Finding a Best Conservation Park Entry Fee for Kruger National Park Gardner Brown1 and Johane Dikgang2

Abstract Whereas most park valuation studies simply value a park our goal is to maximize net revenue. Kruger National Park is regarded as a firm "exporting" products to foreign clientele. In trade theory a profit maximizing firm charges different prices in different countries with different demand functions. Transaction costs limit there to be one price for all foreigners in our case. The travel cost of an individual serves as an indirect determinant of price. We estimate the optimal price to charge for the site using travel costs for trip not the site. By estimating the marginal visitation response to a change in trip cost, due to a park entry fee increase, ceteris paribus, we deftly avoid the standard criticism of travel cost regarding multiple destinations. Using on-site international visitors survey data we estimate truncated count data models of recreational demand taking into account the fact that the number of visitation trips taken is a non-negative integer. Most   importantly,   the   truncated   distribution   function   is   augmented   for   endogenous   stratification.   The population in each country (zone) is limited to those whose income matches the income in our sample, a measure more appropriate than the total population. Our results indicate that the revenue maximizing daily entry fee to charge international visitors is US$191 (2014 prices) based on the truncated population zone. Proper choice of zonal population measure is therefore critically important. This suggests that there is room to substantially raise Kruger entry fees from the present level of $25 per day. In reality, the park agency is unable to charge the revenue maximizing price due in particular to competition from other parks, both locally and regionally.                                                                                                                 1

Department of Economics, University of Washington. Seattle, Washington, United States of America. Email: [email protected]. 2 Department of Economics and Econometrics, University of Johannesburg, Johannesburg, South Africa. Email: [email protected]. Funding from ERSA (Economic Research Southern Africa), and Sida (Swedish International Development Cooperation Agency) is gratefully acknowledged.

 

1  

  Nonetheless, the fact that we found that the fees could be increased significantly over and above the current fees to maximize the revenue collection is quite striking. Keywords: Kruger, endogenous stratification, count data,  international, price, travel cost, truncation.

 

2  

  1. Introduction Big game parks in Africa levy entry fees on visitors entering the park. The entry fee or the fee for conservation is so low for foreign visitors, $25/day that the park authorities do not cover the costs of managing the park (see - Laarman and Gragersen, 1996; Schultz Schultz et al., 1998; Scarpa et al., 2000; Naidoo and Adamowicz, 2005). This implies that most park fees are underpriced creating what many would regard as a perverse phenomena: some of the world’s poorest countries such as Botswana, Kenya, Namibia, Tanzania and South Africa are subsidizing the very predominantly wealthy visitors from the world’s wealthiest countries. For example, the median annual income in our survey of visitors is over US$75,000. It is a pricing policy that few would enthusiastically defend publically. Our intent is to estimate a more defensibly appropriate pricing policy for game parks illustrated by an analysis of foreign tourists visiting Kruger National Park in South Africa. The research has three focal points. First, most park valuation studies rightfully estimate the consumer surplus derived by the mostly domestic clients who visit a park.

In

contrast, only foreign visitors are included in our sample. Therefore Kruger should be treated as just another South African firm whose goal presumably is to maximize profits To the best of our knowledge, there are few published papers that have maximized revenues for a park. Thus our study is distinctive. Had it been possible to collect appropriate data on domestic visitation we could have derived and estimated a two-price policy for Kruger. The two-price policy would have made this study even more unique. Nonetheless, we borrow the shape from a study by Dikgang and Muchapondwa (2013), and scale it to Kruger for illustrative purposes. We expect the slope on price to be significantly negative. We expect it to show that entry price should be dramatically larger. Second, in order to determine an optimal entry price for a park, one needs a demand function for the park. One empirical method to estimate a demand function for a park for which there are inadequate price -quantity data is the travel cost method. In the park

 

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  studied, Kruger, in South Africa, the historical price/quantity data are outside the range of an optimal price, as we shall see. We set forth our version of the travel cost method used to determine the optimal price and explain how our method and the empirical setting of the analysis ameliorates some of the criticisms of the travel cost method. Briefly, we assume that there is an increase in the trip cost, reflecting an increase in the site cost, due to an increase in the park entry fee. In so doing the dilemma about how to treat multiple destinations is avoided. Third, for a park like Kruger where the median airfare is $1302, the tour package that includes visits to the game park is $3100 or more and median annual income of foreign visitors is $75,000, scaling visits by the total population in a zone cannot be the best choice. The probability that the population in the lower deciles of the income distribution would go to Kruger is quite small. Instead, we use the distribution of the population whose median income exceeds $75,000 per year. Fourth, we show the exceptional discrepancy between the actual conservation entry charge per day and the optimal price that should be charged. Over a wide range, demand for park entry is inelastic for virtually all international visitors, and the scale of the entry fee for Kruger is $25 per day where they typically stay for a couple of days, an amount lower by more than an order of magnitude. Fifth, assuming that SANParks should set the entry price per day to Kruger to maximize revenue, it should set the price for international tourists where the elasticity of aggregate demand from all zones is equal to 1, and for the residents maximize consumer surplus (i.e. set price equal to marginal costs – MC). It is obvious that the optimal price depends on the weights of visitation and elasticities for the different zones. In trade theory a firm gets to charge different prices in different countries. Here, transaction costs and perhaps political feasibility limit us to one price for all foreigners. We are not aware of any literature where countries are constrained to charge one price in two or more different markets, where elasticities differ. Moreover, we would ideally like to know the marginal cost per visitor at Kruger, where the cost refers to running the park and not the rondevals

 

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  (i.e. accommodation), restaurants and all other services. We suspect that most of the park costs are fixed, having to do with anti poaching and overall management activities. 2. The Travel Cost Method How does one value the value of a non-market site that people visit? The classical stated virtue of the travel cost method (TC) compared to rivals such as contingent valuation (CV) or stated preference (SP) is that TC is lodged in the indirect revealed preference of consumer actual behavior. Hotelling’s (1947) profound insight developing the travel cost method was that observed behavioral differences in consumers’ travel cost give rise to observed different rates of actual participation. That’s the basis for estimating a demand function for a recreation site while CV or SP studies rely on “hypothetical” non-market behavior. Chase et al. (1998) argued that methods such as contingent valuation and stated preference are “more flexible” than the travel cost method because the former can capture non-use values. True enough if we were interested in determining a total value of a site. However, our intent is a marginal objective - to determine an optimal price to charge for entry into Kruger Park, a use value. Obtaining estimates of existence value is not appropriate for solving this problem. Moreover, as long as something like an individual’s existence value is not a function of use value, then we are not guilty of omission, not considering a social externality of increasing price that could result in the marginal loss of existence value. One of the criticisms of the travel cost model is the difficulty encountered when the site to be valued is part of a trip with more than one destination. How does one estimate the travel cost for one of the joint products? That is not our problem, given our objective. Most other TC studies seek a total value of a particular site for typically a non-market use like a park versus the total value of an alternative allocation of the land for timber cutting. Our objective is different. We are interested in the optimal price to charge for entrance into Kruger. Our survey asks respondents about travel costs for the whole trip that

 

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  includes visiting Kruger. A cost increase in the trip is interpreted as an increase in the park entry price by assuming other elements of the trip remain unchanged. A few words about the goal of setting a conservation fee or entry price that maximizes revenue are in order. The fact that Kruger is the property of the South African government, we judge, has no bearing on the appropriate objective function. Why not maximize consumers’ surplus, as most studies do? A few exceptions include Dikgang and Muchapondwa (2013); and Chase et al. (1998) who find that one park should increase its price to increase revenue, another should decrease the fee and a third park was pricing approximately correctly. A study by Alpizar (2006) used historical data to compute the “optimal” common entrance fees for national parks in Costa Rica. Alpizar (2006) found that price discrimination between residents and non-residents could successfully maximize social welfare and even meet a set revenue target. A study by Naidoo and Adamowicz (2005) simulated fee increases in an SP study and estimated entrance fees that maximized tourism revenue to Mabira Foresty Reserve in Uganda. Wilman (1988) derived Ramsey prices for a multiproduct monopoly, while Anas (1988), determined optimal preservation and pricing of natural public lands in a general equilibrium These last two papers are theoretical and assume a frame of reference quite different for that facing SANParks. 3. Approach The travel cost of a representative individual in a zone serves as an indirect determinant of price. Most importantly, the relevant population for any country should not include people with sufficiently low income that the probability of visiting Kruger is extremely small. We know the income of people who do come. For an accurate measure of zonal population, TC! 𝑁! ,  we included the population in each country in millions where median income is US$75,000 or more, the level determined by our sample. By estimating how visitation rates vary with TC! , one can estimate a demand function for a destination.

 

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  Visitation rates from different origins, V! /𝑁, where𝑁! is the population in the zone from different origins are regressed on travel costs, TC! , and socioeconomic shift variables, 𝑋! :                                                      V! /𝑁! = f  (𝑇𝐶!  𝑇𝑀! , 𝑋! )                                                                                                                                                                         (1)     We run the model with travel cost and time cost as separate variables. Time cost is equal to 0.3 multiplied by wage rate multiplied by round trip flight time where the wage rate is given by a annual income divided by annual hours worked. For each zone, typically an OECD country when there are sufficient data, (Carr and Mendelsohn, 2003) suppose                                  𝑉! /𝑁! = g   𝑇𝐶! + 𝑇𝑀! + 𝑃, 𝑋!   𝑉! /𝑁! = g   𝑇𝐶! + 𝑇𝑀! + 𝑃

(2)

where P is the optimal revenue maximizing price to charge and𝑁!  is the zone’s population truncated to those with incomes over $75,000 Total revenue is: 𝑇𝑅   𝑃 = 𝑃

! 𝑔  (𝑇𝐶!

+ 𝑇𝑀! + 𝑃 , 𝑋! )  𝑁!

(3)

which is maximized by setting the derivative of (3) with respect to P = 0 to find the optimal price, P*. Not surprising revenue is maximized for P where the elasticity of demand = 1. It is instructive to note that the demand for Kruger is constructed by specifying the area above the travel cost from each origin or zone to use Hotelling’s term for each chosen region. So the demand function for the park we are working with is net of costs of access to the park. Relatively early on, researchers including Cesario and Knetsch (1970) and McConnell (1975) set forth the argument that the “full” price of recreation included the monetized time cost of the trip along with some estimate of the money costs of travel. Reasoning from his study, McConnell argued that to estimate the value of time carefully, researchers ought to inquire about a respondent’s time constraint if any and about alternative uses of

 

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  one’s time. We omitted such questions because the questions designed for other directions of our study exhausted the respondent’s patience and concentration. Among the greater uncertain parameters of the travel cost model method is the opportunity cost of time. Following microeconomics textbook principles, it is natural to assume it is the wage rate, particularly if the analysis involves a business trip (Cesario et al., 1970). Empirically, the opportunity cost of time for non-business related trips has been found to be less than the wage rate, perhaps because people enjoy the scenery if travelling to a recreation site, which creates a trip with multiple characteristics. Or perhaps it is because a commuter in a modal choice commuter study enjoys time away from ones family3. And then there is the problem of retired people, of which there are very many in our sample of people on safari whose income budget constraint does not include hours worked. Researchers in the past have assumed that the value of time was a fraction that varied between 20 to 45 percent of a calculated wage rate (see McFadden, 1974; Larsen and Shaikn, 2004). An early study of modal choice by McFadden (1974) estimated that the opportunity cost of time was 32 percent of the wage rate. Larsen and Shaikh (2004) designed a quite interesting study in which the opportunity cost of time was not fixed and they estimated an elasticity of time with respect to the wage rate. Their time value was 32 – 40 percent for wage rates between $30 - $100 per hour. Our median calculated wage rate ranges from $45 - $84 per hour - see table 1. Getting the opportunity cost of time right probably is less onerous in this research project because it is relatively less important compared to other travel cost studies in general and recreation park studies in general. This is because most of the foreign visitors to Kruger have median trip costs of $3580. Time costs are a smaller component of total costs for the

                                                                                                                3

McFadden provided this example during a University of Washington seminar shortly after the publication of McFadden, “The Measurement of Urban Travel Demand,” J. of Public Economics, 1974,…

 

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  Kruger trip than these costs are in studies of recreation sites visited by relatively more local populations4. Like most other researchers, the trail for delineating the opportunity cost of time begins with observing some measure of annual income and follows through to an estimate of the value of an hour. Such a transformation usually requires “knowing” weeks worked per year, days worked per week and hours worked per day to come up with a computed money wage per hour. We believe all travel cost studies have made these sorts of calculations assuming a certain number of hours per year constant across all zones. Since the vacation length of Europeans is a month or more while the American vacation centers closer to two weeks, and the number of holidays greatly varies across countries, computed hours per year across travel zones can exhibit substantial variation. Fortunately, there are databases that provide estimates of hours worked per year for each country and these data allow us to estimate a more accurate imputed wage rate for our visitors to each country – see table 1. The hours worked in a recent year vary. Virtually all visitors to Kruger fly to Johannesburg and then on to Kruger. Since the latter flight is common to all, the physical time cost is the flight time from the origin to Johannesburg-variations in quantity depends on variations in cost- with the time computed from the flight time and opportunity cost. As for the transformation of these estimated wage rates into a time value, instead of choosing a particular fractional weight, when time costs enter the regression, the fraction                                                                                                                 4   Suppose a 3-hour round trip to a park at 50 miles per hour. The American Automobile Association’s mileage cost often has been used in U.S. travel cost studies. A recent average estimate for three representative types of vehicles is $ 0.65 per mile. At this rate the travel cost amounts to about $94. Valuing the 3 hours at $63(1/3(3)) after adjusting for the subjective value of time = $63. In this example Time costs are about 40 percent of the full travel cost amount. The fraction would be much higher if one arguably correct used a marginal cost estimate of a mile. On the other hand, a 10 or 20-hour flight under the above assumptions together with travel cost of $1500 results in time costs of 12 or 24 percent of full travel cost. AAA, your driving costs: how much are you really paying? 2013 edition.

 

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  modifying the calculate wage rate, is varied from McFadden’s proposed 30-45% and the model outcome with the best statistical fit is chosen. The estimation procedure replaces an assumption with an estimable variable to resolve the uncertainty. The median reported travel cost is used for each zone. Some people in a given zone report high travel cost because they have flown first class. We can partially avoid a model with multiple characteristics (quality of travel) by using the median travel cost observation for each zone because naturally it gives lower weight to these upper values5. The values of an hour worked per year per zone are shown in table 1 below: Table 1: Value of an hour worked per worker in each zone Zone

$ Value of an Hour6

France

50

Germany

54

Netherlands

54

RestofEU

46

EU

46

UK

45

U.S. East

84

U.S. Mid- West

84

U.S. West

63

4. Kruger National Park and the Survey Kruger is home to the ‘big five’, has the biggest accommodation facilities, tarred roads and an international airport. It is the flagship of SANParks managed parks and by far the largest park in South Africa. The park has a wide variety of attractions comparable only with the best in Africa.                                                                                                                 5

In truth, this is an endemic problem with the travel cost procedure although it probably is not a crippling one. High quality automobiles (providing a more spacious, lower noise, more comfortable ride) typically have higher marginal cost per mile, in part, because they have lower fuel economy. 6 We obtained the $ value of an hour by dividing the median household income by the average annual hours worked per worker as provided by the OECD 2013 data.

 

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  Kruger has the second highest number of park visitors after Table Mountain national park, accounting for 29.7% percent of total visits. However, given that Table Mountain main attraction is the mountain itself, and that it does not boast of abundance of wildlife, its visitation demand is not of interest in our study. A face-to-face survey was undertaken in July 2014 in the broader Kruger area. Electronic questionnaires on tablets were used instead of paper-based questionnaires during the fieldwork. A survey was conducted with randomly picked park visitors at the Kruger National Park. Due to the vast size of the park, the surveys were mainly carried out at the gates, accommodation facilities and designated resting sites inside the park. Also conducted were surveys in lodges within close proximity to the park. A total of 322 international visitors were surveyed. The sample composition is in line with the total visitor profile at the park. Thus, the top 5 countries are the Netherlands, United Kingdom, Germany, France and the United States of America (SANParks, 2010). In addition to data from the travel cost, the survey collected data on visitor demographics. The questionnaire was designed such that it would provide the necessary information for calculating travel costs and visits per million. The respondents were asked what their approximate round-trip travel cost they paid in their own currency to get to South Africa from where their trip originally started. Truncated   visits per million and median travel costs are shown in table 2 below.

 

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  Table 2: Sample visits, visits per million and median travel costs from each zone Sample

Truncated

Household

Truncated

Travel

Visits

Population7

Populations

Visits/

Cost

(Millions)

Million

Zone France

18

0.254

6.414262

3

1340

Germany

27

0.217

8.696492

3

1206

Netherlands

112

0.34

2.462349

45

1302

RestofEU

45

0.355

17.288274

3

1340

UK

32

0.34

9.000820

4

1512

U.S. East

27

0.33

15.515615

2

1800

U.S. Mid-West

37

0.33

8.494581

4

2000

U.S. West

14

0.33

9.131551

2

2000

The household population in table 1 above its an adjusted population based on those who can afford to visit Kruger. The estimated number of visitors against median travel cost is shown in figure 1 below8:

                                                                                                                7

The median household income for our sample is $75 000. Thus, we define those who can afford as people with a household income of $75 000 or more. The percentages shown in the column is the proportion of the people in each zone that meet these criteria. 8 The Netherlands is an outlier and is not included in the figure.

 

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Travel Costs - Median

1200 1400 1600 1800 2000

 

U.S. West

U.S. Mid-West

U.S. East

Germany

U.K.

France & E.U 2

2.5

3

3.5

4

Trucated Visits/Million Travel Costs - Median

Travel Costs - Median

  Figure 1: Kruger visitation against median travel cost The importance of the figure is to show the strong bunching of observations for Germany,   France,   Europe, the UK and the USA so that we don’t have very good variation and that’s why there are few observations. 5. Estimation and Results A review of the recent recreation demand literature using single site demand equations usually applies truncated and censored poisson and negative binomial regression models (Creel and Loomis, 1990, Grogger and Carson, 1991, Gurmu, 1991, Hellerstein and Mendelsohn, 1993, Shaw, 1988). Using on-site international visitors survey data from Kruger National Park in South Africa, we estimate truncated count data models of recreational demand taking into account the fact that the number of visitation trips taken is a non-negative integer. Our sample is from an on-site survey9 so we need to take into account the fact that our                                                                                                                 9

The implication due to onsite sample is that households who do not visit are excluded (i.e. the endogeneity), hence the sample is not a true refection of the zonal population as those who visit the site

 

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  observations are truncated at positive trip demand and the problem of endogenous stratification. The failure to account for truncation would result in biased and inconsistent parameter estimates (see Shaw, 1988; Englin and Shonkwiler, 1995). Although a poisson model is a popular count data model, it is restrictive; hence oftenalternative models are often used. In poisson models, it is assumed that there is equidispersion. We tested the statistical significance to test for overdispersion. The null hypothesis of no overdispersion is rejected. Thus, the negative binomial is a more suitable alternative model. There is likely to be great variability in the estimated demand elasticities as a result of individual heterogeneity in tastes and opportunity i.e. this is common with micro level data (Phaneuf and Smith, 2004). According to Cameron and Trivedi (1998) the problem of overdeispersion could be due to unobserved heterogeneity that is not captured by the poisson model. Thus, introducing heterogeneity resulting from unobserved individual taste and preferences derives a negative binomial distribution. Negative binomial regression take into account the random component that includes unobserved variance to deal with the incorrect assumption that all differences in the dependent variable are equally accounted for by the process of making the non-linear dependent variable linear (Cameron and Trivedi, 1998; Elhai, et al., 2008; Gardner, et al., 1995; Long, 1997). The Poisson and the Negative Binomial distribution assume a higher dispersion. The alpha in the latter model only checks for overdispersion, and it could be that there is underdispersion. We also run the Generalized Linear Models with negative binomial to account for both over- as well as underdispersion (i.e. pearson statistic).

                                                                                                                                                                                                                                                                                                                                          often than others are more likely to be sampled. Thus, truncation deals with the fact that the sample only deals with households that take a positive number of trips.

 

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  Finally we consider a model that models both observed and unobserved heterogeneity. Greene (2005) proposes alternative approaches to modeling heterogeneity in count data. The alternative entails parameterization of the Negative Binomial model that introduces measured heterogeneity into the scaling parameter. The Negative Binomial variable is argued to be heteroscedastic. A logical extension of the model is to allow this parameter to be heterogenous. It is argued that what Stata calls the “Generalized Negative Binomial” should be more appropriately is called the “Heterogenous Negative Binomial” model. As in Greene’s paper, we also use this label in our analysis. A specific equation describing annual trips to Kruger is as follows:  𝑉𝑖𝑠𝑖𝑡𝑠  /𝑁! =   𝛽!   +    𝛽! (𝑇𝐶! ) +    𝛽! (𝑇𝑀! ) +    𝛽! (𝑋! ) +  𝜀

(4)

where visits is the visitation per million and  𝛽! is the partial effects of the median travel cost on visits, 𝛽! is partial effects of time costs on visits, and 𝛽!  is partial effects of the socio economic variables on visits. We are estimating the price to charge for the site. We do this with travel costs for a TRIP not the SITE. Added travel costs for the trip are attributed to changing the park entry price. But then we basically subtract the costs to get the willingness to pay (WTP) for the site. The TC Model uses annual visits per million as the dependent variable, and uses median travel costs and some demographic information as explanatory variables. The basic model would be to regress travel costs alone to estimate the visitation to the Kruger. The other factors that are likely to explain visitation rates include time costs, flight time, gender, education level, household income and number of members on the trip. The moment the appropriate explanatory variables have been identified, the regression equation yields the demand function for annual trips for the “average” visitor to the Kruger, and the area below this demand curve provides an estimate of the average consumer surplus.

 

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  We undertook analysis of what fraction of the wage rate to use (i.e. which fraction makes the best fit. We believe that this part of the analysis is very novel, and therefore differentiates our paper with the others. We assessed 0.25, 0.30, 0.35 and 0.40, and based on the log-likelihood estimates, a 0.30 of the wage rate is the best fit; hence that is what we report in our modeling.

We construct the aggregate demand function by horizontally summing up the demand functions over all the zones. The estimated demand functions are reported in below. Table 3 presents estimates of the Poisson, Negative Binomial accounting for truncation and endogenous stratification, Generalized Linear Model with Negative Binomial, and Heterogeneous Negative Binomial (i.e. Generalized Negative Binomial with Endogenous Stratification) for international tourists to Kruger National Park.

 

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  Table 3: Travel costs models to Kruger National Park on use accounting for truncation and endogenous stratification10   Poisson

Negative Binomial

Generalized Linear

Heterogeneous Negative

Regression

with Endogenous

Models – Negative

Binomial with

Stratification

Binomial family

Endogenous Stratification

Dependent

Variable:

Truncated Visitation/Million Travel Cost11

-0.390* (0.217)

-0.498** (0.255)

-0.475 (0.331)

-0.4978*** (0.184)

Time Cost (0.3)

-0.00007 (0.0009)

-0.0005

(0.002)

-0.0002 (0.002)

-0.0005 (0.001)

Cons

19.429*** (7.865)

10.387* (5.892)

22.996*** (7.806)

10.387 (318.101)

Log-likelihood

-1097.1136

-22.602

Pseudo R2

0.2447

0.286

Alfa

-35.808

-34.529

1815187 (601943.9)

Dispersion

0.000

5.054

Pearson

3.675

AIC

9.702

BIC

14.872

Observations

8

8

8

9.382

8

Note: robust standard errors in parentheses; legend: * p