Some firms employ the marketing strategy of posting a low price for the good,
but then tack on hidden fees or high prices for add-ons that can add up to an
"all-in" price that is exorbitant compared to the posted price. A television
ad may blare that a perpetually sharp knife sells for \(\$ 20,\) leaving the
additional \(\$ 10\) handling charge-or worse, that the \(\$ 20\) is just one of
three installments-for the small print. A laser printer printing photo-quality
color prints may seem like a bargain at \(\$ 300\) if one doesn't consider that
the five toner cartridges must be replaced each year at \(\$ 100\) each. If
consumers understand and account for these additional expenses, we are firmly
in a neoclassical model, which can be analyzed using standard methods.
Behavioral economists worry about the possibility that unsophisticated
consumers may underestimate or even ignore these shrouded prices and firms do
their best to keep it that way. This question introduces a model of shrouded
prices and analyzes their efficiency consequences.
a. Consumers' demand for a good whose price they perceive to be \(P\) is given
by \(Q=10-P .\) A monopolist produces the good at constant average and marginal
cost equal to \(\$ 6 .\) Compute the monopoly price, quantity,
profit, consumer surplus, and welfare (the sum of consumer surplus and profit)
assuming the perceived is the same as the actual price, so there is no
shrouding.
b. Now assume that while the perceived price is still \(P\), the actual price
charged by the monopolist is \(P+s,\) where \(s\) is the shrouded part, which goes
unrecognized by consumers. Compute the monopoly price, quantity, and profit
assuming the same demand and cost as in part (a). What amount of shrouding
does the firm prefer?
c. Compute the consumer surplus (CS) associated with the outcome in (b). This
requires some care because consumers spend more than they expect to. Letting
\(P_{s}\) and \(Q_{s}\) be the equilibrium price and quantity charged by the
monopoly with shrouded prices,
\\[
C S=\int_{0}^{Q} P(Q) d Q-P_{s} Q_{s}
\\]
This equals gross consumer surplus (the area under inverse demand up to the
quantity sold) less actual rather than perceived expenditures.
d. Compute welfare. Find the welfare-maximizing level of shrouding. Explain
why this is positive rather than zero.
e. Return to the case of no shrouding in part (a) but now assume the
government offers a subsidy s. Show that the welfare-maximizing subsidy equals
welfare-maximizing level of shrouding found in part (d). Are the
distributional consequences (surplus going to consumers, firm, and government)
the same in the two cases? Use the connection between shrouding and a subsidy
to argue informally that any amount of shrouding will be inefficient in a
perfectly competitive market.
