18.4 Offer Curves

Having solve the optimization problem in a trading context, let us now turn to a comparative statics analysis: specifically, what happens to the optimal bundle when prices change?

Recall from Part II the price offer curve illustrates the set of bundles that a consumer might choose at different prices. In other words, it’s drawn by solving the optimization problem for a range of prices, and connecting those dots together:

Two things to notice about this offer curve:

• It must lie above the indifference curve passing through the endowment. The agent always has the option of not trading at all; so if they trade, it follows that they must be trading to a point they prefer to their endowment. To confirm this, try checking the box marked “Show indifference curve through $E$” in the diagram above.
• It depends only on the price ratio, not on individual prices. That’s because, as we mentioned before, the budget line goes through point $E$ with slope $p_1/p_2$; so, for example, the budget line (and therefore the relevant point on the offer curve) is the same for $(p_1 = 10, p_2 = 5)$ and $(p_1 = 20, p_2 = 10)$. You can confirm this in the diagram above.

Because the offer curve is a parametric equation, deriving an expression for the offer curve is difficult and sometimes even intractable. It’s also not terribly important; at this level, it’s sufficient to understand what an offer curve represents.