microeconomics & mathematics

Math Review

Econ 301 - Spring 2015

Q1 Find the first derivatives of the following functions:

• f(x) = a + bx + cx2 + dx3

• f(x) = exx2

• f(x) = ln(4x3)

Q2 Define the Quotient Rule and the Product Rule. Show that the Quotient Rule is an

application of the Product Rule and the Chain Rule by noting that:

f(x)

g(x) = f(x)[g(x)]−1

Q3 Consider the function f(x, y) = x + y.

• Derive the partial derivatives of f(x, y).

Q4 Now consider the function f(x, y) = 4x4y3 − 5x2y + xy2.

• Derive the partial derivatives of f(x, y).

Q5 Consider the following problem

max x

bx − 2x2

• Write the first order condition for this problem.

• Find the value of x that solves the first order condition. This will depend on the parameter b and so we call this a solution function and write it x∗(b)

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