Environmental Economics, EEP101/ECON125 Problem Set 1 James Sallee Spring 2024 Problem set 1 covers core concepts from module 1, as well as some review of optimization and mathematics. Part I. Mathematics and economics review You must turn in answers to questions in Part I, but they will be covered in section and will be scored 5 points for completion and not individually graded. 

1. What is the derivative of 3x3 with respect to x? 

2. What is the derivative of ln(x) with respect to x? 

3. What is the partial derivative of x1/4y2/3 with respect to x? 

4. A consumer has a utility function equal to U = x1/2y1/2 and an exogenous budget constraint equal to Y . Denote the prices of x and y as Px and Py . Write the Lagrangean that represents the consumers optimization problem, using λ to denote the Lagrange multiplier. 

5. What is the intepretation of λ? 

6. Draw the consumer's indifference curve at U=6 and U=8.