## The M Arginal Rate Of Technical Substitution

4.24. An isoquant depicts the different combinations of inputs A' and L that can be used to producc a specific level of output Q. One such isoquant for the output level Q - 2144 is

(0) Use implicit differentiation from Section 3.9 to find the slope of the isoquant dKldL which in economics is called the marginal rate of technical substitution (MRTS). (b) Evaluate the marginal rate of technical substitution at K - 256. L » 108.

a) Take the derivative of each term with respect to L and treat A' as a function of L

Use the product rule since A is being treated as a function of L.

Solve algebraically for dK'dL.

This means that if L is increased by 1 relatively small unit. A must decrease by 7.11 units in order to remain on the production isoquant where the production level is constant. See also Problem 6.51.

•US. The equation for the production isoquant is

25 KMLM = 5400 (a) Find the MRTS and (/>) evaluate it at K = 243. L = 181.

a) Treat K as a function of L and use the product rule to find dK/dL, which is the MRTS.

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