seats are filled. The airline would maximize profit by filling all the seats. The airline would determine the conditions by maximizing revenues. Changes in total costs and profit maximizationA firm maximizes profit by operating where marginal revenue equal marginal costs. A change in fixed costs has no effect on the profit maximizing output or price.[3] The firm merely treats short term fixed costs as sunk costs and continues to operate as before.[4] This can be confirmed graphically. Using the diagram illustrating the total cost-total revenue perspective, the firm maximizes profit at the point where the slopes of the total cost line and total revenue line are equal.[2] An increase in fixed cost would cause the total cost curve to shift up by the amount of the change.[2] There would be no effect on the total revenue curve or the shape of the total cost curve. Consequently, the profit maximizing point would remain the same. This point can also be illustrated using the diagram for the marginal revenue-marginal cost perspective. A change in fixed cost would have no effect on the position or shape of these curves.[2] Markup pricingIn addition to using methods to determine a firm's optimal level of output, a firm that is not perfectly competitive can equivalently set price to maximize profit (since setting price along a given demand curve involves picking a preferred point on that curve, which is equivalent to picking a preferred quantity to produce and sell). The profit maximization conditions can be expressed in a "more easily applicable" form or rule of thumb than the above perspectives use.[5] The first step is to rewrite the expression for marginal revenue as MR = ∆TR/∆Q =(P∆Q+Q∆P)/∆Q=P+Q∆P/∆Q, where P and Q refer to the midpoints between the old and new values of price and quantity respectively.[5] The marginal revenue from an "incremental unit of quantity" has two parts: first, the revenue the firm gains from selling the additional units or P∆Q. The additional units are called the marginal units.[6] Producing one extra unit and selling it at price P brings in revenue of P. Moreover, one must consider "the revenue the firm loses on the units it could have sold at the higher price"[6]-that is, if the price of all units had not been pulled down by the effort to sell more units. These units that have lost revenue are called the infra-marginal units.[6] That is, selling the extra unit results in a small drop in price which reduces the revenue for all units sold by the amount Q(∆P/∆Q). Thus MR = P + Q(∆P/∆Q) = P +P (Q/P)((∆P/∆Q) = P + P/(PED), where PED is the price elasticity of demand characterizing the demand curve of the firms' customers, which is negative. Then setting MC = MR gives MC = P + P/PED so (P - MC)/P = - 1/PED and P = MC/[1 + (1/PED)]. Thus the optimal markup rule is:(P - MC)/P = 1/ (- PED)orP = [PED/(1 + PED)]×MC.[7][8] In words, the rule is that the size of the markup is inversely related to the price elasticity of demand for the good.[7]The optimal markup rule also implies that a non-competitive firm will produce on the elastic region of its market demand curve. Marginal cost is positive. The term PED/(1+PED) would be positive so P>0 only if PED is between -1 and -∝ -that is, if demand is elastic at that level of output.[9] The intuition behind this result is that, if demand is inelastic at some value Q1 then a decrease in Q would increase P more than proportionately, thereby increasing revenue PQ; since lower Q would also lead to lower total cost, profit would go up due to the combination of increased revenue and decreased cost. Thus Q1 does not give the highest possible profit.Marginal product of labor, marginal revenue product of labor, and profit maximizationThe general rule is that firm maximizes profit by producing that quantity of output where marginal revenue equals marginal costs. The profit maximization issue can also be approached from the input side. That is, what is the profit maximizing usage of the variable input? [10] To maximize profit the firm should increase usage of the input "up to the point where the input's marginal revenue product equals its marginal costs".[11] So mathematically the profit maximizing rule is MRPL = MCL, where the subscript L refers to the commonly assumed variable input, labor. The marginal revenue product is the change in total revenue per unit change in the variable input. That is MRPL = ∆TR/∆L. MRPL is the product of marginal revenue and the marginal product of labor or MRPL = MR x MPL.

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