Consider a firm for which production depends on two normal inputs, labour and capital, with prices...

Consider a firm for which production depends on two normal inputs, labour and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. The price of capital (r) then shifts to r = 6 while w remains the same. Use isocost-isoquant analysis to show and explain the following. A. In which direction will the substitution effect change the firm’s employment and capital stock? B. In which direction will the scale effect change the firm’s employment and capital stock? C. Can we say conclusively whether the firm will use more or less labour and more or less capital?

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Rahul Sunny answered 2 years ago

A firm uses two inputs in production: capital and labour. In the short run, the firm...

A firm uses two inputs in production: capital and labour. In the short run, the firm cannot adjust the amount of capital it is using, but it can adjust the size of its workforce. What happens to the firm’s average-total-cost curve, the average-variable-cost curve, and the marginal-cost curve when the cost of renting capital increases? The average-total-cost curve (shifts up/shifts down/do not change) . The average-variable-cost curve (shifts up/shifts down/do not change) . The marginal-cost curve (shifts up/shifts down/do not change) ....

Consider a producer making choices over two inputs, labour (l) and capital (k) with prices w...

Consider a producer making choices over two inputs, labour (l) and capital (k) with prices w = 3 and r = 1. The production technology is f(l, k) = l + 3k. What is the marginal rate of technical substitution (MRTS)? Is there diminishing MRTS? Find the input demands in long-run (as a function of output level)? Find the long-run total cost, marginal cost, and average cost functions? Do the properties of a typical cost function hold for the long...

A firm produces output y using two factors of production (inputs), labour L and capital K....

A firm produces output y using two factors of production (inputs), labour L and capital K. The firm’s production function is ?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of capital r = 2 are taken as parameters (fixed) by the firm. a. Show whether this firm’s technology exhibits decreasing, constant, or increasing returns to scale. b. Solve the firm’s long run cost minimization problem (minimize long run costs subject to the output constraint) to derive this...

A competitive firm uses two inputs, capital (?) and labour (?), to produce one output, (?)....

A competitive firm uses two inputs, capital (?) and labour (?), to produce one output, (?). The price of capital, ??, is $1 per unit and the price of labor, ?? , is $1 per unit. The firm operates in competitive markets for outputs and inputs, so takes the prices as given. The production function is ?(?, ?) = 3? 0.25? 0.25. The maximum amount of output produced for a given amount of inputs is ? = ?(?, ?) units....

A firm uses two inputs in production: capital and labor. In the short run, the firm...

A firm uses two inputs in production: capital and labor. In the short run, the firm cannot adjust the amount of capital it is using, but it can adjust the size of its workforce. -- If the cost of renting capital increases, which of the following curves will be affected? (Check all answers that apply). -- Average variable cost Marginal cost Average fixed cost Average total cost 2 points QUESTION 2 If the cost of hiring workers increases, which...

Suppose there are two inputs in the production function, labor and capital, and these two inputs...

Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 5 machines to do the work of 2 workers. So the production function is f(E, K) = 2K + 5E. The firm wants to produce q units of output, where q > 0 is some number. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the firm use if the...

Suppose there are two inputs in the production function, labor and capital, and these two inputs...

Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 3 machines to do the work of 2 worker. So F(E,K)=2K+3E. The firm wants to produce 60 units of output. Suppose the price of capital is $10 per machine per hour. What combination of inputs will the firm use if the wage rate is $10 or $15 or $20 per hour? What if the firm wants to...

Suppose there are two inputs in the production function, labor and capital, which are substitutes. The...

Suppose there are two inputs in the production function, labor and capital, which are substitutes. The current wage is $10 per hour and the current price of capital is $25 per hour. Given the following information on the marginal product of labor and the marginal product of capital, find the firm’s profit-maximizing input mix (i.e. number of workers and units of capital) in the long-run. Show your work and explain. L MPL K MPK 1 125 1 130 2 100...

Consider a production function of two inputs, labor and capital, given by Q = (√L +...

Consider a production function of two inputs, labor and capital, given by Q = (√L + √K)2. Let w = 2 and r = 1. The marginal products associated with this production function are as follows:MPL=(√L + √K)L-1/2MPK=(√L + √K)K-1/2 a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q. Show how the cost-minimizing quantity of capital depends on the quantity Q. b) Find the equation...

3. A perfectly competitive firm produces output y using two factors of production (inputs), labour L...

3. A perfectly competitive firm produces output y using two factors of production (inputs), labour L and capital K. The firm’s production function is ?(?, ?) = (?^1/2 + ?^1/2) ^2. The wage rate is w = 9 and the rental price of capital is r = 1. a. Find the long run equilibrium price p in this market. b. Suppose in the short run, capital is fixed at K = 1. The output price in the short run is...

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Consider a firm for which production depends on two normal inputs, labour and capital, with prices...

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