Please help me with the following question:Consider the production function ( ₁, ₂) = ₁1/2
₂² for ₁, ₂ > 0. A production function relates the maximum of output that can be obtained from a given amount of inputs.
a) Show that the marginal rate of technical substitution, 12, is constant along any ray from the origin. The MRTS is the amount by which the quantity of one input must be
reduced when the amount of the other input increases by an infinitesimally small amount, while output remains constant.
b) Does any homogeneous production function satisfy such a property? Recall that a function ( , ) is homogenous of if ( , ) = ( , ) for , ∈ .
Thank you so much!
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