A factory that you are managing has an hourly production process that can be represented by...
A factory that you are managing has an hourly production process that can be represented by the following Cobb Douglas Production function: Q = 20K0.5L0.50
The price of one unit of capital per hour is $30 or r =30 and the price of one unit of labour per hour is $10 or w = 10. Your total cost should not exceed $1,000. Thus,
TC = 1,000. Find the optimal amount of labour and capital that you will be using, and compute the total amount of Q. Include a diagram
Homework Answers
Graphically, this takes place at point E, where in the indifference curve is tangent to the budget line.
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A factory that you are managing has an hourly production process
that can be represented by...
3. (5 points) Consider a manufacturing company whose daily production output (number of daily produced goods)...
3. (5 points) Consider a manufacturing company whose daily production output (number of daily produced goods) is described by the Cobb-Douglas production function 20x1/2,1/2, where x is the number of units of labour (number of working hours) and y is the number of units expended on capital (number of machine hours). A unit of labour costs $10 (hourly wage is $10) and a unit of capital costs $40 (cost per machine hour is $40). (a) (2 points Assume that the...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The economy has 27,000 units of capital and a labour force of 1,000 workers. a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. b. If the real wage can adjust to equilibrate labour supply and labour de- mand, what is the real wage? In this equilibrium, what are employment, output, and the total...
* A firm produces output that can be sold at a price of $10. The Cobb-Douglas...
* A firm produces output that can be sold at a price of $10. The Cobb-Douglas production function is given by Q = F(K,L) = K½ L½ If capital is fixed at 1 unit in the short run, how much labor should the firm employ to maximize profits if the wage rate is $2? * Given the Cobb-Douglas production function for Mabel’s factory Q = (L0.4) * (K0.7) a) Based on the function above, does Mabel’s factory experiencing economies...
EXERCISE 1 COST MINIMIZATION, PART I Consider a firm with a Cobb-Douglas production function defined by...
EXERCISE 1 COST MINIMIZATION, PART I Consider a firm with a Cobb-Douglas production function defined by the equation Q = 32K0.5 0.25 where Q is output, K the capital input and I the labour input. The prices of both production factors are given to the firm: labour costs w = 32 per unit, capital r = 16 per unit. Imagine that the firm wants to produce 512 units of output at minimum cost. (a) Determine the (unique) stationary point, say...
Suppose a firm can use either Capital (K) or Labor (L) in a production process. The...
Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firms Production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit. a) (4 points) What is the firm’s Total Cost function? TC(Q) = ____________________________ b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm’s isoquant for...
A company has the following production function: Q = 2(KL)0.5 (please note this is to the...
A company has the following production function: Q = 2(KL)0.5 (please note this is to the power 0.5) Where L = Labour and K = Capital. The cost of labour per hour is K3 and the cost of capital is K42 per unit. The company has a budget of K588 available to spend on the two factors of production a) Formulate the company’s optimization problem b) Calculate the optimal input combination c) Compute the output level associated with the optimal...
A factory produces output (Q) using capital (K) and labor (L) according to the production function...
A factory produces output (Q) using capital (K) and labor (L) according to the production function Y(K,L)=K1/5*L4/5 Let r denote the price per unit capital, and w denote the price per unit labor, so that the total expenditure on these factors is rK + wL. a) As the factory manager, you have been told to produce 625 units of output. Give the equation for the relevant isoquant, written with L as a function of K. b) If r = 80...
3. The White Noise Corporation has estimated the following Cobb-Douglas production function using monthly observations for...
3. The White Noise Corporation has estimated the following Cobb-Douglas production function using monthly observations for the past two years: ln Q = 1.386 + 0.20 ln K + 0.30 ln L + 0.25 ln N where Q is the number of units of output, K is the number of units of capital, L is the number of unit of labor, and N is the number of units of raw materials. With respect to the above results, answer the following...
Output for a simple production process is given by Q = 2KL, where K denotes capital,...
Output for a simple production process is given by Q = 2KL, where K denotes capital, and L denotes labour. The price of capital is $25 per unit and capital is fixed at 8 units in the short run. The price of labour is $5 per unit. What is the total cost of producing 80 units of output? Numeric Answer:
*Help with e,f,g, The White Noise Corporation has estimated the following Cobb-Douglas production function using monthly...
*Help with e,f,g, The White Noise Corporation has estimated the following Cobb-Douglas production function using monthly observations for the past two years: ln Q = 1.386 + 0.20 ln K + 0.30 ln L + 0.25 ln N where Q is the number of units of output, K is the number of units of capital, L is the number of unit of labor, and N is the number of units of raw materials. With respect to the above results, answer the following...
3. (5 points) Consider a manufacturing company whose daily production output (number of daily produced goods) is described by the Cobb-Douglas production function 20x1/2,1/2, where x is the number of units of labour (number of working hours) and y is the number of units expended on capital (number of machine hours). A unit of labour costs $10 (hourly wage is $10) and a unit of capital costs $40 (cost per machine hour is $40). (a) (2 points Assume that the...
Q. 1 Consider an economy with the following Cobb-Douglas production func- tion: Y = 5K The economy has 27,000 units of capital and a labour force of 1,000 workers. a. Derive the equation describing labour demand in this economy as a function of the real wage and the capital stock. b. If the real wage can adjust to equilibrate labour supply and labour de- mand, what is the real wage? In this equilibrium, what are employment, output, and the total...
EXERCISE 1 COST MINIMIZATION, PART I Consider a firm with a Cobb-Douglas production function defined by the equation Q = 32K0.5 0.25 where Q is output, K the capital input and I the labour input. The prices of both production factors are given to the firm: labour costs w = 32 per unit, capital r = 16 per unit. Imagine that the firm wants to produce 512 units of output at minimum cost. (a) Determine the (unique) stationary point, say...
Output for a simple production process is given by Q = 2KL, where K denotes capital, and L denotes labour. The price of capital is $25 per unit and capital is fixed at 8 units in the short run. The price of labour is $5 per unit. What is the total cost of producing 80 units of output? Numeric Answer:
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