Microeconomic Theory

Microeconomic Theory Assignment 6 Name: ________________________

Summer 2021

Note: Students should submit answers only via Canvas. You can choose to hand-write (and scan) or type answers. Make sure your submission is legible. Email submission is not acceptable. Show work for all questions. No work, no credit. If you are submitting photos taken directly by Apple products, make sure you transform .HEIC files to readable files first. Any files that cannot be opened or viewed by Canvas will not be read. Some questions here are obtained on the Internet. Copyright belongs to respective authors.

Question 1

For the following production functions, determine the returns to scale and its MRTS. Show your work.

(Usually we put L (labor) on the horizontal axis, and K (capital) on the vertical axis, so that .)

a)

b)

Question 2

For the following production functions, determine the returns to scale.

Question 3

Suppose that the production function is

a) What is the marginal product of x1?

b) Does this production function have increasing, constant, or decreasing returns to scale?

Question 4

At low levels of production, marginal productivity of labor increases as labor increases. At high levels of production, marginal productivity of labor decreases as labor increases. Are these two statements contradictory? Explain.

Question 5

Suppose the production function for T-shirts can be represented as q = L0.25K0.75. Show that the production function has constant returns to scale.