Question # $1$:

Majeda wrote the following answer on her microeconomics examination: "Virtually every production function exhibit diminishing returns to scale because my professor said that all inputs have diminishing marginal productivities. So$,$ when all inputs are doubled, output must be less than double." How would you grade Majeda's answer?

Question # $2$:

Suppose a firm had a production function with linear isoquants, implying that its two inputs were perfect substitutes for each other. What would determine the firm's expansion path in this case? For the opposite case of a fixed$-$portions production function, what would the firm's expansion path be$?$

Question # $3$:

Suppose that a firm's production function is $q=30\sqrt[\phantom{2}]{L}.$ In the short run, where there are fixed costs of $$2,200,$ and labor is the variable input whose cost is $$6,300$ per units. What is the total cost of producing $20$ units of output?