Frank Cowell Microeconomics March 2007 Exercise 2 6
- Slides: 10
Frank Cowell: Microeconomics March 2007 Exercise 2. 6 MICROECONOMICS Principles and Analysis Frank Cowell
Ex 2. 6(1): Question Frank Cowell: Microeconomics n n purpose: examine properties of an important class of production function method: find MRTS and examine properties in relation to key parameter
Ex 2. 6(1): Find the MRTS Frank Cowell: Microeconomics n Differentiate the production function n Then the marginal product of input i is n From the standard definition the MRTS is
Ex 2. 6(1): Find the elasticity Frank Cowell: Microeconomics n Invert the MRTS formula n Define two convenient changes of variable u u n n z : = log (z 1/z 2) q : = log (f 1(z)/f 2(z)) Then elasticity of substitution is just dz/dq Written out in full:
Ex 2. 6(2): Question and solution Frank Cowell: Microeconomics n The case b → ∞ yields s = 0 n The case b → 0 yields s = 1 n The case b → 1 yields s = ∞
Ex 2. 6(3): Question Frank Cowell: Microeconomics method: n Sketch isoquants for each of the special cases
Ex 2. 6(3): b → ∞ Frank Cowell: Microeconomics z 2 Leontief z 1
Ex 2. 6(3): b → 0 Frank Cowell: Microeconomics z 2 Cobb-Douglas z 1
Ex 2. 6(3): b → 1 Linear Frank Cowell: Microeconomics z 2 z 1
Ex 2. 6: Things to remember Frank Cowell: Microeconomics n n Many standard simple forms of isoquant map belong to same family Parameter of production function is monotonic transform of elasticity of substitution.
