香港科技大学《基础代数学》基础分析学之二_：多元微积分

香港科技大学《基础数学》讲义：基础几何学之二：向量，解析与球面几何

5. Oligopoly Oligopoly: Small number of firms: Firms depend on each other. Identical products: Firms jointly face a downward sloping industry demand No entry: Long-run positive profits are possible

8.1. Independent Firms The downstream firm's problem is max(a-bxc-wT The upstream firm's problem is max(a-2b)3-cr The output is 8.2. Integrated Firm Suppose now that the two firms merge into one firm. This firms problem is max(a-by)y

Problem set 2 Micro Theory S. Wang Question 2. 1. You have just been asked to run a company that has two factories produc ing the same good and sells its output in a perfectly competitive market. The production

Corporate finance 1. Theoretical Approaches 1.1. Corporate Finance in Arrow-Debreu world Complete market, perfect market, perfect competition, symmetric information, private consumption Risk: risk sharing, risk pooling, technology shocks, individual vs aggregate shocks Lucas(1978): existence of equilibrium asset price Merton: continuous-time pricing model

Optimization See Sydsaeter(2005, Chapters 2, 3)and Chiang(1984, Chapters 9, 11, 12 and 21) Positive definite matrix Definite matrices are directly related to optimization. A symmetric matrix A is positive semi- definite(A≥0) if rAr≥0,Vx; positive definite(A>0)

(1)i(p, u) is zero homogeneous in p (2) substitution matrix: Dpi(p, u)<0 (3)symmetric cross-price effects: 23i(p 2=2z(p, u) (4) decreasing:=n≤0

Equilibrium price. Equilibrium allocation: x=xi(p,p·w2), Note: A p* for any >0 is also an equilibrium price. Offer curve: (p)(p, p. w;). The equilibrium is the intersection point of the offer curves. Excess demand function:

香港科技大学《基础数学》讲义：基础几何学之一 定性与定量平面几何/立体几何基础论