A firm produces output using capital (K) and labor (L). Capital and labor are perfect complements...

A firm produces output using capital (K) and labor (L). Capital and labor are perfect complements and 1 unit of capital is used with 2 units of labor to produce 1 unit of output. Draw an example of an isoquant. If wages and rent are $2 and $3, respectively, what is the Average Total Cost?
A firm has a production function given by Q=4KL where K, L and Q denote capital, labor, and output, respectively. The firm wants to produce an output of 16 units at a minimum cost. Show the solution graphically assuming that wages and rent are $1 and $2, respectively.
Consider a perfectly competitive firm in the short run. It has Total Cost and Marginal Cost functions given by TC(Q)=10+2Q2 and MC(Q)=4Q, respectively. The firm faces a price of P=$20. Determine the output that the firm will produce and the profit. Show the solution graphically.

Expert Solution

Rahul Sunny answered 2 years ago

There is a firm who manufacturers and uses capital (K) and labor (L) to product output...

There is a firm who manufacturers and uses capital (K) and labor (L) to product output Q such that Q=10KL. The unit price for K and L are w = $15 and r = $5, respectively. 1).Does the firm’s production exhibit decreasing, constant, or increasing returns to scale? 2)What is the optimal input bundle (K*, L*) to produce 480 unit of output? 3)Derive the long run cost function.

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...

when inputs K, L, are perfect complements, the isoquant is L-shaped, draw the graph, and then...

when inputs K, L, are perfect complements, the isoquant is L-shaped, draw the graph, and then show in the graph that increases in the wage rate cause only scale effect but no substitution effect. Also, will there be any differences between the short-run labor demand curve and the long-run labor demand curve?

Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the...

Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the production function is q = 50K^(1/2)L^(1/2). prices of capital and labor are given as r = 2 and w = 8 a) does the production function display increasing, constant, or decreasing returns to scale? how do you know and what does this mean? b) draw the isoquants for your firms production function using L for the x axis and K for y. how are...

A firm produces output using the technology: Q = 5K0.33L0.5 where capital, K, is measured in...

A firm produces output using the technology: Q = 5K0.33L0.5 where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and Q denotes the yearly output. The hourly wage rate in China WL = $10, and the hourly rental rate of capital (IN EFFECT CAPITAL COSTS $2 PER MACHINE HOUR) is WK = 2 and the Price is $10. a.) Does this production function display increasing returns to scale, constant returns to scale or decreasing returns to...

The auto maker Carbon Motors produces cars using capital (K) and labor (L) according to the...

The auto maker Carbon Motors produces cars using capital (K) and labor (L) according to the production function f(K, L) =K^3/4L^1/4. A different car company, Emissions Inc, produces cars according to the production function f(K, L) =K^1/2L^1/2. The wage rate paid to workers is w and the price of capital is r. (a) Find the cost minimizing input choices of Carbon and Emissions subject to producing q cars. (These will be functions of w ,r, and q.) For the same...

A firm produces output using the technology: Q = (0.001)KL0.5 where capital, K, is measured in...

A firm produces output using the technology: Q = (0.001)KL0.5 where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and Q denotes the yearly output. The hourly wage rate in the United States WL = $10, and the hourly rental rate of capital is WK = 20 and the Price is $1. (a) Does this production function display increasing returns to scale, constant returns to scale or decreasing returns to scale (hint—use labor). Please show how...

Suppose output, Q, is produced by labor, L, and capital, K, according to the following function:...

Suppose output, Q, is produced by labor, L, and capital, K, according to the following function: Q = K ½ L½.. Suppose the firm sells each unit of output in a competitive market for a price P = $100. Suppose the firm hires each unit of labor in a competitive market for a wage W = $25. Suppose the firm has to make do for now with a stock of capital K = 49; moreover, suppose each unit of capital...

Using iso-cost, iso-quant analysis draw the following concepts a. perfect complements of labor and capital b....

Using iso-cost, iso-quant analysis draw the following concepts a. perfect complements of labor and capital b. a long run expansion path of a capital-intensive firm c. substitution effect of a wage increase d. constant returns to scale e. economic efficient point, technological efficient points, technological inefficient points

Suppose you are in the photocopying business, and are using labor (L) and capital (K), in...

Suppose you are in the photocopying business, and are using labor (L) and capital (K), in the form of copy machines. You can hire workers for $150 a week and lease copy machines for $300 a week. (a) Suppose your current total cost of production is $3,000. Use the information above to depict the isocost you are currently operating on, carefully labeling the relevant intercepts (put L on the x-axis and K on the y-axis). (b) You are producing 10,000...

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