Question

Suppose a firm produces an output measured in units Q. The cost of

producing Q units is given by the cost

function C(Q) = aQ2 + bQ + c,

where you can assume a 0,b 0,c 0. In Economics we also think

about cost per unit (average cost) given by: AC(Q) = C(Q) divided by Q .Economists

also estimate the cost of producing 1 more unit of output by what we call marginal cost given by: MC(Q) = C′(Q) . Use calculus to help you graph both the AC(Q) and MC(Q) functions in one diagram and show that the MC(Q) function intersects the AC(Q) function from below at the point where AC(Q) is at its minimum.

Economics