15.6 Markets, Efficiency, and the Welfare Theorems

The links between the marginal rate of transformation, marginal rate of substitution, and input and output prices have implications for the ability of markets to create efficient outcomes.

In our discussions of exchange, input, and output efficiencies, we acted as if it would be easy to shift input and output allocations through some basic interventions. But, the examples were by nature oversimplified—two inputs, two outputs, two firms, and two consumers. We also had, by virtue of constructing the example ourselves, full knowledge of firms’ production functions and consumers’ utility functions.

The real economy is vastly more complicated. Trying to centrally coordinate the allocations of inputs to production and consumption bundles to consumers, while also getting the optimal output mix, would be astronomically difficult. Whenever central coordination has been tried on a large scale, it failed spectacularly. For example, the government of Venezuela has become increasingly involved in markets for certain basic consumer goods like milk, sugar, meats, toilet paper, and soap. This has resulted in frequent shortages, rationing, long lines for goods that are available, and smuggling. While Venezuelan officials have blamed these problems on many sources (in one case, on Venezuelan citizens’ overeating), these are the classic symptoms of misallocation in a managed economy.

Do the harsh realities of this complexity mean that our Pareto-efficient outcomes are only theoretical fantasies? Perhaps not. As we suggested earlier in discussing the relationship between exchange efficiency and utility-maximizing behavior, markets and prices might achieve efficiency even in the absence of an all-knowing, omnipotent economic controller.

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In the section on exchange efficiency, we learned that if consumers maximize their utility (taking goods’ prices as given), they will end up with the same marginal rates of substitution. Markets can meet the exchange efficiency condition in this way.

On the production side, for any given set of input prices, profit-maximizing firms will choose their input mix so that their marginal rate of technical substitution (MRTS) equals the input price ratio. This outcome equates firms’ MRTS levels, the condition for input efficiency.

Prices, then, create two of the three efficiency conditions. The final link, output efficiency, ties these two conditions together. One way to think about output efficiency’s MRS = MRT condition is that it sets the ratio of goods’ prices equal to their marginal costs of production. If the goods are produced by a perfectly competitive industry, price will equal marginal cost. Therefore, the price and cost ratios are equal, satisfying output efficiency while preserving input and exchange efficiency. Decentralized, competitive markets can achieve all three efficiency conditions.

First Welfare Theorem

Theorem stating that perfectly competitive markets in general equilibrium distribute resources in a Pareto-efficient way.

This is the ending we gave away at the start of our discussion of efficiency—markets can create efficient outcomes, even in the absence of interventions and forced allocations, by letting prices do the work: Input prices equate marginal rates of technical substitution in production, and output prices lead to the optimal output mix among producers and cause consumers to equate their marginal rates of substitution. The result, that perfectly competitive markets in general equilibrium distribute resources in a Pareto-efficient way, is called the First Welfare Theorem. It formalized Adam Smith’s notion of the “invisible hand.”

The First Welfare Theorem comes with a lot of conditions. A big one is that firms and consumers take as given all the prices of goods and inputs. In other words, there is no market power. Market power prevents markets from reaching an efficient outcome because the output price ratio, which is now set by producers rather than taken as given, no longer needs to equal the marginal cost ratio. As a result, market power supports markups that drive a wedge between the two ratios and create output inefficiency. If firms or individuals have market power in buying goods, this, too, will create inefficiencies.

The First Welfare Theorem relies on other assumptions we shouldn’t ignore. These include the absence of asymmetric information, externalities, and public goods. We discuss exactly what these are and why they can lead to market failures in Chapters 16 and 17.

Application: Output Efficiency among Manufacturing Firms in India

We learned how the output-efficient product mix reflects both cost (marginal rate of transformation or MRT) and demand (marginal rate of substitution or MRS) factors, and how well-functioning markets can lead firms to produce that optimal mix. In reality, those cost and demand factors are constantly changing. When changes occur, prices in competitive markets should change accordingly and spur firms to switch to the new optimal product mix.

10Pinelopi K. Goldberg, Amit K. Khandelwal, Nina Pavcnik, and Petia Topalova, “Multiproduct Firms and Product Turnover in the Developing World: Evidence from India,” Review of Economics and Statistics 92, no. 4 (November 2010): 1042–1049.

Economists have documented a lot of evidence that firms, when choosing what products to make, do respond to market signals. In one study, however, a group of economists found that these sorts of product mix shifts are slower and less frequent among firms in India than in other economies.10 As a result, India may lag behind other countries in output efficiency.

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The study looks at the products made by over 4,000 Indian manufacturing firms and tracks their production of about 2,000 separate products. (To give you an idea of the level of detail this involves, example products from the iron and steel industry include welded steel tubular poles, stranded wire, and malleable iron castings.) Some of the firms made only one product, but many manufactured multiple products.

The results show an interesting contrast. In some ways, Indian firms’ production choices look a lot like those in more developed countries. Bigger firms, on average, make a larger variety of products than smaller firms, for example. And when firms grow, they often do it by adding products. However, the results also show that overall product turnover—the frequency with which firms add new products or drop old ones—is significantly lower in India. For example, this “product churn” rate is less than two-thirds that computed using comparable U.S. data. What’s particularly interesting is that this lower product turnover does not seem to occur because Indian firms are less likely to start making new products. Instead, they are less likely to drop old ones.

What might this result say about output efficiency in India? As costs and tastes change, the efficient quantity of certain products will rise while others will fall. If markets are working well, prices should change to reflect the new costs and tastes, and firms should respond to these price changes by shifting what they manufacture. More firms will begin making products whose markets are growing. Those making products for which the markets are shrinking will shut down or cut back on the manufacture of such products. This shift allows the inputs used to make those dying products to be put toward making ascending products instead. (Or, it might also be that a product itself isn’t dying, but there is a cost change that makes particular firms much less capable of manufacturing the product than before. In this case, those firms can shut down those product lines and allow more able firms to pick up the lost production.)

In India, firms appear reluctant to stop manufacturing products whose consumption levels (and likely profitability) are shrinking. Too many resources are devoted to making low-marginal-utility goods, upsetting the MRT = MRS condition and output efficiency.

Why isn’t the market in India output-efficient? The study’s authors speculate that the tight regulations on when and how firms can change the level and location of employment (part of the extensive Indian regulatory structure often referred to as the “license raj”) make it costly for firms to shut down existing production lines, even if they are making a faltering product or one that is a bad match for their abilities. As a result, the product mix becomes skewed away from the efficient combination and firms make too many things that people don’t value very much.

As we come to the end of our analysis of general equilibrium efficiency, remember: Efficiency does not imply equality nor does it have to match anyone’s concept of fairness. Efficient markets can (and do) lead to unequal outcomes. Does this mean that any effort to increase equity will necessarily harm efficiency? In theory, no. In practice, however, the answer is often yes.

Second Welfare Theorem

Theorem stating that any given Pareto-efficient allocation in a perfectly competitive market is a general equilibrium outcome for some initial allocation.

It is theoretically possible to change how equitable market outcomes are while still ensuring that the outcome is efficient. This result is a prediction of the Second Welfare Theorem?. This theorem says that (under the same assumptions made for the First Welfare Theorem) any Pareto-efficient equilibrium can be achieved by choosing the right initial allocation of goods. What this means is that, if we want efficient outcomes that are also equitable (by whatever standard we judge this), we can get to those outcomes by being careful about how we initially allocate goods and inputs across consumers and producers. Imagine, for example, shuffling the allocation of goods among consumers along the contract curve from an undesirable unequal market outcome to whatever particular point we feel is most equitable. By doing that, we’re changing the allocation in a way that preserves efficiency while moving toward what we believe is a more equal outcome.11 We could also do similar reshufflings in the input market and along the production possibilities frontier, preserving overall efficiency while obtaining a particular outcome we prefer.

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lump-sum transfer

Transfer to or from an individual for which the size is unaffected by the individual’s choices.

Achieving this goal is not easy. First, there is the practical issue of how society would gather enough information about preferences and production technologies to know what the exact transfers should be. Second, the necessary reallocations would have to be what are called lump-sum transfers, transfers to or from an individual where the size of the transfer cannot be affected in any way by the individual’s choices. These are the sort of reach-in-and-reshuffle reallocations we imagined the magical economist undertaking in our earlier discussions. In reality, lump-sum transfers are almost never used (and we could probably drop the “almost”) because it is difficult to legislate taxes or subsidies that bear absolutely no relation to people’s actions.12

In reality, governments must try to achieve equity through transfers (taxes and subsidies) that depend on individuals’ actions, such as taxes on income and payroll (which depend on how much you work), sales (how much you buy), and property (how valuable your home is), and subsidies like social security payments (which depend on how much you worked in the past and currently), Medicare (how many health services you consume), and so on. The problem is that these kinds of transfers change the relative prices of the actions or goods that are taxed or subsidized. This creates wedges between the costs of goods and services and the post-tax or post-subsidy prices that consumers face, creating losses in efficiency (just as market power does).

This doesn’t mean seeking more equitable outcomes is wrong. It just says that there will likely be some inefficiency introduced when trying to promote it.