Retail Location and Market Competition

Why is there a small grocery shop near your home but a large shopping centre farther away? Why do competing clothing shops gather in one mall? And why might its largest tenant pay less rent per square foot than a small shop? Retail property makes sense when we follow the shopper: the journey, the purchase, and the reasons to visit several stores together.

Learning goals

Explain shopping frequency, derive store spacing, distinguish competition from clustering benefits, calculate percentage rent, and use a simple customer-choice model. Keep the assumptions and units of each model visible.

1. A hierarchy of shopping trips

Routine necessities usually support frequent local visits. A destination with a wider range of goods can justify a longer journey, especially when shoppers compare alternatives or combine purchases. Size and visit frequency are related through shopping purpose, not a rule that every large centre has infrequent customers.

Gross Leasable Area (GLA) is floor area available for tenant leasing under the applicable measurement convention. It is not site area or necessarily the entire building’s gross floor area.

Centre type in the supplied notes	Approximate GLA	Approximate store count	Typical role
Specialised/neighbourhood	50,000 sq ft	11	Local necessities and services
Community	165,000 sq ft	20	Broader local shopping
Regional mall	450,000 sq ft	69	Comparison and destination shopping
Super-regional mall	1,000,000+ sq ft	139	Extensive regional choice

These figures are lecture reference averages, with no current survey or classification date supplied. They are not universal category thresholds or current market benchmarks. A modern centre may combine groceries, services, dining, entertainment, and comparison shopping, generating different trip patterns within the same property.

Teach it back: Why might you visit a small supermarket weekly but travel farther for furniture only occasionally?

2. How often should a household shop?

Imagine buying a year’s coffee in one trip. Travel is cheap because you make few journeys, but you must finance and store a large inventory. Buying tiny quantities frequently reverses the trade-off.

The supplied inventory model minimises annual consumption cost:

CC = pu + kV + i[pu/(2V)].

Symbol	Meaning
p	Price per unit of the product
u	Units consumed per year
V	Shopping trips per year
k	Cost per shopping trip, including relevant time cost
i	Annual inventory holding-cost rate

With steady consumption and equal replenishment quantities, average inventory is half a purchase batch. Its value is pu/(2V). The three cost terms are product expenditure, travel, and inventory holding cost. The model assumes fixed annual demand, positive inputs, no shortages, and a continuous choice of trip frequency.

Differentiating with respect to V gives:

dCC/dV = k - ipu/(2V^2).

At the optimum, *V = sqrt[ipu/(2k)]**. The second derivative, ipu/V^3, is positive, so this is a minimum. The household balances the cost of another trip against the inventory cost it saves.

A shopping-frequency example

Let annual expenditure pu = 2,400, holding-cost rate i = 0.20, and trip cost k = 10. Then V = sqrt(24), approximately 4.90 trips per year*. At that frequency, annual travel and holding costs are each approximately 48.99; total annual cost is approximately 2,497.98. Real shopping trips are discrete, so nearby feasible frequencies should be compared.

Quadrupling k halves V*. Quadrupling i doubles V*. Higher spoilage or storage burdens can motivate more frequent replenishment, although perishability and capacity limits may require a richer model than a constant holding rate.

Important correction: Higher p alone increases V* in this equation, holding u, i, and k fixed. It does not explain low-frequency furniture or jewellery shopping. Those categories can have very low annual unit demand, different storage burdens, infrequent replacement, and different trip costs. Their observed frequency reflects the combination of inputs and behaviour.

Teach-back self-check: why not shop just once a year?

Fewer trips save travel, but require larger average inventory and higher holding costs. An interior optimum balances those costs. For goods bought only once every several years, steady-flow inventory assumptions may be inappropriate.

3. Store spacing and price competition

Now change models. Place identical stores along a line, with neighbouring stores D distance units apart and a uniform population density f. Each consumer makes v purchases per year. Stores have annual fixed cost c and marginal cost mc per purchase. Consumers buy one standardised basket per purchase and face a delivered price P + kT, where T is distance to the store.

Here k is travel cost per distance per purchase, not the total cost per trip in the previous section. Uppercase V and lowercase v also belong to different exercises. In the spacing model, v is treated as given rather than jointly solved with prices and distance.

Under the supplied symmetric spatial-pricing assumptions, the pricing condition is:

P = mc + kD.

The market segment served by each store has length D, giving annual purchases Dvf. Free entry drives economic profit to zero:

(P-mc)Dvf - c = 0, hence P = mc + c/(Dvf).

Combining the conditions gives:

*D = sqrt[c/(kvf)]**,

P = mc + sqrt[kc/(vf)].*

These are conditional symmetric-equilibrium formulas, not general laws for every retail market. They assume comparable retailers, the specified travel-cost structure, fixed demand per purchase, and feasible entry. Zero economic profit includes a normal return through the cost accounting; it does not mean no cash income or no accounting profit.

A store-spacing example

Let c = 10,000 per year, k = 1 per distance unit per basket, v = 10 purchases per consumer per year, f = 100 consumers per distance unit, and mc = 20 per basket.

Then D = sqrt(10), approximately 3.162*, the markup is 3.162, and price is approximately 23.162. Each store serves about 3,162 purchases per year. Markup times purchase volume equals 10,000, covering fixed cost.

Change, holding other inputs fixed	Store spacing D*	Markup P*-mc	Purchases per store D*vf
Population density f doubles	Multiplied by 1/sqrt(2)	Multiplied by 1/sqrt(2)	Multiplied by sqrt(2)
Travel-cost coefficient k doubles	Multiplied by 1/sqrt(2)	Multiplied by sqrt(2)	Multiplied by 1/sqrt(2)
Fixed store cost c quadruples	Doubles	Doubles	Doubles

Denser population supports both more closely spaced stores and more purchases per store in this equilibrium. Higher travel friction encourages closer spacing but also increases the equilibrium markup: consumers become less willing to travel to competing stores. This is a long-run entry result; existing stores cannot instantly relocate when fuel prices change.

Teach it back: How can stores get closer together while each store sells more when population density rises?

Self-check: population per market segment

Doubling f increases the number of customers per unit distance. The segment length falls only by 1/sqrt(2), so Df rises by sqrt(2). With v fixed, annual purchases per store rise by that same factor.

4. Why cluster with a competitor?

An isolated shop avoids nearby substitutes but may attract too few shoppers. A cluster can offer a more valuable shopping trip: more choice, easier comparison, and complementary purchases.

Relationship	Shopping mechanism	Example
Complementary	Visiting one shop encourages a purchase at another	Clothing and shoes
Comparative	Several shops make it easier to compare alternatives	Different furniture showrooms
Competitive	Close substitutes divide a given demand pool	Identical products at comparable prices

One pair of stores can exhibit more than one relationship. Comparison shopping can attract visitors to the cluster even while individual stores compete for their spending.

The supplied simplified visit equation is s = v n^(alpha-beta), where s is visits per store, n is store count, v is a baseline visit level, alpha measures attraction, and beta captures demand division through competition. Here v is a baseline scale, not automatically the consumer frequency in the spacing model.

With alpha = 0.8 and beta = 0.3, visits per store increase with sqrt(n). Increasing n from 4 to 9 raises visits per store from 2v to 3v. With alpha = 0.5 and beta = 1, visits per store instead fall as the cluster grows.

Alpha greater than beta implies increasing visits per store, not automatically increasing profit. Conversion rates, spending, margins, rent, and operating costs must also be considered. Even falling visits per store can coexist with rising total cluster visits, since total visits are ns. The stylised beta values of zero for pure complements and one for pure competitors are model conventions rather than universal measured constants.

5. Anchors create traffic that other tenants can monetise

A supermarket or major department store can attract shoppers who then visit smaller stores. A landlord may rationally charge that anchor less per square foot because the anchor raises the rent other shops can support.

Write annual base-rent income as sum of A_j R_j, where A_j is each tenant’s leased area and R_j is annual rent per area. This notation avoids confusing tenant area with the sales S used later. A larger anchor can affect other tenants’ R_j through shopper traffic, but it also uses space that could have been leased differently.

Suppose an anchor rent concession costs the landlord 100,000 annually, but the resulting traffic supports 140,000 more annual rent from other tenants. Before other costs and risks, centre-wide income improves by 40,000. Maximising the rent of each shop separately would miss that interaction.

The supplied figures of roughly 2 or 20 per square foot for anchors and 30-40+ for inline stores are historical lecture examples with unspecified lease coverage and dates. They are not current quoted rents. Actual comparisons must account for incentives, ownership arrangements, service charges, fit-out obligations, and other terms.

Teach it back: Why might a landlord prefer a low-rent anchor to a higher-rent tenant occupying the same space?

6. Percentage rent: a base plus a sales-linked payment

One percentage-rent structure is:

Annual rent per area = R + max[0, r(S-B)].

R is annual base rent per square foot, S is annual gross sales per square foot, B is the sales breakpoint on the same basis, and r is the percentage rate written as a decimal. Multiply by leased area to obtain total annual payment. Actual lease structures vary; percentage rent is not present in every retail lease.

A lease example

Let R = 30, r = 0.05, and B = 600. At sales S = 500, rent remains 30 per square foot per year. At S = 800, additional rent is 0.05 x 200 = 10, so total rent is 40. For a 2,000-square-foot shop, annual rent is therefore 80,000 at S = 800.

With the natural breakpoint B = R/r, this expression is equivalent to max(R, rS). A negotiated breakpoint can differ. Check the contract rather than assuming that “base plus a percentage” always means a percentage of every sales unit from zero.

Percentage rent shares some sales upside and exposes the landlord to some sales variation. The base creates a floor, so risk sharing is asymmetric: below B, another fall in sales does not reduce the rent in this formula.

Sales-linked rent can also give a landlord a more immediate incentive to maintain a centre and manage the tenant mix well. A fixed-rent landlord still has incentives through renewals, vacancy, reputation, asset value, and contractual duties; the accurate distinction is the strength and timing of the sales link, not the complete absence of incentives under fixed rent. Sales reporting and audit provisions matter because the payment depends on measured sales.

Teach-back self-check: when do sales affect the payment?

Above B, another unit of sales increases percentage rent by r. Below B, payment remains at the base R under this formula. Percentage rent does not fully insure the tenant against weak trading.

7. Predicting centre choice with a logit model

Suppose a household chooses between shopping centres. Each centre offers attractions but requires travel. Represent its systematic utility as:

U_ijk = alpha_j T_ik + sum over l of mu_lj Z_lk.

i identifies the residential origin, j the shopper group, and k the centre. T_ik is travel time. Z_lk are centre attributes such as GLA, parking, or store mix. Alpha_j is a negative travel-time coefficient; mu_lj measures the contribution of an attribute for group j.

U here is the systematic part of utility. Under the usual independent, identically distributed extreme-value random-utility errors, multinomial logit gives:

P_ijk = exp(U_ijk) / sum over m of exp(U_ijm).

Utilities are relative scores, not monetary amounts or probabilities. For numerically stable calculation, subtract the largest U from every U before exponentiating; probabilities are unchanged.

A two-centre example

A local centre has an attribute score of 1 and requires 10 minutes of travel. A regional centre has an attribute score of 2 and requires 30 minutes. With alpha = -0.05 per minute, their utilities are 0.5 and 0.5, giving equal choice probabilities of 50%.

If the travel penalty becomes alpha = -0.10, utilities become 0 and -1. The local centre’s probability becomes 1/[1+exp(-1)], approximately 73.11%. The regional centre’s probability falls to 26.89%. Stronger travel friction changes which centre shoppers choose, even though centre attributes have not changed.

For 1,000 fixed annual shopping trips from this origin and group, the model allocates approximately 731 to the local centre and 269 to the regional centre. With several origins and groups, weight probabilities by each segment’s trip count and sum. Revenue also requires spending per visit; visit share is not automatically sales share.

8. Interpret demand simulations carefully

An income group’s travel coefficient must be estimated or justified. Lower-income shoppers may be more sensitive to fares or fuel costs, while higher-income shoppers may attach a greater monetary value to time. It is not generally valid to assume lower-income households always have a larger travel-time disutility.

A fuel-price shock is not mechanically the same as changing a travel-time coefficient. Include monetary travel cost, transport mode, or a justified mapping into generalised cost. If the shock increases the relative cost of a distant centre more, demand can shift toward nearer centres, as the example illustrates. The size of the change is conditional on the calibrated model.

Standard multinomial logit also has independence of irrelevant alternatives (IIA): odds between two options do not depend on a third option’s utility. A nearly identical new mall may therefore draw demand in unrealistic proportions. Nested or mixed logit can represent richer substitution patterns when justified by the data.

Finally, include an outside option if the question allows shoppers to buy online, visit another region, or not make the trip. Without one, the model reallocates every fixed trip among the listed centres and cannot establish a change in total shopping trips. Store entry, purchase frequency, and centre choice are connected economically, but these separate classroom models do not solve them jointly.

Feynman study lab

Explain it simply

Shopping uses time as well as money. Frequent necessities favour convenient locations, while greater choice can justify a longer journey. Stores may benefit from clustering even when they compete. An anchor can create traffic for everyone else, and a percentage lease can give the landlord a stake in sales. A choice model compares each centre’s attractions with its travel burden.

Teach it back without looking

Explain the inventory-versus-travel trade-off and the two-centre choice example aloud in two minutes. Define fixed cost, markup, anchor, and breakpoint without relying on symbols. Then answer:

Why can higher travel costs support more closely spaced stores in a long-run entry model while shifting current shoppers toward a nearby existing centre?

Check your explanation after you try

These are different adjustment margins. Current shoppers can change destination among existing centres. Over time, entry and location choices can change the spacing of stores. The first does not require immediate construction or relocation; the second does. Both favour convenience under the stated assumptions.

Transfer questions

1. In the inventory model, what happens to V* if trip cost quadruples?
2. Does a higher product price alone lower V* in that equation?
3. In the spacing model, if population density quadruples, what happens to spacing and purchases per store with v fixed?
4. Base rent is 25, the percentage rate is 5%, breakpoint is 500, and annual sales are 700 per square foot. What is annual rent per square foot?
5. Two centres have utilities 0 and ln(3). What are their probabilities?
6. If alpha exceeds beta in the clustering model, has profitability been proved?

Check the transfer questions

1. V* halves.
2. No. It raises V* when other inputs stay fixed.
3. Spacing halves; purchases per store double because the market segment becomes half as long but has four times the population density.
4. 35: base 25 plus 0.05 x (700-500) = 10.
5. 25% and 75%, since exponentiated utilities are 1 and 3.
6. No. Visits per store rise in that specification, but profit still depends on spending, conversion, margins, rent, and other costs.

Find the gap and try again

Identify where your explanation became vague: average inventory, trip cost versus travel cost per distance, visits versus profit, base rent versus percentage rent, or utility versus probability. Rework that example and explain it again without formulas. Change one input and predict the direction before calculating. Tomorrow, reconstruct the shopping-frequency trade-off and explain one limitation of the logit forecast.