Competition and Pricing in Medicare Advantage

Ian McCarthy | Emory University

Outline for Today

Question: How do more firms affect market prices?
From earlier micro:
- Firms compare marginal revenue (MR) and marginal cost (MC).
- Market power is the ability to set $p > MC$.
Guiding idea:
- When there are more firms, competition is stronger and prices tend to be lower, all else equal.

Perfect competition:
- Many firms, identical product, free entry.
- Each firm is a price taker, so $p = MC$ and markups are zero.
Monopoly:
- One firm facing the market demand curve.
- Chooses $q$ so that $MR = MC$, which implies $p > MC$ and a positive markup.
These two cases give a range:
- The competitive price is at the low end, the monopoly price is at the high end.

Oligopoly: a few firms that interact strategically.
Examples from intermediate micro:
- Cournot competition, where firms choose quantities.
- Bertrand competition, where firms choose prices.
With homogeneous products:
- As the number of firms increases, outcomes become closer to perfect competition.
- Prices move closer to $MC$ as the number of firms grows.

In many markets, products are differentiated by brand, quality, or features.
Even with Bertrand-style price setting:
- Each firm faces its own residual demand curve.
- Demand for each firm is less elastic than demand for the whole market.
- This allows $p > MC$ and positive markups, even when there are several firms.
Adding more firms usually:
- Makes each firm’s demand more elastic.
- Reduces prices and markups, but prices typically remain above $MC$ because of differentiation.

Perfect competition: many firms, $p = MC$, no market power.
Monopoly: one firm, $p > MC$, strong market power.
Oligopoly with differentiated products:
- Firms still choose prices above marginal cost.
- More firms and lower concentration generally mean lower prices and smaller markups, but not zero markups when products remain differentiated.

Inverse demand: $P(Q) = a - bQ$, with $a > c$ and constant marginal cost $c$.
There are $n$ identical firms. Firm $i$ chooses $q_i$ to maximize \[\pi_i = \big(P(Q) - c\big) q_i = \big(a - b(q_i + Q_{-i}) - c\big) q_i.\]
In a symmetric Cournot equilibrium, $q_i = q$ for all $i$, so $Q = nq$ and \[Q^*(n) = \frac{n(a - c)}{b(n + 1)}, \qquad p^*(n) = P(Q^*(n)) = \frac{a + nc}{n + 1}.\]
As $n$ increases, $p^*(n)$ falls: \[\frac{dp^*(n)}{dn} = \frac{c - a}{(n + 1)^2} < 0 \quad \text{when } a > c.\]
IRL, effect of $n$ will depend on substitutability of products/firms

Firm $i$ chooses its price $p_i$ to maximize \[\max_{p_i} \ \pi_i(p_i, p_{-i}) = (p_i - c)\, q_i(p_i, p_{-i}).\]
First-order condition: \[\frac{\partial \pi_i}{\partial p_i} = q_i(p_i, p_{-i}) + (p_i - c)\frac{\partial q_i}{\partial p_i} = 0.\]
Define the own-price elasticity of demand \[\varepsilon_i = \frac{\partial q_i}{\partial p_i}\frac{p_i}{q_i} < 0.\] Rearranging the first-order condition gives the Lerner condition \[\frac{p_i - c}{p_i} = -\frac{1}{\varepsilon_i}.\]
Markup $(p_i - c)/p_i$ falls with the number of firms, assuming entry increases own-price elasticity due to presence of substitutes

Many ways to think about measuring competition:

Existed since 1980s, formalized in the 1990s, expanded in 2000s
Medicare+Choice as part of Balanced Budget Act in 1997
Largest expansion: Medicare Modernization Act in 2003 (also brought Medicare Part D)

In its current form…

Insurers submit plan details and a price needed to cover traditional Medicare (“bid”)
If approved, Medicare pays risk-adjusted bid or benchmark
Bid $<$ benchmark, insurer gets a rebate and sets premiums to 0
Bid $>$ benchmark, insurer charges premium
Seperate bidding for Part D

Let’s take a look at the Medicare Advantage plan options…

Premiums are relative to standard Medicare Part B premiums
Many plans listed as $0 premium
- Enrollees stil pay Part B premium ($185 per month in 2025)

Definition of “product” in MA is a little complicated…

Insurer is the corporate entity like UnitedHealth, Humana, etc.
Insurers seek approval to offer a “contract”
- Dictates the type (HMO, PPO, etc.)
- Sets legal terms of CMS/Insurer relationship, including counties in which contract can be offered (service area)
- Level of quality measurement (more on this in the next module)
Within a contract, insurers offer “plans” (i.e., benefit packages)
- Networks, formularies, covered services
- Premiums, deductibles, co-insurance, co-payments

Tons of Medicare Advantage data publicly available from CMS
For this section, we’re focused on “pricing” and “competition”
- Measure competition based on HHI
- Measure price in two ways: 1) average premiums; and 2) count of positive premiums