Economics · Production Theory - Expansion Path

Which of the following statements regarding the Expansion Path in production theory are correct? 1. It is a special isocline that connects cost-minimising input combinations as output changes, holding input prices constant. 2. Geometrically, it joins all points of tangency between isoquants and isocost lines where the Marginal Rate of Technical Substitution equals the factor price ratio. 3. If the expansion path is a straight ray from the origin, it indicates that optimal input proportions change continuously with the scale of output. 4. If the expansion path curves, it signifies that optimal input proportions change with scale, as the firm uses relatively more of one input as it expands.