Suppose that production q, capital k and labour 1 satisfy g(q, k, 1) = O. In other words, the production function q(k, I) is defined implicitly, and it satisfies g(q(k, I),k, 1) = 0 identically. How do you think we might calculate the partial derivatives in a manner similar to that developed in this chapter for functions g of only two variables? Illustrate your method by working out the partial derivatives when q is

Suppose that production q, capital k and labour 1 satisfy g(q, k, 1) = O. In other words, the production function q(k, I) is defined implicitly, and it satisfies g(q(k, I),k, 1) = 0 identically. How do you think we might calculate the partial derivatives in a manner similar to that developed in this chapter for functions g of only two variables? Illustrate your method by working out the partial derivatives when q is

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.11P

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Assume that Donnell Corp. is currently producing 500 units of output per period, using 25 units of labor and 20 units of capital. Values for the marginal product of each input and the prices of the inputs are as follows: MPK = 100, MPL = 200, w = 2, and r = 3. Given the information above, which of the following is true? a. The firm is currently using the optimal levels of capital and labor. b. The firm should increase labor and reduce capital usage. c. The firm is not using the optimal levels of capital and labor, and it is impossible to determine the optimal levels from the given information.
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A bitcoin miner, Alex, needs only electricity (E) and computer (K) to mine bitcoin. Assume that the production function for his bitcoin business is of Cobb-Douglas type,?(?,?)=???? with?+?< 1, resulting in strictly convex isoquants and is the same in South Korea and USA. Suppose that, similar to the podcast, the price per unit of electricity is higher in South Korea than in USA. Suppose that the price of a computer is the same in both countries. i. Determine whether it is more expensive to mine one bitcoin in South Korea than in USA based on the above assumptions by using appropriate diagram and explain your answer. Please keep electricity on the horizontal axis and computer on the vertical axis while drawing your diagram.