Math for Economists Midterm.

Modified at 9:15am, March 11th

Fan Wang

March 11, 2021

Note: The test has 115 points.

1 Derivatives

1.1 Production Functions and Elasticity (10 points, 2 each)

1. What is a linear equation? give one example below:

2. Firm A has Cobb-Douglas production function with K and L inputs, write down the produc-tion function:

3. Firm B has Cobb-Douglas production function with K as input and the production function has constant returns to scale, write down the production function:

4. Firm C has a linear production function with input K. Output when K = 0 is a, and each additional unit of capital leads to b units of increase in output, write down the production function:

5. For firm C, what is the elasticity of output with respect to input?

1.2 Derivatives (15 points)

Take derivative below:.

1.3 First Order Taylor Approximation (15 points)

2 Log and Exponential (10 points, 2.5 each)

3 Household Problem (25 points)

4 Firm Maximization with K and L and Z (40 points)

4.1 A Firm with Three Inputs

4.2 A Firm with N Inputs

Typos modifications:

1. 1.5, wording adjusted "elasticity of output with respect to input"

2. 3.5, wording adjusted to "elasticity of optimal borrowing/savings with respect to first period endowment"