Construction of a cost-function Ralph must select the best combination of four f

Question

Construction of a cost-function Ralph must select the best combination of four factors of production denoted, z1, z2, z3 and z4 (all of them are greater or equal to zero), to produce q units of output. technical requirements are defined by the following constraints. z1 + z2 <=q, z3 + z4 <=q, z <=5 and z3 <= 6. factor prices are 1, 2, 3 and 4 per unit (respectively)

a) determine the cost curve for 0 <= q <= 10 and plot the cost curve: How do you interpret the shadow price b) Repeat for a particular short-run setting z1 (sign above z) = 3 Thanks for you help in advance

Explanation / Answer

Theory of production

Production theory is the study of production, or the economic process of producing outputs from the

inputs. Production uses resources to create a good or service that are suitable for use or exchange in

a market economy. This can include manufacturing, storing, shipping, and packaging. Some economists

define production broadly as all economic activity other than consumption. They see every commercial

activity other than the final purchase as some form of production.

Production is a process, and as such it occurs through time and space. Because it is a flow concept,

production is measured as a “rate of output per period of time”. There are three aspects to production

processes:

1. The quantity of the good or service produced.

2. The form of the good or service created.

3. The temporal and spatial distribution of the good or service produced.

A production process can be defined as any activity that increases the similarity between the pattern of

demand for goods and services, and the quantity, form, shape, size, length and distribution of these

goods and services available to the market place.

Production is a process of combining various material inputs and immaterial inputs (plans, know-how) in

order to make something for consumption (the output). It is the act of creating output, a good or

service which has value and contributes to the utility of individuals.

Production Function

In economics, a production function relates physical output of a production process to physical

inputs or factors of production.

It is a mathematical function that relates the maximum amount of output that can be obtained from

a given number of inputs - generally capital and labor.

The production function, therefore, describes a boundary or frontier representing the limit of output

obtainable from each feasible combination of inputs.

Firms use the production function to determine how much output they should produce given the

price of a good, and what combination of inputs they should use to produce given the price of

capital and labor.

Increasing marginal costs can be identified using the production function. If a firm has a production

function Q=F(K,L) (that is, the quantity of output (Q) is some function of capital (K) 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

constant returns to scal

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