$1.$ Is the production function f$($x$1,$ x$2)=$ x $1/21$ x $3/42$ constant returns, increasing returns, or decreasing returns to scale? $2.$ Suppose x$1$ and x$2$ are used in fixed proportions and f$($x$1,$ x$2)=$ min$[$x$1,$ x$2].($a$)$ Suppose that x$1<$ x$2.$ What is the marginal product of x$1?$ What is the marginal product of x$2?$ Is f constant, increasing, or decreasing returns? $($b$)$ Suppose that x$1=$ x$2=20.$ What is the marginal product of x$1?$ What is the marginal product of x$2?3.$ Suppose the production function is Cobb$-$Douglas and f$($x$1,$ x$2)=$ x $1/21$ x $3/22.($a$)$ Write an expression for the marginal products of x$1$ and x$1.($b$)$ Is the marginal product of x$1$ increasing or decreasing for small increases in x$1,$ holding x$2$ fixed? $($c$)$ Is the marginal product of x$2$ increasing or decreasing for small increases in x$2,$ holding x$1$ fixed?