MRT (Marginal Rate of Transformation) curve:

The MRT curve represents the rate at which one good must be given up to produce an additional unit of another good while keeping the total level of production constant. It is usually depicted as a convex curve due to the following reasons:

1. Law of Diminishing Marginal Rate of Transformation:
The MRT curve is convex because of the law of diminishing marginal rate of transformation. According to this law, as more and more of a particular good is produced, the opportunity cost of producing an additional unit of that good increases. This means that to produce more of one good, we need to sacrifice increasing amounts of the other good. As a result, the MRT curve becomes steeper and convex.

2. Nonlinear Production Possibilities:
The MRT curve is derived from the production possibilities frontier (PPF), which represents the maximum possible combination of goods that can be produced with the available resources and technology. In most real-world scenarios, production possibilities are not linear but exhibit increasing opportunity costs.

PPF (Production Possibilities Frontier) curve:

The PPF curve shows the various combinations of two goods that an economy can produce given its available resources and technology. It is usually depicted as a concave curve due to the following reasons:

1. Law of Increasing Opportunity Cost:
The concave shape of the PPF curve is a result of the law of increasing opportunity cost. This law states that as an economy produces more of one good, the opportunity cost of producing an additional unit of that good increases. This occurs because resources are not perfectly adaptable to producing both goods, and as more resources are allocated to one good, the best-suited resources for producing the other good are gradually used up. Consequently, the economy has to shift less efficient resources towards the production of the second good, resulting in increasing opportunity costs.

2. Scarcity of Resources:
The concave shape of the PPF curve also reflects the scarcity of resources. Resources in an economy are limited, and therefore, as more resources are devoted to the production of one good, fewer resources are available for producing the other good. Since resources are typically not equally efficient in producing different goods, the opportunity cost of producing more of one good increases, leading to the concave shape of the PPF curve.

In summary, the convex shape of the MRT curve is a result of the law of diminishing marginal rate of transformation, while the concave shape of the PPF curve arises due to the law of increasing opportunity cost and the scarcity of resources. These curves help economists analyze the trade-offs and efficiency of resource allocation in an economy.