Study on Production Possibility Frontier Under Different Production Function Assumptions

Abstract

Increasing marginal rate of transformation (MRT) in production is a generally accepted economic presumption. So how to reflect the increasing MRT in linear and non-linear production functions? However, in Leontief’s input-output model, it is assumed that production is performed on a fixed proportion of inputs and usually leads to the constant MRT. This paper analyzes the linear output possibility frontier under the Leontief production function in detail, the author tried to fix this problem by considering the non-unique primary inputs in a simplified two-sector economy. Then we discuss the production possibility frontier under the assumption of nonlinear production function: First, when there are many primary inputs (heterogeneity) constraints, it is possible to curve the net output possibility frontier of Leontief production function and make it meet the assumption of increasing MRT. Second, in the intertemporal production process, a total output possibility frontier with increasing MRT can be obtained under a general production function without the assumption of non-unique primary inputs.

The research was supported by grant number 14AZD085, a key project titled “Research on the Evolution Trend and Countermeasures of China’s Economic Growth Quality under the Background of New Normal” financed by the Social Science Foundation of China, and grant number 71373106, a project titled “Transformation Dynamic Research and Policy Simulation of Industrial Value-added Rate: A Case Study of Manufacturing Industry in the Yangtze River Delta Region” financed by the Natural Science Foundation of China.