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Marginal revenue productivity theory of wages
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<h2 id="mathematical-relation">Mathematical relation</h2> <p>The marginal revenue product of labour M R P L {\displaystyle MRP_{L}} is the increase in revenue per unit increase in the variable input = Δ T R Δ L {\displaystyle {\frac {\Delta TR}{\Delta L}}} </p> M R = Δ T R Δ Q M P L = Δ Q Δ L M R × M P L = Δ T R Δ Q × Δ Q Δ L = Δ T R Δ L {\displaystyle {\begin{aligned}MR&={\frac {\Delta TR}{\Delta Q}}\\[5pt]MP_{L}&={\frac {\Delta Q}{\Delta L}}\\[5pt]MR\times MP_{L}&={\frac {\Delta TR}{\Delta Q}}\times {\frac {\Delta Q}{\Delta L}}={\frac {\Delta TR}{\Delta L}}\end{aligned}}} <p>Here: </p> <ul><li> T R {\displaystyle TR} is the Total Revenue (a money amount).</li> <li> M P {\displaystyle MP} is the marginal product (units created with the marginal labor time and effort).</li> <li> Q {\displaystyle Q} is the amount of goods (a measure of the quantity or volume sold).</li> <li> M R {\displaystyle MR} is marginal revenue (the money revenue received from the marginal product produced).</li> <li> L {\displaystyle L} is Labour (amount of labor time or effort).</li></ul> <p>[This page is incomplete. Please define each and every variable and include their dimension] </p><p>The change in output is not limited to that directly attributable to the additional worker. Assuming that the firm is operating with diminishing marginal returns then the addition of an extra worker reduces the average productivity of every other worker (and every other worker affects the marginal productivity of the additional worker). </p><p>The firm is modeled as choosing to add units of labor until the M R P {\displaystyle MRP} equals the wage rate w {\displaystyle w} — mathematically until </p> M R P L = w M R ( M P L ) = w M R = w M P L M R = M C , which is the profit maximizing rule. {\displaystyle {\begin{aligned}MRP_{L}&=w\\[5pt]MR(MP_{L})&=w\\[5pt]MR&={\frac {w}{MP_{L}}}\\[5pt]MR&=MC,{\text{ which is the profit maximizing rule.}}\end{aligned}}} <h2 id="marginal-revenue-product-in-a-perfectly-competitive-market">Marginal revenue product in a perfectly competitive market</h2> <p>Under <a href="/facts/Perfect_competition/les89UG3">perfect competition</a>, marginal revenue product is equal to marginal physical product (extra unit of good produced as a result of a new employment) multiplied by price. </p> M R P = M P P × M R ( D = A R = P ) as perfectly competitive labour market M R P = M P P × Price {\displaystyle {\begin{aligned}MRP&=MPP\times MR(D=AR=P){\text{ as perfectly competitive labour market}}\\[5pt]MRP&=MPP\times {\text{Price}}\end{aligned}}} <p>This is because the firm in <a href="/facts/Perfect_competition/les89UG3">perfect competition</a> is a <a href="/facts/Price_taker/oyYb7b3L">price taker</a>. It does not have to lower the price in order to sell additional units of the good. </p> <h2 id="mrp-in-monopoly-or-imperfect-competition">MRP in monopoly or imperfect competition</h2> <p>Firms operating as monopolies or in imperfect competition face downward-sloping <a href="/facts/Demand_curve/lALNI8BX">demand curves</a>. To sell extra units of output, they would have to lower their output's price. Under such market conditions, marginal revenue product will not equal M P P × Price {\displaystyle MPP\times {\text{Price}}} . This is because the firm is not able to sell output at a fixed price per unit. Thus the M R P {\displaystyle MRP} curve of a firm in <a href="/facts/Monopoly/BXIQWUmR">monopoly</a> or in <a href="/facts/Imperfect_competition/uqdBDpU9">imperfect competition</a> will slope downwards, when plotted against labor usage, at a faster rate than in perfect specific competition. </p> <h2 id="further-reading">Further reading</h2> <ul><li>Pullen, J. (2009). <a href="https://books.google.com/books?id=9VF5AgAAQBAJ"><i>The Marginal Productivity Theory of Distribution: A Critical History</i></a>. Routledge Advances in Heterodox Economics. Taylor & Francis. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-134-01089-9.</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Daniel S. Hamermesh. 1986. The demand for labor in the long run. Handbook of Labor Economics (Orley Ashenfelter and Richard Layard, ed.) p. 429. <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> </ol>