Answer:
Marginal Rate of Transformation (MRT) refers to the amount of good Y that must be sacrificed in order to gain an additional unit of X, with full and efficient utilization of available resources. It is also known as marginal opportunity cost. MAT indicates the slope of PPC.
\[PPC=\frac{\Delta Y}{\Delta X}=\frac{\text{Amount}\,\,\text{of}\,\,\text{Good}\,\,\text{Y}\,\,\text{sacrificed}}{\text{Amount}\,\,\text{of}\,\,\text{Good}\,\,\text{X}\,\,\text{gained}}\]
Production Possibility Curve
Production Possibilities
Consumer Goods (units)
Capital Goods (units)
A
50
0
B
48
1
C
44
2
D
35
3
E
0
4
In the above figure, AE represents the PPC for good X and good Y. Suppose, the initial production point in B, where 1 unit of good X and 48 units of good Fare produced. To produce one additional unit of good X, 4 units of good Y must be sacrificed (point C). Thus, at point C, the MRT is 4 units of good Y.
\[MR{{T}_{\text{at}\,\,\text{point}\,\,C}}=\frac{\Delta Y}{\Delta X}=\frac{44-48}{2-1}=-4\]
Similarly, at point D, the MRT is 9 units of good Y.
\[MR{{T}_{\text{at}\,\,\text{point}\,\,D}}=\frac{\Delta Y}{\Delta X}=\frac{35-44}{3-2}=-9\]
Thus, as we move down the PPC, MRT (or the opportunity cost) increases. This increasing MRT indicates the concave shape of PPC.
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