A. Players

There are three players in the model economy: a government, a state-owned enterprise (SOE), and private suppliers. Firstly, the government chooses a procurement policy. Details pertaining to this government’s choice problem are examined later in the paper.

Secondly, a representative SOE is a main economic player in this model. For a given procurement policy set forth by the government, the SOE decides on the contractors and amounts of objects to procure, such as goods or services. In the real world, the government not only selects a procurement policy but also procures objects to fulfill its own needs. For instance, the Ministry of Economy and Finance(MOEF) in Korea designs and implements a procurement policy based on which other ministries and SOEs procure objects. At the same time, however, the MOEF also procures objects by itself. Nevertheless, I assume that the government in the model economy as presented here chooses only a procurement policy without a loss of generality. It should also be noted that the theoretical framework is built on the standard principal-agent model. For expositional simplicity, I assume that the principal is the government and that the agent is an SOE. However, the main result still holds if readers view the principal as the general citizens of the national economy who maximize their total surplus by designing and implementing a procurement policy and the agent as any public procurement demand organization such as a central or local government or an SOE.

The last players in the model economy are private suppliers. They provide the procurement objects ordered by the SOE. They are classified into either ‘general contractors' or ‘innovative contractors.’ General contractors provide standard objects for which there is no uncertainty in quality. These objects have long been provided for many SOEs and, hence, are standard in the sense that procurers are certain of their quality. In contrast, innovative contractors invent new products. These new ‘innovative products’ apparently outperform existing standard objects in terms of quality. However, because they are new, there is uncertainty with regard to the actual quality. Despite the excellent appearance of some innovative products before use (i.e., ex-ante), SOEs can be disappointed with them after use (i.e., ex-post). Each supplier can choose its own type. If it invents a new product and the government determines that this invention is ‘innovative,’ the supplier is classified as an innovative contractor. If a supplier does not invent a new object but simply provides a standard one, it is classified as a general contractor. If a supplier invents a new object but the government determines that it is not innovative enough, the supplier fails to obtain the moniker ‘innovative contractor’ and, hence, is classified as a general contractor.

B. Quality and cost of the procurement goods

In actuality, SOEs procure goods and services. However, for simplicity and without a loss of generality, I assume that the SOE procures only goods. The total amount of goods that a representative SOE procures is normalized as 1. The SOE procures x units of the procurement goods from innovative contractors and the remaining (1 − x) units from general contractors.

The quality of procurement goods depends on the type of the private supplier. If a supplier is a general contractor, its good has quality of m > 0. This quality m is nonrandom and hence the SOE is certain of its level. Instead, if a supplier is an innovative contractor, it provides a procurement good with random quality y . Prior to procurement, the SOE has only an expectation of the quality of the product. After procurement, in contrast, by using the innovative good, the SOE realizes the true quality y , which is modeled as the following random variable:

Where m′ is the expected quality. For a supplier to become an innovative contractor, it must submit a prototype of its newly invented good to a governmental body that assesses its innovativeness. This authority tests the invented good and determines whether or not it is innovative enough. The test result is summarized in a report or a certificate. The SOE can also test the prototype by itself or read the certificate. Based on this examination, it can form an expectation of the quality of the new good. Of course, the expected quality may differ from the true quality. This difference ε follows a normal distribution with a zero mean and variance of σ² . The higher the variance is, the larger the uncertainty of the quality of the new good becomes.

Assumption 1: Δ = (m′ − m) > 0

Let Δ ≡ (m′ − m) denote the difference in the ex-ante quality between an innovative product and a standard product. Δ may be greater than zero, as a private supplier must pass a test to be designated as an innovative contractor. To pass the test, a supplier must demonstrate that a newly invented good outperforms existing standard goods. Of course, the supplier cannot prove the true quality given that the true quality can be proven only after an SOE actually uses the product. However, the supplier can at least attempt to persuade the referees appointed by a governmental body in charge when the referees assess the innovativeness of their newly invented good. To persuade the referees, the new good must be clearly outstanding and should outperform existing standard goods at least in an experimental environment. For instance, the Ministry of SMEs and Startups in Korea designates a new good as an innovative product only if it satisfies the following three conditions of innovativeness: innovativeness of technology, marketability, and social value (see Table 1).

The SOE may regard an innovative product as a risky asset with a high return and high risk while considering a standard product as a risk-free asset. In this model, the production costs of a standard product and an innovative product are denoted by c and c′ , respectively. The cost of an innovative product may be greater given that the invention of a new product that improves on an existing one is costly. The production cost of a standard product is lower than its quality (i.e., c < m), as otherwise production is meaningless. Similarly the production cost of an innovative product is lower than its expected quality (i.e., c′ < m′).

Assumption 2: δ ≡ (c′ − c) > 0, c < m, and c′ < m′

The procurement market for standard products is competitive. There are many private suppliers that are ready to provide standard products. The SOE can then buy standard products by paying the production cost c per unit due to price competition. However, the market for innovative products is shallow. Only a few suppliers try to invent new products. Furthermore, very few of the newly invented products are innovative enough to be designated as ‘innovative products.’ Therefore, the SOE must pay more than the production cost. In particular, the SOE is assumed to pay c′ + p, where c′ is the production cost of an innovative product and p > 0 is the margin for an innovative contractor. This assumption is consistent with real-life procurement. In Korea, SOEs must hold auctions if they want to procure standard goods or services according to the relevant procurement laws. However, if a SOE considers buying an innovative product, it is allowed to trade with a contractor bilaterally without holding an auction. There are multiple competitors in an auction, while only a single competitor exists in bilateral contracting. Payments to contractors usually decrease with the degree of competition. For instance, Hwang and Lee (2020) empirically find that with more participating bidders in a procurement auction in Korea, the winning bidder makes a lower payment.

Private suppliers can specify their types. If a supplier chooses to be a general contractor, she will obtain a zero payoff, as the payment from the SOE and the corresponding production cost are equal. If instead a supplier chooses to be an innovative contractor, she has to pay a fixed cost k to invent a new product. If the newly invented product turns out to be sufficiently innovative such that the relevant authority designates it as an innovative product, she will get c′ + p as a payment from the SOE. However, if the new product fails to be designated as an innovative product, she does not receive any payment (nor does she incur the production cost, as she does not produce the good). Let θ denote the probability that a newly invented product is designated as an innovative product. Then, the expected utility of a supplier who pays the cost of invention k equals θ(c′ + p − c′ − k) + (1 − θ)(−k − ρ) , where ρ > 0 represents the magnitude of risk aversion of the supplier. If the invention is in the end a failure, the supplier suffers from disutility ρ . The more risk-averse a supplier is, the higher the disutility ρ becomes. A supplier chooses to be an innovative contractor if this expected utility is greater than or equal to the reservation payoff, which is zero. If this expected utility equals the reservation payoff, general contractors and innovative contractors receive the same zero payoff. Thus, the following condition must be met for the co-existence of both types of contractors in equilibrium.

C. SOE’s optimal choice

When the SOE procures a good of quality q ∈ {y, m} , its ex-post payoff (before-paying-the-price) is αq + β , where α ∈ [α, 1) , α > 0 , denotes the quality-contingent payoff and β is the base payoff.

The quality-contingent payoff can have nonpecuniary and pecuniary components. For instance, suppose that a power-generating SOE wants to procure a new gas turbine. If this gas turbine performs well and causes no problems, the employees in the gas-fired power plant feel a sense of reliability. This is a nonpecuniary benefit an SOE obtains from a high-quality procurement good.

In addition, this SOE can obtain some pecuniary compensation from the government if the quality of the gas turbine is high. The Ministry of Economy and Finance in Korea regularly evaluates the management performance of SOEs and pays SOE employees performance-based bonuses. Safety is an important component in these evaluations. If the high-quality gas turbine causes no accidents, the government may award a high score and hence the SOE will receive bonus payments.

The magnitude of the pecuniary component of the quality-contingent payoff is determined by the government and is hence an outcome of a government policy. In contrast, the nonpecuniary component affects the SOE employees’ utilities directly and is hardly a choice variable of the government. In this regard, there is a lower bound α for the size of quality-contingent payoff α . Later in this paper, we examine the government problem of considering α as a choice variable. However, the SOE considers α as a given rule. The base payoff β is non-contingent on the quality of the procurement good and is assumed to be set by the government. For instance, the government may provide some fixed payments to SOEs.

If the SOE procures x units of new products from innovative contractors, the government provides some benefits bx to the SOEs. Recently, the Ministry of Economy and Finance in Korea awarded bonus points to SOEs after evaluating their management performance if they purchased a large enough amount of innovative products from innovative contractors. These bonus points are useful for SOEs to obtain a higher final grade and hence receive more bonus payments. That is, the government subsidizes SOEs to encourage the procurement of innovative products. It should also be3 noted that bx depends on the ex-ante quantity of the innovative products, while αy depends on the ex-post quality of these products. That is, bx is independent of the ex-post quality. The government compensates the SOE for the mere purchase of the innovative products by giving a subsidy bx . In this sense, bx is quantity-dependent compensation while αy is quality-dependent compensation.

The price c′ + p paid by the SOE to an innovative contractor also depends on certain government choices. In particular, the margin p is a procurement policy outcome. In Korea, government forces SOEs to hold auctions if they want to procure an object. However, if the object is an innovative product, the SOE is allowed to conduct bilateral trading with the relevant innovative contractor. Rules and conditions for payment to contractors are more generous under bilateral trading than under auctions. This is why it is assumed here that the margin p is affected by the government’s choice.

Given a procurement policy (α, β, b, p) , if the SOE purchases x units of procurement goods from innovative contractors and (1− x) units from general contractors, it will receive the following ex-post payoff (after-paying-the-price) X .

X is the ex-post payoff, which is realized only after the procurement is finalized and the SOE actually uses the procurement product. It is assumed here that the SOE is risk-averse. If the quality of an innovative product turns out to be disappointing, the SOE suffers. The SOE employees would also feel inconvenience as they then must exert efforts to fix related problems. If a failed product is a large piece of equipment, for instance, it could even cause safety issues. Furthermore, the SOE may face criticism from the media and the general public. For instance, Korea National Oil Corporation and Korea Gas Corporation purchased a number of oil fields, gas fields, and mining areas during a period in which oil prices were high in the early 2010, anticipating high profits. However, as oil price declined thereafter, these SOEs not only experienced significant financial losses but also faced substantial criticism from the media. Some employees in these SOEs were prosecuted for their failures in these procurement decisions. In this sense, I assume that the SOE is risk-averse with respect to procurement decisions.

Some may argue that SOEs are large corporations and hence are risk-neutral. If the SOE’s payoff from procurement goods is only pecuniary, the costs from some procurements can be offset to some extent by the benefits from other procurements. However, the SOE also obtains a nonpecuniary payoff. The media criticizes failures but usually does not compliment successes to the same extent. A government auditor or a competent authority can penalize failures severely but gives minor rewards. For instance, some employees of Korea National Oil Corporation had to leave the company due to the unsuccessful purchases of oil fields, facing large cuts in their permanent income. However, even if they were successful, an equivalent amount of lifetime compensation would not be forthcoming.

Furthermore, most regular procurement decisions are made by procurement managers rather than senior management. Suppose that there are two procurement managers A and B. A decides to purchase good 1 and B purchases good 2. If it turns out that good 1’s quality is poor while the good 2’ quality is good, manager A is blamed and usually cannot share the good outcome manger B achieves. Therefore, from the point of view of the procurement manager, the quality risks associated with the procurement of goods is not fully diversified.

In this sense, the SOE’s utility function u(X) is assumed to be increasing and concave in X . In particular, for tractability, I consider the following exponential utility function with a measure of risk aversion, γ .

The SOE chooses the share of innovative products x during procurement to maximize the expected utility. The following lemma shows that this expected utility has a simple functional form.

Lemma 1: E[u(X)] equals

Proof: Using identity (3), the ex-post payoff X can be rewritten and simplified as follows:

Then, the expected utility is given by

where the third inequality above is derived by using the mathematical property that for any real number A . ■

Let x^* denote the optimal choice of innovative goods. Given that the expected utility function in Lemma 1 is a monotonic increasing function of , the optimal choice is characterized by the following first-order condition with respect to the function W .1

Equation (5) shows what determines the optimal choice of innovative goods. It should be noted here that x^* is the value-to-risk ratio. The numerator is the ‘value’ of procurement from innovative contractors as opposed to general contractors. Innovative goods are superior to standard goods in terms of the expected quality as much as Δ . The SOE enjoys only α fraction of this improvement in quality through quality-dependent compensation αΔ . Therefore, if there is no ex-ante quantity-dependent compensation (i.e., if b = 0), the SOE will choose a positive amount of innovative goods only if the ‘effective quality improvement’ αΔ outweighs the sum of ‘added cost’ δ and ‘added payment’ p . However, if the government introduces a quantity-dependent subsidy bx , the SOE obtains additional value b from innovative goods. In sum, the value of procurement from innovative contractors equals αΔ − δ − p + b .

The denominator is the ‘risk’ of procurement from innovative contractors. As noted above, buying an innovative good is similar to purchasing a risky asset. If the realized quality of an innovative good is lower than the expected quality, the outcome is detrimental to the SOE. If the SOE is more risk-averse (i.e., if γ is high), it suffers more. If the underlying uncertainty is the larger (i.e., σ² is large), the SOE is hurt more. Note that the SOE is responsible for quality only to the extent of α . Thus, higher levels of risk arise if the compensation depends more on performance (i.e., if α is large). As a result, the risk of procurement from innovative contractors equals γα²σ² .

Note that the ex-post quality-dependent compensation factor α affects both the value and risk associated with the procurement of innovative goods. As this factor determines the performance-based payment αΔ , both the value and risk are increasing in α for a given b . That is, an increase in α provides both an incentive and a disincentive to procure innovative goods. However, this is not the case when the procurement policy (α, β, b, p) is endogenously set by the government. I show that the value is independent of α , while the risk remains dependent on α by solving the government’s policy choice problem below.

In addition, if the value exceeds the risk, x^* should equal 1 because it cannot be greater than 1 by definition. Thus, in this case, we have the following corner solution:

Hitherto, I focus on the case where the value of procurement from innovative contractors is positive. However, some contractors may invent only marginally superior goods at high additional costs. In such cases, the new goods are not innovative enough and, hence, the SOE wants to buy nothing from these contractors. However, the government can still push the SOE to purchase from these contractors by raising the ex-ante subsidy b . Therefore, the optimal choice of innovative goods is zero if the quality improvement or the ex-ante subsidy is small enough:

The following proposition summarizes these optimal procurement choices.

Proposition 1: Suppose Assumptions 1 and 2 hold. Given a procurement policy (α, β, b, p) , the optimal procurement choice x^* is characterized by (5), (6), and (7).

Proof: Omitted.

D. Government’s optimal choice

The SOE chooses an optimal procurement from innovative contractor x^* considering the procurement policy (α, β, b, p) as given. Below, I solve the government’s policy choice problem. I consider a benevolent government who wants to maximize social welfare. Although I use the term ‘government,’ this actually refers to a virtual economic agent that maximizes the social welfare of the whole economy. In this sense, this economic agent, or the government, can also be understood as general citizens. Because general citizens constitute the whole national economy, with an enormous size, it would be reasonable to assume that general citizens can diversify risks in the sizable national economy and that they are hence risk-neutral. Let V denote the objective function of the government, which is expressed as

The higher the quality of a procurement good (i.e., y or m ), the greater the social welfare. Also, I assume that the larger the payment to the SOE is, the weaker the social welfare is. Some readers may argue that the SOE is a constituent of the broader government and hence that the payment to the SOE should not be subtracted from the government’s objective function. However, this payment could be used for other social purposes if it were not paid to the SOE. Therefore, given the scarcity of resources, the payment to the SOE should be considered as an opportunistic cost.

Basically, this model is an example of the principal-agent framework, where the principals are general citizens (or the benevolent government) and the agents are SOEs and private suppliers. In the standard principal-agent framework, the principal’s own utility is the objective function that should be maximized. The agent’s utility does not always need to be added into the objective function. However, the agent’s utility should be considered as a constraint. In the standard principal-agent framework, the principal maximizes its own utility but at the same time must make the agent participate (by satisfying the participation constraints) and must ensure that the agent behaves in the manner desired by the principal (by satisfying the incentive-compatibility constraints). All of these participation and incentive-compatibility constraints are explicitly considered in this model (see equations (2), (5), (6), (7), and (9)). The production costs of private suppliers are also considered explicitly in this model through the private suppliers’ participation constraints (see equation (2)).

The government can set the policy variables (α, β, b, p) but cannot set the procurement variable x . Although x is a one-dimensional real variable in this model, it is a metaphor of a much more complicated real world in which hundreds of SOEs procure millions or more of different products and services. Furthermore, each product or service must be procured at different times. The government has to incur prohibitively high costs of calculating and planning what products and services to be procured for which SOE at what time. In addition, management and ownership of SOEs are legally separated in many countries, including Korea; hence, the government cannot dictate to SOEs the exact details of their daily operations, including their procurements. Although government payments to SOEs depend on the amount of innovative goods, this dependence is usually on the aggregate amount rather than on individual amounts of each of many different types of innovative goods. Considering these realities, I assume that the government cannot choose x but can implement a x -dependent procurement policy. For instance, in Korea, SOEs choose the amounts and types of procurement objects by themselves, while the government evaluates the management performance of SOEs and correspondingly pays bonuses based on the aggregate amount of procurement objects.

Therefore, the government must set a procurement policy under which SOEs and private suppliers find it optimal to participate (i.e., participation constraints). Also, the government needs to induce SOEs to choose the proper amounts and types that the government renders desirable (i.e., incentive-compatibility constraint). Let W denote the ex-post reservation payoff to be received by the SOE if it does not participate. I normalize W to zero. The SOE’s participation constraint is then given by

Recall that condition (2) is the participation constraint for private suppliers. The incentive-compatibility constraints are expressed as (5), (6), and (7). Thus, the government faces the following problem:

The procurement choice x is the share of innovative goods relative to the total amount of goods. Hence, there are potentially two corner solutions, i.e., x = 0 and x = 1. The first corner solution arises when the SOE chooses all goods from general contractors. This could be a realistic scenario, as many (but not all) SOEs procure only from general contractors in Korea. However, the second corner solution may be unrealistic given that no real-life SOEs procure all products and services entirely from innovative contractors. If the government provides decent compensation, SOEs may procure more from innovative contractors. Nevertheless, they hardly purchase all of their goods and services from nonstandard suppliers. Therefore, I use the following assumption, which rules out the second corner solution. This assumption is used only for simplicity and tractability. The main messages with regard to procurement policies do not change if the assumption is relaxed.

Assumption 3:

The following proposition 2 is the main result of this paper. It states the optimal procurement policy of the government and the optimal procurement choice by the SOE given the optimal policy.

Proposition 2: Suppose Assumptions 1, 2 and 3 hold. The optimal procurement policy (α^*, β^*, b^*, p^*) , the optimal procurement choice x^* , and the social welfare at the optimum V^* are characterized as follow:

(i) Suppose that . Then,

(ii) Suppose that . Then, x^* = 0, and V^* = m − c .

Proof: The government’s objective function V can be rewritten as

The SOE’s participation constraint is always binding. Suppose that it is nonbinding to reach a contradiction. Then, by reducing β slightly, the government becomes better off, as V increases while the incentive constraints (5), (6), and (7) are unaffected and the participation constraint is still satisfied, which is a contradiction.

The private suppliers’ participation constraint (2) is satisfied if and only if the margin p equals p^* , defined as shown below.

Proof of (i): I shall prove this by using a guess-and-verify method. Guess that 0 < α^*Δ + b^* − δ − p^* < γ(α^*)²σ² . Then, the optimal procurement choice x^* is characterized by equation (5). By substituting for x in (10) with x^* in (5), the government’s objective function becomes

Recall that the SOE’s participation constraint (9) is binding. Accordingly, by replacing x in the participation constraint (9) with x^* in (5), the constraint can be rewritten as shown below.

By rewriting the equality above, the following expression for β can be obtained:

By replacing β in (12) using equation (13), the government’s objective function is rewritten as

In this way, the government’s problem is reduced to maximize V(α, b) in (14) without any constraint. The first-order condition with respect to b implies that

It can easily be shown that the second-order condition is satisfied. Under this optimal bonus scheme, equation (5) implies that the optimal procurement choice equals

These two equations (15) and (16) imply that the government’s objective function equals

Because Δ > δ + p^* , the government’s objective function is maximized if x(α) is maximal. As x(α) is decreasing in α , the optimal quality-dependent compensation factor equals α^* = α . Equations (13), (15), (16), and (17) imply that , and . Note that α^*Δ + b^* − δ − p^* equals Δ − δ − p^* , which is greater than zero and less than γα^*δ^* according to Assumption 3. That is, the guess is verified.

Guess instead that αΔ + b − δ − p^* ≤ 0 . Then, according to equation (7), x^* = 0 , which means β = −αm + c given the binding participation constraint (see equation (9)). The government’s objective function in equation (10) then becomes V = m − c , which is strictly less than . As the government can further increase its welfare by choosing a different procurement policy (α^*, β^*, b^*, p^*) , we reach a contradiction.

Guess that αΔ + b − δ − p^* ≥ γ(α)²σ² at the optimum. Then, according to equation (6), x^* = 1 , which means due to the binding participation constraint. In this case, the government’s objective function in the equation (10) becomes . Because V is decreasing in α , it must be that α = α . Then, V equals . This is smaller than as the function is maximized at . Note that is less than 1 according to Assumption 3. Note also that the function equals at the maximum , while it equals at the suboptimum x = 1 . As the government can further increase its welfare by choosing a different procurement policy (α^*, β^*, b^*, p^*) , we reach a contradiction.

Proof of (ii): According to the SOE’s binding participation constraint, it follows that

By plugging β in equation (18) into the government’s objective function in (10), it follows that

Given that Δ ≤ δ + p^* , the government must induce x = 0 to maximize the objective function. To this end, given the incentive-compatibility constraint (6), it must set low levels of α and b so that α^*Δ + b^* − δ + p^* ≤ 0 . Then, x^* = 0 and V^* = m − c . ■

Below, I provide an intuition of Proposition 2. Firstly, consider the case where Δ ≤ δ + p^* . In this case, newly invented goods are not innovative enough such that the improvement in quality Δ is less than the added cost δ and added payment p^* . The risk-neutral government (which behaves in the best interest of the general public) then finds it optimal to procure only from general contractors, (i.e., x^* = 0). Therefore, the government must discourage the procurement of innovative goods by providing low or zero benefits such that the SOE perceives zero or negative value from procuring innovative goods (i.e., α^*Δ + b^* − δ − p^* ≤ 0). In this case, the SOE purchases all goods from general contractors and, hence, the social welfare equals the quality of a standard good minus the cost of its production (i.e., V^* = m − c).

Secondly, consider a more interesting case where Δ > δ + p^* . The newly invented goods are sufficiently innovative such that the improvement in quality outweighs the added cost and the margin. The risk-neutral government (and the general public) then wants to maximize the amount of procurement from innovative contractors. However, the SOE is risk-averse and considers not just the improvement in quality but also the associated risk. Consequently, it is reluctant to purchase innovative goods. To solve this agency problem, the government must align the SOE’s perceived value of innovative goods (i.e., αΔ + b − δ − p^*) with the social value (i.e., Δ − δ − p^*) and minimize the perceived risk (i.e., γα²σ²). There are two ways to adjust the SOE’s perceived value: through a quality-dependent payment and with a quantity-dependent payment. If the ex-post quality-dependent payment increases (i.e., α increases), both the perceived value and risk increase. In contrast, if the ex-ante quantity-dependent payment increases (i.e., b increases), the risk does not change while the value increases. Therefore, it is optimal for the government to minimize the power of the quality-dependent payment (i.e., α^* = α) while raising the power of the quantity-dependent payment (i.e., b^* = (1 − α)Δ ) so that the SOE’s perceived value agrees with the social value (i.e., α^*Δ + b^* − δ − p^* = Δ − δ − p^* ). Consequently, the SOE chooses and the social welfare becomes . Finally, the procurement of innovative goods contributes to social welfare as much as .