$3\mathrm{.}4$ Suppose that the technology of a firm is given by the Cobb$-$Douglas production

function, $y=A{z}_1^{}{z}_2^{},$ where $A,,$ and $$ are all positive constant. Calculate the marginal

product of both inputs. What is the constraint we have to impose on parameters to have

diminishing marginal products? What is the effect of an increase in capital on the marginal

product of labor? Derive the average product of both inputs and calculate the elasticities

of output wit respect to inputs. Calculate the $MRT{S}_{21}$ and the elasticity of substitution.

What kind of returns to scale does this function have? What is the scale elasticity?