Basic Properties of Utility and Production Functions
I have attached the screenshot of the question so it's easier to understand because of formatting....
(3 points) Consider the utility function u(c) = −c−2 + γ, where γ > 0.
- (a) Is marginal utility decreasing for this utility function? Show your work to prove
- your answer.
- (b) Find the coefficient of relative risk aversion.
- (c) Does this utility satisfy the first and second Inada conditions?
(2 points) Prove whether or not the following production functions exhibit constant returns to scale:
(a) F(K,L) = AKαL1−α, where α is between 0 and 1 and A > 0. (b) F(K,L) = AKL where A > 0.
(5 points) Consider a firm that uses capital K and land M as inputs to produce a final good, Y . Suppose that the technology for this firm is given by:
11 F(K,M)=2K2 +3M3
The firm must pay rental rate μ(1 + τK ) for each unit of capital rented, where τK > 0 represents a capital tax. It also must pay γ for each unit of land rented. Set up the firm's profit maximization problem and take FOCs. Find the optimal capital-land ratio. What happens when τK increases? Give some intuition.
Recently Asked Questions
- How many atoms are directly bonded to the central atom in a tetrahedral and trigonal pyramidal structure?On paper, draw the molecular geometry of a tetrahedral
- I can't understand what this question is asking for. Consider whether it is possible to represent the surface xy-ayln(z)+4(z^2-1)=0 in the form z=f(x,y), where
- The vapor pressure of water at 40.0oC is 7.34103 N/m2 . Using the ideal gas law, calculate the density of water vapor in g/m3 that creates a partial pressure