What is the Marginal Rate of Technical Substitution? 

MRTS reaches a manufacturer when a part of the product is lowered to sustain the manufacturing level when the other part is extended. It is the level of the quantity that is lowered when one extra volume is used, and the output is unchanged.

It depicts the interplay between factors like capital (K) and labor (L) that will help a manufacturer to stay at an unchanged output. It may vary from the Marginal rate of substitution (MRS) as it is related to consumer equilibrium but MRS is related to producer equilibrium.

The isoquant on a graph depicts the different combinations of the two raw goods which gives the same volume of final goods.

Here is the formula for calculating the Marginal Rate of Technical Substitution (MRTS) below,

$$MRTS=\Delta K/\Delta L$$

• Where ΔK is the change in the capital,
• ΔL is the change in the Labor,

Isoquant curve 

The concept is related to the study of microeconomics wherein this curve shows the graph of charts for all the raw goods required to produce specified units of final goods. Generally, this graph is used as a metric to estimate the impact of all the raw goods on the products that can be obtained. 

Calculations:

The above graph depicts the union of K and L that gives the same result. The slant in the graph shows that how much K will be required to replace a unit of L at that manufacturing level. Then the slant at any point is given by ⧍L / ⧍ K. From the above, it seems that the ratio of the change in the capital and the worker is the same as the fraction of the MP of labor and capital.

What Does the Marginal Rate of Technical Substitution depict? 

The slant of the curve, on the graph, shows the amount at which a given input (worker or capital), can be interchanged for the other while the level of output is unchanged. It is given by the value of an isoquant's line at a given point.

When there is a decrease in the marginal rate of technical substitution along with the slant curve for the given same level of final goods then it is known as the diminishing marginal rate of substitution.

Clearly from above, the marginal rate of technological substitution is-

Between a and b = 5, between b and c = 3, between c and d = 2, between d and e = 2.

The above numerical denotes that as the firm employs more and more units of workers, the sacrifice of capital units to raise the work units will decline. So, this means the marginal rate of technical substitution for a production process is diminishing like MRS in the consumer theory. This further means that its standard shape is convex to the origin.

In this model, it is quite applicable that both L and K are considered as the perfect substitute for each other because MRTS (L, K) is constant at all the points on the isoquants. However, it can be stated as an unrealistic case because K and L are not the same production factors, and hence, they can’t be accounted as a perfect substitute.

Benefits 

It shows the amount at which the other can be replaced for a given input (L or K) so that the final goods produced are not changed.

• A decline in it along with an isoquant is called the declining marginal rate of substitution (DMRS).
• All manufacturers aim for the less amount cost to get the maximum value of profit which is known as Producer equilibrium. For reaching the equilibrium level, the manufacturer uses all output factors together that will result in less amount of cost at the manufacturing level.
• The manufacturer is responsible for deciding the combination of the factors of production, which give the best-produced goods. The decision made by the manufacturers is related to the marginal rate of technical substitution and the substitution principle.

For example, there are two factors of production in the manufacturing unit i.e. factor A and factor B. Factor A can produce a higher quantity of finished goods than factor B which can be done by using the same level of capital for both the factors. Then the manufacturer will choose factor A for producing the goods instead of factor B.

• When both the marginal products are positive, the slope of it is negative and if it declines as the number of workers increases then they are rounded to the origin.

Related Terms 

Labour Market : It is known as the job market which relates to the supply and the worker's demand in which the supply is provided by the workers and demand is provided by the employers. Their productivity is a measure of the finished goods produced by workers.

What is the Isoquant Curve? : It refers to the study of microeconomics in a graph, which shows all the factors that give a manufacturer a finished good. It is a concave-shaped line on the graph. It suggests the manufacturers adjust the inputs to increase production to earn large profits.

Marginal Revenue : It is the amount gained by selling the extra unit produced by the manufacturers. If the manufacturer is only increasing the profit, then it will produce the goods till where the marginal costs equal its marginal revenue.

Variable Cost : The costs fluctuate with the level of manufacturing of the goods in a firm. There is a direct relationship between variable cost and production as when the production increases, the variable cost increases, and vice-a-versa.

Demand for Labor : It is the demand that a manufacturer urges at a given point of time by giving them wages/salaries. If the manufacturing of goods is increased, then the demand for workers will be increased and manufacturers will employ more workers.

Production Function : Production function in economics means the number of products used, and the finished goods manufactured. It can be calculated as below:

$$Q=f\left(K,L,P,H\right)$$

Where the quantity manufactured is the function of all product rates of factors. The factors of production here mean land, labor, capital, and entrepreneur. The production function includes:

• The positive marginal product of a good.
• The decreasing marginal product of a good.

Cobb-Douglas production function can be calculated by the below formula:

$$Y=A*L\beta *K\alpha$$

Where Y is the total production/final finished goods. 

The production function of complementary goods 

Complementary goods are those goods whose demand increases with popularity. It shows the cross negative elasticity of demand as demand for complementary goods increases when the price of other goods decreases.

The production function of substitute goods 

Substitute goods are the goods manufactured that can be replaced by other goods to be used by the consumers/the end users for the same purpose.

Key Takeaways 

• The manufacturers produce raw goods to final goods.
• The term used between raw goods and final goods is the production function.
• The slant curve on the graph depicts the change in raw goods without changing the final quantity of goods produced.
• The K and L are perfect substitutes in the production function.
• Some goods are easy to change in the short run.
• Long-run goods are costly to adjust to easily.

Practice Problem 

Question 1: Let Q = 4LK, MPL= 4K, MP = 4 L. Find MRTSL, K? 

Solution: 

$\begin{array}{l}MRTSL,K =MPL /MPK\hfill \\ =4k/4L\hfill \\ =K/L.\hfill \end{array}$

Question 2: Let Q=4LK, MP_L=4K, MP_K=4L, MRTS_L, K=K/L. Show the diminishing when Q=16. 

Solution:

$\begin{array}{l}WhenQ=16,\left(L,K\right)=\left(1,4\right),\left(2,2\right),\left(4,1\right)\hfill \\ MRTS\left(1,4\right)=4/1=4\hfill \\ MRTS\left(2,2\right)=2/2=1\hfill \\ MRTS\left(4,1\right)=1/4.\hfill \end{array}$

Limitations to Diminishing Marginal Rate of Technical Substitution 

• When there is no substitution possible between workers and capital. 
• When workers and capital are perfect substitutes for each other. 

Context and Applications 

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

• B.A in Economics
• M.A in Economics