Tối đa hóa lợi nhuận
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Tối đa hóa lợi nhuận là hành vi của một hãng (người sản xuất) điển hình kinh tế.
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[sửa] Giả thiết
- Quy trình sản xuất của hãng chỉ sử dụng hai yếu tố đầu vào là lao động và vốn.
- Để có vốn, hãng phải đi vay và phải trả lãi suất.
- Để có lao động, hãng phải đi thuê lao động và trả lương.
- Lợi nhuận của hãng bằng chênh lệch giữa doanh thu và chi phí sản xuất.
[sửa] Ký hiệu
- Π là lợi nhuận,
- p là giá bán hàng,
- F(L,K) là sản lượng biểu diễn dưới dạng một hàm sản xuất,
- w là tiền công trả cho một đơn vị lao động,
- L là số lượng đơn vị lao động,
- r là lãi suất phải trả vì đi vay tính trên một đơn vị vốn,
- K là số đơn vị vốn.
[sửa] Bài toán tối đa hóa lợi nhuận
- Ta có, doanh thu bằng giá bán sản phẩm nhân với sản lượng.
- Lại có, chi phí sản xuất bao gồm chi phí thuê mướn nhân công và chi phí thuê vốn (giả định là hãng đi vay để đầu tư mua máy móc và nguyên vật liệu). Chi phí thuê mướn nhân công lại bằng tiền công nhân với số lượng lao động. Còn chi phí thuê vốn bằng lãi suất nhân với số tiền đi vay.
Từ đó, công thức tính lợi nhuận là:
Π=p×F(L,K)-(wL+rK)
Trong vế phải của công thức trên, nhóm số bị trừ chính là doanh thu, còn nhóm số trừ chính là tổng chi phí.
Tối đa hóa lợi nhuận chính là giải bài toán tính vi phân cả hai vế của công thức nói trên lần lượn theo L và K, đồng thời cho đạo hàm của Π theo L và K bằng 0.
[sửa] Kết quả
Kết quả giải bài toán nói trên là doanh thu biên bằng chi phí biên bằng giá bán.
Tối đa hóa lợi nhuận là phương pháp các công ty quyết định giá thành và sản lượng sao cho thu được nhiều lợi nhuận nhất. Có nhiều cách để giải bài toán này.
- Cách thứ nhất dựa trên nguyên tắc xác định lợi nhuận bằng doanh thu trừ chi phí.
- Cách thứ hai dựa trên giả thuyết cho rằng trong một thị trường cạnh tranh, lợi nhuận sẽ cao nhất khi doanh thu biên bằng chi phí biên.
[sửa] Phương pháp doanh thu trừ chi phí
[sửa] Phương pháp doanh thu biên trừ chi phí biên
In economics, profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. There are several approaches to this problem. The total revenue -- total cost method relies on the fact that profit equals revenue minus cost, and the marginal revenue -- marginal cost method is based on the fact that total profit in a perfectly competitive market reaches its maximum point where marginal revenue equals marginal cost.
[sửa] Basic Definitions
Any costs incurred by a firm may be classed into two groups: fixed cost and variable cost. Fixed costs are incurred by the business at any level of output, including none. These may include equipment maintenance, rent, wages, 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. Fixed cost and variable cost, combined, equal total cost.
Revenue is the total amount of money that flows into the firm. This can be from any source, including product sales, government subsidies, venture capital and personal funds.
Average cost and revenue are defined as the total cost or revenue divided by the amount of units output. For instance, if a firm produced 400 units at a cost of 20000 USD, the average cost would be 50 USD.
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 quantity 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 approximately 80 dollars, although this is more accurately stated as the marginal cost of the 5.5th unit due to linear interpolation. Calculus is capable of providing more accurate answers if regression equations can be provided.
[sửa] Total Cost-Total Revenue Method
To obtain the profit maximizing output quantity, we start by recognizing that profit is equal to total revenue minus total cost. Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph. Finding the profit-maximizing output is as simple as finding the output at which profit reaches its maximum. That is represented by output Q in the diagram.
There are two graphical ways of determining that Q is optimal. Firstly, we see that the profit curve is at its maximum at this point (A). Secondly, we see that at the point (B) that the tangent on the total cost curve (TC) is parallel to the total revenue curve (TR), the surplus of revenue net of costs (B,C) is the greatest. Because total revenue minus total costs is equal to profit, the line segment C,B is equal in length to the line segment A,Q.
Computing the price at which to sell the product requires knowledge of the firm's demand curve. The price at which quantity demanded equals profit-maximizing output is the optimum price to sell the product.
[sửa] Marginal Cost-Marginal Revenue Method
If total revenue and total cost figures are difficult to procure, this method may also be used. For each unit sold, marginal profit equals marginal revenue minus marginal cost. Then, if marginal revenue is greater than marginal cost, marginal profit is positive, and if marginal revenue is less than marginal cost, marginal profit is negative. When marginal revenue equals marginal cost, marginal profit is zero. 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. This is because the producer has collected positive profit up until the intersection of MR and MC (where zero profit is collected and any further production will result in negative marginal profit, because MC will be larger than MR). The intersection of marginal revenue (MR) with marginal cost (MC) is shown in the next diagram as point A. If the industry is 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 profits are represented by area P,A,B,C. The optimum quantity (Q) is the same as the optimum quantity (Q) in the first diagram.
If the firm is operating in a non-competitive market, minor changes would have to be made to the diagrams..
[sửa] Modes of Operation
It is assumed that all firms are following rational decision-making, and will produce at the profit-maximizing output. Given this assumption, there are four categories in which a firm's profit may be considered.
A firm is said to be making an economic profit when its average total cost is less than the price of the product at the profit-maximizing output. The economic profit is equal to the quantity output multiplied by the difference between the average total cost and the price.
A firm is said to be making a normal profit when its economic profit equals zero. This occurs where average total cost equals price at the profit-maximizing output.
A firm is said to be making a zero economic profit when its marginal revenue equals marginal cost.
If the price is between average total cost and average variable cost at the profit-maximizing output, then the firm is said to be in a loss-minimizing condition. The firm should still continue to produce, however, since its loss would be larger if it was to stop producing. By continuing production, the firm can offset its variable cost and at least part of its fixed cost, but by stopping completely it would lose equivalent of its entire fixed cost.
If the price is below average variable cost at the profit-maximizing output, the firm is said to be in shutdown. Losses are minimized by not producing at all, since any production would not generate returns significant enough to offset any fixed cost and part of the variable cost. By not producing, the firm loses only its fixed cost.
[sửa] See also
- Supply and demand
- Market forms, Microeconomics
- pricing
- production, costs, and pricing
- corporation
- business organization