<div class="container">
  <div class="element element-1">
    I have a minimum width of 450px. Even if my <code>width</code> is set to less than 450px, it will not have any effect since it will be overridden by the <code>min-width</code> value.
    <div class="child">
      I have the same minimum width as my parent.
    </div>
  </div>
  <div class="element element-2">
    I will always have a minimum width which is equal to 3em.
  </div>
</div>
body {
  background-color: #F5F5F5;
  color: #555;
  font-size: 1.1em;
  font-family: 'Helvetica Neue', Helvetica, Arial, sans-serif;
}

.container {
  margin: 40px auto;
  max-width: 700px;
}

.element {
  padding: 20px;
  background-color: #0099cc;
  color: white;
  margin-bottom: 150px;
}

.element-1 {
  height: 200px;
  min-width: 450px;
}

.child {
  background-color: salmon;
  padding: 30px;
  margin: 20px;
  min-height: inherit;
}

.element-2 {
  min-width: 3em;
}