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.

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

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

4. Consider an economy with the following Cobb-Douglasproductionfunction:
Y = K1/3 L2/3.
The economy has 1,000 units of capital and a labor force of 1,000 workers.
a. What is the equation describing the demand for labor in this economy? (Hint: Review the appendix to Chapter 3.)
b. If the real wage can adjust to equi

A firm used a combination of inputs that was to the left of its isocost line, it would indicate that
a. it is exceeding its budget.
b. it is not spending all of its budget.
c. it is operating at its optimal point because it is saving money.
d. None of the above.
When the exponents of a Cobb-Douglasproduction func

1. Consider the cost function:
C = 60 + 20Q + 30Q^2
with MC = 20 +60Q (here Q denotes output)
Part A) Write down the expression for the average cost.
Part B) What is the output elasticity of the total cost at output level of Q = 1 ?
Part C) At an output of 1, does the cost function exhibit economies of scale, diseconomies o

1. Graph the US capital-labor ratio since 1948 (use thee sum of private equipment capital and private structures capital as the measure of capital, and civilian employment as the measure of labor). Do you see evidence of convergence to a steady state during the postwar period? Now graph output per worker for the same period.