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# Basie Preperties ef Utility and Preduetieu Funet inns (1E! paints) . {3 points} Consider the uti]it_r,r funetiun tulle] = r:_2 + 1', where &quot;r

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.

1. (a) Is marginal utility decreasing for this utility function? Show your work to prove
3. (b) Find the coefficient of relative risk aversion.
4. (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.

Basie Preperties ef Utility and Preduetieu Funet inns
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