利润最大化范里安英文106页

Short-Run Iso-Profit Lines 短期等利润线
A $ iso-profit line （等利润线） contains all the production plans that provide a profit level $ .
A $ iso-profit line’s equation is
How?
Economic Profit
Suppose the firm is in a short-run circumstance in which（假定公司处于 短期的生产环境） x2x ~2.
Its short-run production function is
y f(x 1 ,x ~ 2 ).
Chapter Nineteen
Profit-Maximization
Economic Profit
A firm uses inputs j = 1…,m to make products i = 1,…n.
Output levels are y1,…,yn. Input levels are x1,…,xm. Product prices are p1,…,pn. Input prices are w1,…,wm.
Q: What is this constraint?（生产计划 约束？）
Short-Run Profit-Maximization
The firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the firm’s constraint on choices of production plans. （生产计划的选择约束）
Then the present-value of the firm’s economic profit stream is
PV 01 1r(1 r2)2
Economic Profit
A competitive firm seeks to maximize its present-value.一个竞争性企业为最 大化利润流现值。
Economic Profit
How do we value a firm?如何为一个公 司订价？
Suppose the firm’s stream of periodic economic profits is 0, 1, 2, … and r is the rate of interest.
Economic Profit
Suppose the firm is in a short-run circumstance in which x2x ~2.
Its short-run production function is
y f(x 1 ,x ~ 2 ).
The firm’s fixed cost is F C w 2 x ~ 2 and its profit function is p y w 1 x 1 w 2 x ~ 2 .
p y w 1 x 1 w 2 x ~ 2 . I.e. yw p 1x1p w 2x ~2.
Short-Run Iso-Profit Lines短期等利润线 yw p 1x1p w 2x ~2
has a slope of
w1 p
and a vertical intercept of
The Competitive Firm
The competitive firm takes all output prices p1,…,pn and all input prices w1,…,wm as given constants.
Economic Profit
The economic profit generated by the production plan (x1,…,xm,y1,…,yn) is
p 1 y 1 p n y n w 1 x 1 w m x m .
Economic Profit
Output and input levels are typically flows.(流量）
E.g. x1 might be the number of labor units used per hour.（每小时劳动投入 量）
p y w 1 x 1 w 2 x ~ 2 .
Short-Run Iso-Profit Lines
A $ iso-profit line contains all the production plans that yield a profit level of $ .
The equation of a $ iso-profit line is
w2x~2. p
Short-Run Iso-Profit Lines
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p
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Short-Run Profit-Maximization 短期公司利润最大化
The firm’s problem is to locate the production plan that attains the highest possible iso-profit line, given the firm’s constraint on choices of production plans.（给定公司的生产计 划约束，使生产计划尽可能地达到最高 的等利润线上。）
And y3 might be the number of cars produced per hour.（每小时产出量）
Consequently, profit is typically a flow also; e.g. the number of dollars of profit earned per hour.