Silviase/jgov_v1.4_full_ann huggingface dataset:
purchase. Shepard (1991) focused on U.S. gas station service and tested if the market is competitive or not by using pricing information from full and self service stations. In the case of gas stations, it is common for service providers to supply both full and self services at the same place.

In retail trade service, however, each shop or firm may specialize in a certain level of service and tries to differentiate the service content from others. In this sense Shepard's model should be modified to apply to the retail trade service provision, especially in Japan. Traditionally, Japanese retail trade service has been quite regional. Small shops form a shopping arcade in the downtown and provide the regional market. There are not competitive, but cooperative, relationships between shops, which is welcomed by consumers because everyone is a member of the regional community.

According to economic growth and an expansion of the retail market size, regional shopping arcades are about to face competition with large superstores. Although the purpose of the Large-Scale Retail Store Law was to protect small shops from the competition, the law prevented large stores from opening in traditional store areas, and eventually led to less competitive and regionally monopolistic markets. Early in the 1990s, under the stream of deregulations, the law was relaxed for large stores to more easily enter the traditional market. $ ^{4} $ Considering the situation mentioned above, it might be reasonable to interpret that the Japanese retail trade service market has changed from a regionally monopolistic one to more competitive, but not perfectly competitive, where a large store and a group of small shops are conscious of each other and searching for suitable business strategies. We will write a scenario that illustrates the changes of Japanese retail trade service market conditions and attempts a simulation analysis to derive policy implications.

The rest of the paper is organized as follows. The next section introduces the Shepard model of the retail trade service market and explains the modified version for this paper's analysis. In Section 3 we try a numerical experiment using the model. In the following section we consider the policy implications based on the simulation results. The final section provides the conclusions.
## 2 Modified Shepard's Model

Suppose there are two kinds of retail trade service firms: one providing high quality service, h, and one providing low quality service, $ \ell $ . We assume a consumer makes a choice of purchasing one unit of service from one of the two providers or no purchase. We also assume that the consumer's income m has a uniform distribution from M - 1 to M. The consumer's choices can be described as follows:

$$ U_{h}=V_{h}(m-P_{h}) $$

$$ U_{\ell}=V_{\ell}(m-P_{\ell}) $$

$$ U_{0}=V_{0}\cdot m, $$

where $ V_{h} $ and $ V_{\ell} $ show the utility a consumer obtains from the purchase of high and low quality retail trade services respectively, and $ P_{h} $ and $ P_{\ell} $ stand for the corresponding prices. $ V_{0} $ is the reservation utility of retail trade service purchase.

### 2.1 Monopoly

In the case of a monopolistic market, each retail trade service provider faces its own customers' demand function. Following Shepard's model, a retail trade service provider maximizes profit equation defined as

$$ \pi_{h}^{M}=\left(P_{h}-w-\alpha\right)\left(M-\frac{V_{h}P_{h}}{V_{h}-V_{0}}\right) $$

$$ \pi_{\ell}^{M}=\left(P_{\ell}-w\right)\left(M-\frac{V_{\ell}P_{\ell}}{V_{\ell}-V_{0}}\right), $$

where w stands for the marginal cost of retail trade service common to low and high quality services and $ \alpha $ for the additional marginal cost for high quality service. The superscript M symbolizes a monopolistic market situation. The profit maximizing prices are derived as follows:

$$ P_{h}^{M}=\frac{V_{h}-V_{0}}{2V_{h}}M+\frac{w+\alpha}{2} $$

$$ P_{\ell}^{M}=\frac{V_{\ell}-V_{0}}{2V_{\ell}}M+\frac{w}{2}. $$
Figure 1: Thresholds and service demand

### 2.2 Bertrand equilibrium

Under the assumption of a consumer’s rational choice among the three alternatives above, we can derive the following two threshold points that equalize $ U_{h} $ with $ U_{\ell} $ , and $ U_{\ell} $ with $ U_{0} $ :

$$ m\big|_{U_{h}=U_{\ell}}=\frac{V_{h}P_{h}-V_{\ell}P_{\ell}}{V_{h}-V_{\ell}} $$

$$ m\big|_{U_{\ell}=U_{0}}=\frac{V_{\ell}P_{\ell}}{V_{\ell}-V_{0}}. $$

The demand function for high quality and low quality services can be described as:

$$ X_{h}=M-\frac{P_{h}V_{h}-P_{\ell}V_{\ell}}{V_{h}-V_{\ell}} $$

$$ X_{\ell}=\frac{P_{h}V_{h}-P_{\ell}V_{\ell}}{V_{h}-V_{\ell}}-\frac{P_{\ell}V_{\ell}}{V_{\ell}-V_{0}}. $$

As Figure 1 shows, the demand for high and low quality services correspond to the areas between M and $ m\big|_{U_{h}=U_{\ell}} $ , and between $ m\big|_{U_{h}=U_{\ell}} $ and $ m\big|_{U_{\ell}=U_{0}} $ respectively.

Here we assume each provider maximizes profit under the given competitor's price, which leads to the Bertrand equilibrium. The reaction functions can be derived as follows:

$$ P_{h}=\frac{w+\alpha}{2}+\frac{V_{h}-V_{\ell}}{2V_{h}}M+\frac{V_{\ell}}{2V_{h}}P_{\ell} $$

$$ P_{\ell}=\frac{w}{2}+\frac{V_{h}(V_{\ell}-V_{0})}{2V_{\ell}(V_{h}-V_{0})}P_{h}. $$
Figure 2: Reaction Functions

It can be shown that both the coefficient of $ P_{\ell} $ in (12) and that of $ P_{h} $ are less than 1/2. The reaction functions are illustrated in Figure 2. The intersection of the two lines corresponds to the Bertrand equilibrium prices, $ P_{h}^{B} $ and $ P_{\ell}^{B} $ .

The results of comparative statics are summarized in Table 1.

We can make a comparison of retail trade service prices between monopolistic and Bertrand's cases. Subtracting RHS of (12) from that of (4) and RHS of (13) from that of (5), we get

$$ \frac{V_{\ell}-V_{0}}{2V_{h}}-\frac{V_{\ell}}{2V_{h}}P_{\ell}=\frac{V_{\ell}(M-P_{\ell})-V_{0}M}{2V_{h}}>0 $$

$$ \frac{V_{\ell}-V_{0}}{2V_{\ell}}M-\frac{V_{h}(V_{\ell}-V_{0})}{2V_{\ell}(V_{h}-V0)}P_{h}=\frac{V_{\ell}-V_{0}}{2V_{\ell}(V_{h}-V_{0})}\big[V_{h}(M-P_{h})-V_{0}M\big]>0. $$
$ P_{h} $	$ P_{\ell} $
w	+	+
$ \alpha $	+	-
M	+	+

Table 1: Comparative statics of Model 2

A move from pure monopoly to the Bertrand equilibrium lowers retail trade service prices.

The effects of the changes in M, $ \alpha $ , and w differ between the monopoly and Bertrand situations. The simple calculation leads to the results that the effects of $ \alpha $ and w are greater in the case of the Bertrand case, and that of M is greater in the monopoly case.

The total output of retail trade service Y is defined as:

$$ Y=V_{h}X_{h}+V_{\ell}X_{\ell}. $$

The input for service production is evaluated in terms of cost: $ w + \alpha $ for high quality and w for the low. Then, we have the total input X as

$$ X=(w+\alpha)X_{h}+w X_{\ell}. $$

Therefore, the productivity $\phi$, is

$$ \phi=\frac{V_{h}X_{h}+V_{\ell}X_{\ell}}{(w+\alpha)X_{h}+w X_{\ell}}. $$

The nominal indicator of productivity can be mark-up rate ( $ \theta $ ):

$$ \theta=\frac{P_{h}X_{h}+P_{\ell}X_{\ell}}{(w+\alpha)X_{h}+w X_{\ell}}. $$

And finally consumer’s welfare indicator in real term can be defined as

$$ W=\frac{V_{h}X_{h}+V_{\ell}X_{\ell}}{P_{h}X_{h}+P_{\ell}X_{\ell}}. $$

## 3 Numerical Experiment

### 3.1 Scenario Writing

Based on the modified Shepard model, we make a numerical experiment giving certain values to the parameters: $ w = 0.2, \alpha = 0.1, V_{h} = 0.75, V_{\ell} = 0.5, V_{0} = 0.1, M = 1 $ for the
Stage	Environmental change	Corresponding variables
0	Regional monopoly
1	Bertrand equilibrium
2	Change in consumer's evaluation	$ V_{h} $ 1% fall
3	Left shift of income distribution	$ M $ 1% fall
4	Wage rate reduction	$ w $ 1% fall
5	Labor quality reduction	$ w $ , $ V_{h} $ , and $ V_{\ell} $ 1% fall

Table 2: Scenario

simulation A, $ w = 0.1, \alpha = 0.2, V_{h} = 0.75, V_{\ell} = 0.5, V_{0} = 0.1, M = 1 $ for the simulation B, and $ w = 0.2, \alpha = 0.05, V_{h} = 0.75, V_{\ell} = 0.5, V_{0} = 0.1, M = 1 $ . We present a scenario that approximately depicts a recent environmental changes of a retail trade service market in Japan.

We begin with the “monopoly” situation where the market is divided into the two areas, one providing high quality service, another providing low quality service, and consumers have no choice among the two at purchase. The first move to the Stage 1 means the change from the monopolistic market to the Bertrand equilibrium. It corresponds to the deregulation of the Japanese retail trade service market after the amendment of the Large-Scale Retail Store Law. At the Stage 2, we assume consumers depreciate high quality service. According to the collapse of regional communities, traditional shopping arcades in downtown are losing customers. The Stage 3 shows the effect of economic recession and the shift of consumers’ income distribution to the left. The deepening of the recession lowers the wage rate at Stage 4. The wage reduction makes the high quality labor force quit working in the retail trade services. $ ^{5} $ This is at the final stage. The scenario is summarized as in Table 2.

### 3.2 Results

The simulation results based on the scenario in Table 2 are summarized in Table 3, 4 and 5. In simulation A, we assume there is no productivity difference between low and high quality service providers. Simulation B considers a case where a low quality service provider gains higher productivity, and the simulation C proposes a case of high quality service that has
$P$ is the aggregated price of $P_{h}$ and $P_{\ell}$ by Theil=Trönqvist index formula.

Stage 0	Stage 1	Stage 2	Stage 3	Stage 4	Stage 5	Total
Ph	0.583	0.532	0.529	0.527	0.525	0.523
Pl	0.500	0.345	0.345	0.344	0.342	0.339
P	1.000	0.784	0.782	0.780	0.775	0.770
Xh	0.663	0.191	0.180	0.168	0.175	0.186
Xl	0.375	0.945	0.958	0.953	0.951	0.944
πh	0.188	0.044	0.041	0.038	0.040	0.042
πl	0.113	0.138	0.139	0.137	0.136	0.135
φh	2.500	2.500	2.475	2.475	2.475	2.475
φl	2.500	2.500	2.500	2.500	2.500	2.500
φ	2.500	2.500	2.495	2.495	2.495	2.494
θh	1.944	1.773	1.765	1.758	1.761	1.766
θl	2.500	1.727	1.724	1.719	1.725	1.731
θ	2.096	1.738	1.733	1.727	1.733	1.739
W	1.192	1.439	1.440	1.444	1.453	1.448
ΔPh/Ph	-8.8%	-0.5%	-0.4%	-0.5%	-0.4%	-10.6%
ΔPl/Pl	-30.9%	-0.2%	-0.3%	-0.7%	-0.7%	-32.7%
ΔP/P	-21.6%	-0.3%	-0.3%	-0.6%	-0.6%	-23.4%
ΔXh/Xh	-71.2%	-5.8%	-6.6%	4.5%	6.1%	-73.1%
ΔXl/Xl	152.1%	1.4%	-0.6%	-0.2%	-0.7%	151.9%
Δπh/πh	-76.5%	-6.8%	-7.4%	4.1%	6.0%	-80.5%
Δπl/πl	22.2%	0.8%	-1.2%	-0.4%	-1.0%	20.5%
Δφh/φh	0.0%	-1.0%	0.0%	0.0%	0.0%	-1.0%
Δφl/φl	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Δφ/φ	0.0%	-0.2%	0.0%	0.0%	0.0%	-0.2%
Δθh/θh	-8.8%	-0.5%	-0.4%	0.1%	0.3%	-9.2%
Δθl/θl	-30.9%	-0.2%	-0.3%	0.3%	0.3%	-30.7%
Δθ/θ	-17.1%	-0.3%	-0.3%	0.3%	0.4%	-17.1%
ΔW/W	20.6%	0.1%	0.3%	0.6%	-0.4%	21.3%

Table 3: Simulation A: Recent movement of Japanese retail market
$P$ is the aggregated price of $P_{h}$ and $P_{\ell}$ by Theil=Trönqvist index formula.

Stage 0	Stage 1	Stage 2	Stage 3	Stage 4	Stage 5	Total
Ph	0.583	0.453	0.450	0.448	0.447	0.447
Pf	0.450	0.259	0.258	0.257	0.256	0.255
P	1.000	0.670	0.667	0.664	0.662	0.661
Xh	0.663	0.318	0.307	0.296	0.299	0.310
Xe	0.438	1.034	1.047	1.041	1.040	1.030
πh	0.188	0.049	0.046	0.044	0.044	0.046
πe	0.153	0.165	0.166	0.164	0.163	0.162
φh	2.500	2.500	2.475	2.475	2.475	2.475
φe	5.000	5.000	5.000	5.000	5.000	5.000
φ	2.950	3.800	3.818	3.839	3.830	3.798
θh	1.944	1.510	1.501	1.494	1.495	1.501
θe	4.500	2.591	2.581	2.572	2.587	2.606
θ	2.405	2.072	2.075	2.076	2.079	2.078
W	1.227	1.834	1.840	1.849	1.855	1.840
ΔPh/Ph	-22.3%	-0.6%	-0.4%	-0.3%	0.1%	-23.6%
ΔPf/Pf	-42.4%	-0.4%	-0.3%	-0.4%	-0.3%	-43.9%
ΔP/P	-33.0%	-0.5%	-0.4%	-0.4%	-0.2%	-34.4%
ΔXh/Xh	-52.0%	-3.4%	-3.9%	1.3%	3.5%	-54.5%
ΔXe/Xe	136.4%	1.3%	-0.6%	-0.1%	-1.0%	136.0%
Δπh/πh	-74.1%	-5.2%	-5.1%	1.0%	4.5%	-78.9%
Δπe/πe	7.4%	0.7%	-1.1%	-0.2%	-0.8%	6.0%
Δφh/φh	0.0%	-1.0%	0.0%	0.0%	0.0%	-1.0%
Δφe/φe	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Δφ/φ	28.8%	0.5%	0.6%	-0.2%	-0.8%	28.7%
Δθh/θh	-22.3%	-0.6%	-0.4%	0.0%	0.4%	-22.9%
Δθe/θe	-42.4%	-0.4%	-0.3%	0.6%	0.7%	-41.9%
Δθ/θ	-13.8%	0.1%	0.1%	0.1%	0.0%	-13.6%
ΔW/W	49.5%	0.3%	0.5%	0.4%	-0.8%	49.8%

Table 4: Simulation B: Recent movement of Japanese retail market
$P$ is the aggregated price of $P_{h}$ and $P_{\ell}$ by Theil=Trönqvist index formula.

Stage 0	Stage 1	Stage 2	Stage 3	Stage 4	Stage 5	Total
Ph	0.558	0.502	0.500	0.498	0.495	0.493
Pl	0.500	0.332	0.331	0.330	0.328	0.325
P	1.000	0.776	0.773	0.771	0.766	0.761
Xh	0.678	0.314	0.305	0.293	0.300	0.309
Xl	0.375	0.857	0.868	0.862	0.860	0.855
πh	0.209	0.079	0.076	0.073	0.074	0.076
πl	0.113	0.113	0.114	0.112	0.112	0.111
φh	3.000	3.000	2.970	2.970	2.970	2.970
φl	2.500	2.500	2.500	2.500	2.500	2.500
φ	2.847	2.657	2.643	2.640	2.643	2.646
θh	2.233	2.009	1.999	1.991	1.996	2.003
θl	2.500	1.659	1.655	1.651	1.656	1.661
θ	2.315	1.769	1.760	1.752	1.759	1.767
W	1.230	1.502	1.502	1.507	1.516	1.512
ΔPh/Ph	-10.0%	-0.5%	-0.4%	-0.6%	-0.5%	-12.0%
ΔPl/Pl	-33.6%	-0.2%	-0.3%	-0.7%	-0.7%	-35.6%
ΔP/P	-22.4%	-0.3%	-0.3%	-0.6%	-0.6%	-24.4%
ΔXh/Xh	-53.7%	-2.9%	-3.9%	2.6%	2.9%	-55.0%
ΔXl/Xl	128.5%	1.3%	-0.7%	-0.2%	-0.6%	128.3%
Δπh/πh	-62.1%	-3.8%	-4.6%	2.3%	2.8%	-65.6%
Δπl/πl	0.4%	0.7%	-1.4%	-0.4%	-0.9%	-1.6%
Δφh/φh	0.0%	-1.0%	0.0%	0.0%	0.0%	-1.0%
Δφl/φl	0.0%	0.0%	0.0%	0.0%	0.0%	0.0%
Δφ/φ	-6.7%	-0.5%	-0.1%	0.1%	0.1%	-7.1%
Δθh/θh	-10.0%	-0.5%	-0.4%	0.2%	0.3%	-10.4%
Δθl/θl	-33.6%	-0.2%	-0.3%	0.3%	0.3%	-33.5%
Δθ/θ	-23.6%	-0.5%	-0.4%	0.4%	0.5%	-23.7%
ΔW/W	22.2%	0.0%	0.3%	0.6%	-0.3%	22.8%

Table 5: Simulation C: Recent movement of Japanese retail trade service market
higher productivity.

In all cases, throughout the all stages, the service prices, $ P_{h} $ and $ P_{\ell} $ , continue falling. Especially, the change in retail trade service market environment, from monopoly to the Bertrand equilibrium, has drastic and contrasting effects on high and low quality service providers. For a high quality service provider, market integration reduces sales by 50 to 70% and profit by nearly 80%. The low quality service provider, on the contrary, gains an expansion of sales and growth of profit. What looks interesting is that the largest fall in price, P, occurs in simulation B, from monopoly to Bertrand. The market share expansion of more productive service providers brings consumers more benefits because they have the potential power to allow price reductions.

In this paper we define retail trade service output in terms of a consumer's evaluation, utility level V. The productivity remains at the same level regardless the change in nominal variables such as wage, because the constant returns to scale technology for service production is assumed. $ ^{6} $ One essential factor affecting productivity is a change in the consumer's evaluation of retail trade service. In fact, to see the productivity indicator for each service provider, $ \phi_{h} $ and $ \phi_{\ell} $ , the values stay at the same level except at Stage 2. $ ^{7} $ In Simulation A, no productivity difference is shown between the two services at Stage 0, the aggregated productivity shows a slight decline, only -0.2%. Simulations B and C, on the other hand, shows a quite different story. In the case of B, the aggregated productivity level rises nearly 30%, because of the low quality service, productivity level of which is twice as much as that of high quality service, and gains sales market share about 40% point. Simulation C shows a productivity fall in 7%.

The nominal productivity indicator, $ \theta $ , on the contrary, receives a substantial negative effect from deregulation. A decline in consumers' service evaluations and their incomes also lower the mark-up rate. The consumer's welfare indicator, the utility level per expenditure, is drastically improved by deregulation. A fall in labor quality raises the mark-up rate, but
lowers consumer’s welfare.

If we use retail trade service price index P as a deflator of nominal productivity, the “real” productivity growth is 6.3% in Simulation A, 20.8% in B, and 0.7% in C. The overestimation is observed in A and C, and the underestimation in B.

## 4 Policy implications

The simulation results in Table 3, 4 and 5 clearly show the difference between nominal output (gross margin), P, and real output, V. Retail trade service is highly differentiated according to a variety of consumers' preferences. If the market is not perfectly competitive, the retail trade service margin may include the provider's rents and inefficiencies. We must be careful to discuss retail trade service productivity in a nominal term.

The three tables also explain that the deregulation policy in the retail trade service market obviously brings benefits to consumers through decreasing prices. In the simulation study, we assume that large-scaled superstores correspond to low quality service providers. As is shown in Simulation B, if they have higher productivity than traditional retail trade service stores, the effect of deregulation becomes much larger compared to other cases.

Nominal output is deflated by price index to obtain real output. This traditional procedure would have a problem when the price reflects the service quality. A change in the market share of high and low quality services would lead to a biased estimate of a real output measure even if service prices are constant.

If service output is evaluated by the consumer’s utility level, the following two points should be considered. Firstly, a simple productivity comparison between different services is misleading. Small stores in local shopping arcades are not necessarily less productive than huge superstores in suburban areas. They provide different services. If a consumer’s evaluation is of one of the service categories, ambiance, even a local small store would have high productivity. In this case, as Simulation C shows, macro productivity in retail sectors would decline as a result of the market competition.

Secondly, the international productivity comparison is almost meaningless. The same service would be appreciated in one country but not necessarily in others. What matters is whether a consumer’s freedom to choose is guaranteed or not. Indicators of market conditions, such as the degree of competition and a variety of choices, are comparable among
nations. In fact the simulation results clearly explain how drastically prices fall as the market condition shifts from monopoly to the Bertrand equilibrium.

## 5 Conclusion

Measurement of productivity requires input and output definition. Different from manufactured products, service output is invisible and highly differentiated. Because production and consumption activities simultaneously occur, a consumer’s purchase behavior should be taken into account to define output.

In this paper we have applied the theoretical model of Shepard (1991) to the Japanese retail trade service market. We assume that the market is composed of low and high quality service providers and investigate how retail margins and productivity move according to the change in market conditions. A numerical experiment is designed to illustrate recent environmental changes in the Japanese retail trade service market: deregulation, a change in life style, and an economic recession.

Since the early 1990s, the Japanese retail trade service market has been gradually deregulated. A symbolic event has been the moderation of the Large-Scale Retail Store Law, which previously had an effect of preventing huge superstores from competing in traditional shopping arcades in downtown areas. Not only the deregulation but also progress in personal transportation has integrated suburban and downtown retail trade service markets and led to competition between superstores and small shops. In the simulation study, we measure the deregulation effect by a shift from regional monopoly to the Bertrand equilibrium. As a result, retail margins drastically falls by 20 to 30%, and consumers' welfare is improved by 20 to 50%.

Shopping arcades in the downtown area are consistent with regional communities. Consumers in such communities not only go shopping there but also exchange information with neighbors, thus keeping their communities comfortable. Small shops play an important role in providing an area for communication and maintaining a peaceful environment. A recent drastic change in life style has depreciated the value of these services. Consumers now prefer a rich assortment of goods in superstores to local communications in small shops. In the simulation this trend shows the effect of lowering the retail margins.

The long term economic recession has caused less income, wage reduction, and, eventu-
ally, declining labor quality. The simulation results show that all these changes lead to a fall in retail margins. To summarize, environmental changes that occurred in the last ten years unexceptionably dropped retail margins.

Academic papers on the Japanese retail trade services published early in the 1990s mostly focused on the deregulation issues. Big margin were considered as evidence of imperfect competition and regulations. This view has completely changed. Raising retail trade service productivity seems to be a key to the recovery of the Japanese economy. This policy is quite misleading from the following two points. Firstly, if the service output is measured by retail margins, a shift from competition to monopoly would raise the productivity. Secondly, the causality could be reverse. Although it is ambiguous that productivity gains in the retail trade service sector cause economic growth, the business recovery would raise retail productivity through the expanding market share of productive retail trade service providers.

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