# Discount Rate

Question1: The EPA is interested in implementing a policy to increase the

amount of "brownfield" remidiation. Each policy possesses separate benefits

listed below (attachment) over a 5 year horizon. Cost of implementation is

10 million. Which policy would you recommend with a discount rate of 20%?

(see attachment)

Question 2: Calculate the marginal utility (for x and y) and the marginal

rate of substitution for the following utility functions:

1.) U(X,Y) = 4*X^0.3Y^0.5

(i just need one done to figure it out)

Question 3: Solve the following problems using the Lagrangian optimization

criterion to determine the optimal consumption of goods x and y and utility

derived from their consumption.

1.) U(x,y) = 8x^0.5y^0.25 Px = 4 Py = 2 I =$40

Lagrangian Formula: U(x,y) + lambda[I-PxX-PyY].

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#### Solution Preview

See the attached file.

Question1: The EPA is interested in implementing a policy to increase the amount of "Brownfield" remediation. Each policy possesses separate benefits listed below over a 5 year horizon. Cost of implementation is 10 million. Which policy would you recommend with a discount rate of 20%?

Policy 1: Total benefits over 5 years = 10+6+4+3+2 = 25m

Total benefits after discount = 0.80*25m = 20m

Profit = 20m - 10m = ...

#### Solution Summary

The solution calculates the marginal utility (for x and y) and the marginal rate of substitution.