Power Price-Response Function
The power price-response function is one function with the reverse S-shape:
where D > 0, a > 0 and в >0 are parameter values estimated by fitting equation (6.3) to the price/demand data. The power price-response function is shown for different values of в in Figure 6.9. Higher values of в represent more price-sensitive markets. As в grows larger, the market approaches the perfectly competitive price-response function. Different values of a, a >0, shift the curves left and right along the horizontal price-axis.
Logit Price-Response Function
The second common price-response curve that has a reverse S-shape functional form is the logit function:
where C >0, a, and b >0 are parameter values that are estimated by fitting equation (6.4) to the price/demand data. The shape of the logit function is similar to the shape of the power functions shown in Figure 6.9. One advantage the logit function has over the power function is that it can be estimated using logistics regression, a methodology that is commonly available in most statistical software packages. Table 6.1 summarizes the commonly used price-response functions.
Figure 6.9 Power Price-Response Function.
Table 6.1 Price-Response Functions
Price-Response Function |
Formula |
WTP Distribution |
Linear |
d(p) = D + m ? p (D > 0, m < 0) |
Uniform |
Constant Elasticity |
d (p) = C ? p^{e }(C > 0, e< 0) |
Variant of a Power-Law Distribution |
Power |
d (p) = a ? D P^{e} + a (D > 0, a > 0, p> 0 |
Weibull |
Logit |
d (p) = C ? ef+^{b} ? f 1 + e“+^{b} ‘^{p }(C > 0, b < 0) |
Logistic |
The most useful feature of price-response functions is that, once estimated, they can be used to determine the price sensitivity of a product or how demand will change in response to a change in price. In the next section, we look at some ways that price sensitivity is measured.