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Letting TR be the total revenue function: () = (), [1] where Q is the quantity of output sold, and P(Q) is the inverse demand function (the demand function solved out for price in terms of quantity demanded).
Total revenue, the product price times the quantity of the product demanded, can be represented at an initial point by a rectangle with corners at the following four points on the demand graph: price (P 1), quantity demanded (Q 1), point A on the demand curve, and the origin (the intersection of the price axis and the quantity axis).
Marginal cost and marginal 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 to produce 5 units ...
where R is total revenue, P(Q) is the inverse of the demand function, and e < 0 is the price elasticity of demand written as = (). [ 27 ] Monopolist firm, as a price maker in the market, has the incentives to lower prices to boost quantities sold. [ 17 ]
The marginal revenue function has twice the slope of the inverse demand function. [9] The marginal revenue function is below the inverse demand function at every positive quantity. [10] The inverse demand function can be used to derive the total and marginal revenue functions. Total revenue equals price, P, times quantity, Q, or TR = P×Q ...
To calculate the break-even point in terms of revenue (a.k.a. currency units, a.k.a. sales proceeds) instead of Unit Sales (X), the above calculation can be multiplied by Price, or, equivalently, the Contribution Margin Ratio (Unit Contribution Margin over Price) can be calculated:
The marginal profit per unit of labor equals the marginal revenue product of labor minus the marginal cost of labor or M π L = MRP L − MC L A firm maximizes profits where M π L = 0. The marginal revenue product is the change in total revenue per unit change in the variable input assume labor. [10] That is, MRP L = ∆TR/∆L.
The marginal revenue function is the first derivative of the total revenue function; here MR = 120 - Q. Note that the MR function has the same y-intercept as the inverse demand function in this linear example; the x-intercept of the MR function is one-half the value of that of the demand function, and the slope of the MR function is twice that ...