Economics problem set

A Short Note on How to do Maximization

February 22, 2019

Suppose your objective is to maximize the functional value of a objective function

y = −x2 + 2x + 3 (1)

Step 1 Take the first order derivative of y with respect to x, and set it to zero.

dy/dx = −2x + 2 = 0 (2)

This is also called the first order condition(FOC). Step 2 Solve the above condition, then we have

x∗ = 1

which is the solution to the maximization problem. Step 3 At x∗ = 1, the we have the maximum value of y as

y∗ = −12 + 2 × 1 + 3 = 4

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