The Inverse Demand Function: Direct and Indirect | Microeconomics

There are two alternative ways of presenting the aggregate demand function:

(i) As expressing quantity as a function of price or

(ii) As expressing price as a function of quantity.

If we adopt the second approach we arrive at the inverse demand function, P(X), which measures what p₁ would have to be for x₁ units of the first commodity to be demanded, as pointed out by Hal Varian. We know that the price of a good measures the MRS between it and another good (or all other goods). This means that the price of a good shows the marginal willingness to pay for an extra unit of the good by anyone who is demanding that good.

If all consumers face the same prices for the two goods, then they will have the same MRS in equilibrium situations. Thus the inverse demand function, P(X), measures the MRS, or the marginal willingness to pay, of every consumer who is purchasing the good.

Fig. 14.2 shows two demand curves. Part (a) shows a direct demand curve and part (b) shows an inverse demand curve. In each case we arrive at the market demand curve by horizontally summing up individual demand curves. How this is done is illustrated in Fig. 14.2.

Example: Adding Up ‘Linear’ Demand Curves:

Suppose one individual’s demand curve is D₁ (p) = 20 -p and another individual’s is D₂ (p) = 10 – p. What is the market demand function?

Since negative quantities do not carry any economic sense, the individual demand function have the form:

D₁ (p) = max {20 – p, 0}

D₂ (p) = max {10 – 2p, 0}

The sum of the two demand-curves looks like the one shown in Fig. 14.3. The market demand curves has a kink at p = 5.