Cobb-Douglas Production function: Optimal Labor capital mix

Suppose a firm assumes the following production function:
Log Q=2 + .8 log K + .1 log L
a) Currently, the firm hires 10,000 workers and employs 50 units of capital. The "wage" of capital and labor are $500 and $800 respectively, what would you suggest would be the firm's mix of labor and capital if it produces 2,000,000 units?
b) Is this an example of a Cobb-Douglas Production function?
c) Would you suggest this firm merge with similar firms? Explain.

Suppose a firm assumes the following production function:
Log Q=2 + .8 log K + .1 log L
a) Currently, the firm hires 10,000 workers and employs 50 units of capital. The "wage" of capital and labor are $500 and $800 respectively, what would you suggest would be the firm's mix of labor and capital if it produces 2,000,000 units?
Log Q=2 + .8 log K ...

Solution Summary

This problem explains the concepts related to production functions in microeconomics. Shows the calculations in step-by-step manner for easy understanding. Solution presented in formatted word document.

The following Cobb-Douglasproduction function,
Q = 1.8L0.74K0.36
exhibits
a. increasing returns.
b. constant returns.
c. decreasing returns.
d. both a. and b

Subject: Analytical question about capital, labor, and TFP, using Cobb Douglas function
Details: 4. Output in an economy is produced when labor hours (H) are combined with capital (K) in a way which reflects TFP to produce output (y). The relation is: y=TFP.K0.^0.27 * H^1-.0.27 What is the share of labor income in output? Wh

Suppose we have an economy described by the Solow growth model, with a Cobb-Douglasproduction function (Y=F(K,AL) = K^α(AL)^-α), a capital share of 0.5; with population, labor-augmenting productivity growth, and depreciation rates given by n =0.01 per year, x = 0.02 per year, and depreciation = 0.045 per year; and with a sav

This is an analytical exercise from my macroeconomics book chapter 4, The Theory of Economic Growth. I need help in answering these questions in order to be better understand this model.
(1) Consider the Cobb-Douglasproduction function
Y/L = (K/L)^α (E)^1-α
Show that multiplying both sides of this expressio

Assume Firm Y's production function is given by the following Cobb Douglas equation
Q = 0.5 x L^0.6 x K^0.5
where L denotes labor and K denotes capital.
The production function exhibits (increasing/decreasing/constant) returns to scale.
1. If labor hours increase by 10%, what is the percentage change in output (provi

Hi,
I am fairly new to economics with only a basic understand of the topic and because of this I am struggling to answer (and understand the explanation for the answer) a question about the Cobb Douglas production function.
Q. Under what conditions does a Cobb-Douglasproduction function (q=AL^(alpha)K^(beta)) exhibit decr

Production Function is Q = 25L^1/2(K^1/2)
Where: Q = Output Rate
K = units of capital
L = units of labor
a) Suppose that the price of capital (r) is $40.00 per unit and the price of labor (w) is $160.00 per unit.
If the firm wants to produce 5000 units, what is the optimal combination of inputs

Suppose we have an economy described by the Solow growth model, with Cobb-Douglasproduction function (Y=F(K,AL) = K^α (AL)^1-α ), a capital share of 0.5; with population, labor-augmenting productivity growth, and depreciation rates given by n = 0.01 per year, x = 0.02 per year, and depreciation = 0.045 per year; and w

An indirect utility function is, among other properties, zero-degree homogeneous in the prices and nominal income. That is, if you scale up each price and nominal income in the same positive proportion t, indirect utility remains unchanged. Explain why this is true. (Hint: real income remains constant).
Now demonstrate t