Substitution and Output Effects

Let factor inputs are substitutes, and the price of one factor input (input 1) has changed. How will demand change for second factor input (input 2)?

Price of input1(Price of substitute) SE vs OE Demand for input2
increase SE > OE increase
increase SE < OE decrease
decrease SE > OE decrease
decrease SE < OE increase

where SE is substitution effect, OE is output effect.

Let’s show the given conclusions graphically.

Isocost curves 1 and 3 represent all combinations of factors of production (input 1 and input 2) which in a sum cost C1 and C2 (not depicted on the graph) respectively. Isoquant curves 2 and 4 depict technological limits of the firm – all combinations of input 1 and input 2 that give equal total output Y1 and Y2 (not depicted on the graph) respectively.

An increase in the price of input 1 shifts isocost 1 into isocost 3. The dotted isocost is parallel to isocost 3 and tangent to the isoquant 2. There is new resource allocation and substitution effect in this case equals SE, where “substitution” is movement along isoquant 2 from the point (I1_1,I2_1) to the point x. Output effect OE depends on tangency point of new isoquant 4 to isocost 3. Thus in the upper graph (img 1) we can see that if OE > SE then demand for input 2 decreases from I2_1 to I2_2.  Similarly if OE < SE (img 2) then demand for input 2 increases.

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