An isoquant map where production output Q3 > Q2 > Q1. Typically inputs X and Y would refer to labour and capital respectively. More of input X, input Y, or both are required to move from isoquant Q1 to Q2, or from Q2 to Q3.
MRTS equals the slope of the Isoquant.
Difference with the Indifference Curve
Isoquant and indifference curves behave similarly, as they are all kinds of contour curves. The difference is that the Isoquant maps the output, but the indifference curve maps the utility.
In addition, the indifference curve describes only the preference of individuals but does not capture the exact value of utility. The preference is the relative desire for certain goods or services to others. However, the Isoquant can capture the exact number of production.
Shape of the Isoquant
The shape of the Isoquant depends on whether inputs are substitutions or complements.
Convexity
As we always assume diminishing returns, so MRTS normally is declining. Thus, the Isoquant is convex to the origin.
However, if there is an increasing return of scale, or there is a negative elasticity of substitution ( as the ratio of input A to input B increases, the marginal product of A relative to B increases rather than decreases), then the Isoquant could be non-convex.
A nonconvex isoquant is prone to produce large and discontinuous changes in the price minimizing input mix in response to price changes. Consider for example the case where the isoquant is globally nonconvex, and the isocost curve is linear. In this case the minimum cost mix of inputs will be a corner solution, and include only one input (for example either input A or input B). The choice of which input to use will depend on the relative prices. At some critical price ratio, the optimum input mix will shift from all input A to all input B and vice versa in response to a small change in relative prices.
Reference
Learned from Wikipedia.