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Show that Eulers theorem implies that, for a constant returns-to-scale production function[q = f (k, l)],q = fkk + fll.Use this result to show that, for such a production function, if MPl>APlthen MPkmust be negative. What does this imply about where production must take place? Can a firm ever produce at a point where APlis increasing?
Answer : q = f (k, l) Using differential equation :- dq = fk*dk + fl*dl Applying integration on both the sides , we get :- Integration (dq) = Integration (fk*dk) + Integration (fl*dl) As, Production function is having constant returns to scale , So, fk and fl are independent of k and l respectively. We get , q =…

fk.k + fl.l , Hence prooved. Example of a constant returns to scale PF : q = k^-1* l^2 MPL = 2l/k APL =l/k So, MPL > APL MPK = – (l/k)^2 , which is negative Hence, If MPL > APL , MPk is negative. MPL =

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