Question

Suppose a firm has a Cobb-Douglas production function. Show graphically that an increase in the rental rate of capital will increase the amount of labor hired if production remains at the same amount(10pts).

Answer 1

In economics, a construction operate relates physical output of a construction system to physical inputs or explanations of production. It is a mathematical perform that relates the highest amount of output that may be got from a given number of inputs more often than not capital and labor. The production function, hence, describes a boundary or frontier representing the limit of output available from every viable blend of inputs.

Companies use the construction function to examine how a lot output they should produce given the rate of a good, and what mixture of inputs they will have to use to supply given the rate of capital and labor. When firms are identifying how so much to produce they on the whole in finding that at excessive stages of production, their marginal expenditures increasing. That is also known as diminishing returns to scale increasing the number of inputs creates a less-than-proportional expand within the variety of output. If it weren't for diminishing returns to scale, give would develop with out limits without growing the price of a excellent.

Manufacturing facility creation: Manufacturing corporations use their construction operate to check the optimum blend of labor and capital to produce a distinctive quantity of output.
Increasing marginal costs can be identified making use of the production perform. If a organization has a creation perform Q=F(k,L) (that is, the variety of output (Q) is some operate of capital (ok) and labor (L)), then if 2Q<F(2K,2L), the production function has increasing marginal costs and diminishing returns to scale. Similarly, if 2Q>F(2K,2L), there are increasing returns to scale, and if 2Q=F(2K,2L), there are steady returns to scale.

Examples of fashioned creation features

One quite simple example of a creation perform perhaps Q=ok+L, where Q is the quantity of output, okay is the quantity of capital, and L is the quantity of labor used in creation. This construction operate says that a corporation can produce one unit of output for every unit of capital or labor it employs. From this production function we are able to see that this enterprise has constant returns to scale that is, the quantity of output will increase proportionally to any increase in the amount of inputs.

Yet another usual creation operate is the Cobb-Douglas construction operate. One instance of this type of perform is Q=K0.5L0.5. This describes a firm that requires the least complete number of inputs when the mixture of inputs is reasonably equal. For instance, the company would produce 25 units of output with the aid of using 25 models of capital and 25 of labor, or it might produce the same 25 units of output with one hundred twenty five models of labor and just one unit of capital.

In the end, the Leontief creation operate applies to occasions where inputs must be used in constant proportions; opening from those proportions, if usage of 1 enter is expanded without one other being increased, output will not trade. This production operate is given with the aid of Q=Min(ok,L). For illustration, a firm with 5 workers will produce five units of output as long as it has as a minimum five items of capital.