Question

In: Economics

A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and...

A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and ? stand for inputs capital and labour respectively. The price of capital is ?, and the price of labour is ?. Which of the following is true?

  1. Regardless of ? and ?, cost minimisation requires that ? = ?.

  2. If ? > ?, contingent demand for labour is 0.

  3. The technology has increasing returns to scale.

  4. If ? < ?, profit maximisation requires that no labour is used in production.

Solutions

Expert Solution

From the above analysis we know that:----

if w > v => contingent demand of capital is greater than zero & contingent demand of labor is 0.

if w < v => contingent demand of labor is greater than zero & contingent demand of capital is 0.

if w = v => contingent demand of both capital & of labor is greater than zero.

Hence only D is true as A & B cannot be true due to above analysis.

Also f(tK,TL) = (1/2)(tK + tL) = t*[(K+L)/2] = t*f(K,L) => constant return to scale. hence C is also false.

only D is true.

Rahul Sunny answered 1 year ago
Next > < Previous

Related Solutions

A competitive firm has the production function Q = (Lw + Lb) 1/2 , where Lw...
A competitive firm has the production function Q = (Lw + Lb) 1/2 , where Lw and Lb are the respective numbers of white and black workers employed. The price of output is constant at P = 36. The market wage is wb = 3 for black workers and ww = 9 for white workers. If a firm has a discrimination coefficient of d > 0, then it behaves as if the wage is wb(1 + d) for black workers...
A perfectly competitive firm has a production function ?(?1, ?2) = ?1?2. Input prices are given...
A perfectly competitive firm has a production function ?(?1, ?2) = ?1?2. Input prices are given by ?1 = 2 and ?2 = 1. a. Does this production function exhibit decreasing, constant, or increasing returns to scale? b. In the short run, input factor 2 is fixed at x2=8 and the firm chooses the optimal input quantity x*1 to minimize the cost of producing output y=72. Derive x1*. c. Calculate the costs cs associated with the above short-run solution. d....
A profit-maximizing competitive firm has the production function ? = ?^.25?^.25 , where output ? is...
A profit-maximizing competitive firm has the production function ? = ?^.25?^.25 , where output ? is produced using capital (?) and labor (?). The price of labor is $2 and the price of capital is $6. The price of the firm’s output is $100. a. Write the firm’s profit function and calculate the first-order conditions. Provide an economic interpretation for each of the first-order conditions. b. Find the profit-maximizing quantities ?* and ?*. c. Find the firm’s total costs. d....
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q...
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q = Output and L = labor input       a. At what value of L will Diminishing Returns take effect?       b. Calculate the range of values for labor over which stages I, II, and III occur?      c. Suppose that the wage rate is $30 and the price of output is $2 per unit. How many           workers should the firm hire?       d....
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q...
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q = Output and L = labor input       a. At what value of L will Diminishing Returns take effect?       b. Calculate the range of values for labor over which stages I, II, and III occur?      c. Suppose that the wage rate is $30 and the price of output is $2 per unit. How many           workers should the firm hire?       d....
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q...
The Production Function of a perfectly competitive firm is Q = 80L +12L2 -0.5L3, where Q = Output and L = labor input       a. At what value of L will Diminishing Returns take effect?       b. Calculate the range of values for labor over which stages I, II, and III occur?      c. Suppose that the wage rate is $30 and the price of output is $2 per unit. How many           workers should the firm hire?       d....
Problem 3: A firm has the following production function: ?(?1, ?2 ) = ?1 + 4?2...
Problem 3: A firm has the following production function: ?(?1, ?2 ) = ?1 + 4?2 A)  Does this firm’s technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly ? units and that input 1 costs $?1 per unit and input 2 costs $?2 per unit. What are the firm’s conditional input demand functions? C) Write down the formula for the firm’s total cost function as a function of ?1, ?2, and ?....
Problem 3: A firm has the following production function: ?(?1, ?2 ) = ?1 + 4?2...
Problem 3: A firm has the following production function: ?(?1, ?2 ) = ?1 + 4?2 A) Does this firm’s technology exhibit constant, increasing, or decreasing returns to scale? B) Suppose the firm wants to produce exactly ? units and that input 1 costs $?1 per unit and input 2 costs $?2 per unit. What are the firm’s conditional input demand functions? C) Write down the formula for the firm’s total cost function as a function of ?1, ?2, and...
Problem 2: A firm has the following production function: ?(?, ?) = ? + ? A)...
Problem 2: A firm has the following production function: ?(?, ?) = ? + ? A) Show whether this firm’s technology exhibits constant, increasing, or decreasing returns to scale. B) Suppose the firm wants to produce exactly ? units and that input ? costs $?? per unit and input ? costs $?? per unit. What are the firm’s input demand functions? C) Write down the formula for the firm’s total cost function as a function of ?? , ??, and...
A firm has a production function of Q = KL + L, where MPL = K...
A firm has a production function of Q = KL + L, where MPL = K + 1 and MPK = L. The wage rate (W) is $100 per worker and the rental (R) is $100 per unit of capital. a. In the short run, capital (K) is fixed at 4 and the firm produces 100 units of output. What is the firm's total cost? b. In the long run, what is the total cost of producing 100 units of...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT