Aims of this lecture Summarize properties of the rhizosphere, especially Gradients in Nutrient concentration Redox potential Exudates Microbial activity Non-infecting rhizosphere microorganisms Infecting rhizosphere microorganisms that are relevant to plant mineral nutrition red from H Marschner:

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

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

《数学分析》课程教学资源（试题集锦）华中科技大学数学分析

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)

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:

(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

《数学分析》课程教学资源（试题集锦）华中科技大学99年高等代数

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

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