商业经济学的模型公式与批注
1, The Fundamentals of Managerial Economics
未来价值流的现值pv=∑FVt/(1+i)t
2, Market Forces: Demand and Supply
3, Quantitative Demand Analysis
4, The Theory of Individual Behavior
5, The Production Process and Costs
生产率衡量标准TP/AP----APL=Q÷L---APK=Q÷K/MP-----MPL=▶Q÷▶L---MPK=Q÷K
生产函数的代数形式 –Linear: Assumes a perfect linear relationship between all inputs and total output
Q=F(K,L)=aK+bL, where a and b are constants.
–Leontief: Assumes that inputs are used in fixed proportions
Q=F(K,L)=min{aK,bL}, where a and b are constants.
–Cobb-Douglas: Assumes some degree of substitutability among inputs
Q=F(K,L)=K^a L^b, where a and b are constants.
生产率的代数计量
–Linear:
•Marginal products: 〖MP〗_K=a and 〖MP〗_L=b
•Average products: 〖AP〗_K=(aK+bL)/K and 〖AP〗_L=(aK+bL)/L
–Cobb-Douglas:
•Marginal products: 〖MP〗_K=aK^(a-1) L^band 〖MP〗_L=bK^a L^(b-1)
Average products: 〖AP〗_K=(K^a L^b)/K and 〖AP〗_L=(K^a L^b)/L
边际数列替代率
〖MRTS〗_KS=〖MP〗_L/〖MP〗_K
等值
•Isocost –Combination of inputs that yield cost the same cost.
wL+rK=C
or, re-arranging to the intercept-slope formulation:
K=C/r-w/r L
成本最小化输入规则
•Cost-minimizing input rule –Produce at a given level of output where the marginal product per dollar spent is equal for all input:
〖MP〗_L/w=〖MP〗_K/r
–Equivalently, a firm should employ inputs such that the marginal rate of technical substitution equals the ratio of input prices:
〖MP〗_L/〖MP〗_K =w/r
成本函数
•Short-run costs
–Fixed costs (FC): do not change with changes in output; include the costs of fixed inputs used in production
–Sunk costs
–Variable costs [VC(Q)]: costs that change with changes in outputs; include the costs of inputs that vary with output
–Total costs: TC(Q)=FC+VC(Q)
平均成本和边际成本
•Average costs
–Average fixed cost: AFC=FC/Q
–Average variable costs: AVC=VC(Q)/Q
–Average total cost: ATC=C(Q)/Q
•Marginal cost (MC)
–The (incremental) cost of producing an additional unit of output.
MC=∆C/∆Q
多重输出成本函数
•Economies of scope –Exist when the total cost of producing Q_1 and Q_2 together is less than the total cost of producing each of the type of output separately.
C(Q_1,0)+C(0,Q_2 )>C(Q_1,Q_2 )
•Cost complementarity –Exist when the marginal cost of producing one type of output decreases when the output of another good is increased.
(∆〖MC〗_1 (Q_1,Q_2 ))/(∆Q_2 )<0
多产品成本函数的代数形式
C(Q1, Q2)=f+aQ1Q2+(Q_1 )^2+(Q_2 )^2
•For this cost function:
MC1 = aQ2 + 2Q1
-When a < 0, an increase in Q2 reduces the marginal cost of producing product 1. -If a < 0, this cost function exhibits cost complementarity -If a > 0, there are no cost complementarities -Exhibits economies of scope whenever f - aQ1Q2 > 0
6, Managing in Competitive, Monopolistic, and- Monopolistically Competitive Markets
7, Basic Oligopoly , Models
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