Coffee Cart at the Railway Station: Pricing Under Capacity Limits
A sole trader runs a coffee cart on a railway station concourse under a licence costing $1,800 a month. Each coffee sells for $4.50. Beans, milk, and a cup cost $1.20 per coffee; the cart's only other variable cost is a part-time barista paid $26 an hour who can make 40 coffees an hour at full stretch. The cart operates 6am–10am, 22 days a month. On a typical morning it sells 90 coffees in the first two hours and 40 in the last two. At 8am the queue often reaches 12 people and some leave. The station authority offers the trader a second cart site 40 metres away for an extra $900 a month, or alternatively a larger single site for $2,700 a month total that would allow a second barista and a faster machine, lifting capacity to 70 coffees an hour.
1. Calculate the cart's current monthly contribution and identify whether the 8am queue represents a capacity constraint or a demand constraint.
Read the worked answer
Contribution per coffee = $4.50 − $1.20 = $3.30.
Monthly output = (90 + 40) × 22 = 130 × 22 = 2,860 coffees.
Total contribution = 2,860 × $3.30 = $9,438.
Fixed costs = licence $1,800 + barista. Barista hours: the cart is open 4 hours × 22 days = 88 hours. At $26/hour that is $2,288. Total fixed = $4,088.
Profit ≈ $9,438 − $4,088 = $5,350 per month.
Capacity or demand? The barista can make 40/hour, so in 4 hours the maximum is 160 coffees-but sales are 130. However, the timing matters: 90 coffees in two hours is 45/hour, above the 40/hour capacity, so the queue at 8am is a genuine capacity constraint during the peak. The last two hours (20/hour) are a demand constraint-capacity sits idle. The binding constraint is peak-hour throughput, not total daily capacity.
This distinction matters: adding capacity helps only if it relieves the peak, while stimulating demand helps only in the quiet period.
2. Compare the two expansion options using the figures, and recommend one with reasoning.
Read the worked answer
Option A-second site ($900 extra fixed): requires another barista (88 hours × $26 = $2,288) and duplicates stock costs proportionally. If the new site captures the 12-person queue and adds, say, 40 coffees a day, extra contribution = 40 × 22 × $3.30 = $2,904, against extra fixed costs of $900 + $2,288 = $3,188. That is a loss of about $284 a month unless volume exceeds roughly 44 extra coffees a day (break-even = $3,188 ÷ ($3.30 × 22) ≈ 44). Given the queue is only 12 deep at peak, 44 extra is unlikely.
Option B-larger site ($2,700 total, i.e. $900 extra fixed, plus a second barista): capacity rises to 70/hour. To justify the second barista ($2,288) plus $900 extra licence, the cart needs about 44 extra coffees a day, but a 70/hour capacity in a 2-hour peak allows up to 140 coffees-well above current 90. If even half the queue is converted and demand grows, the marginal contribution per extra coffee ($3.30) is high because fixed costs are already covered.
Recommendation: Option B is superior because it attacks the binding constraint (peak throughput) at the existing demand location, whereas Option A adds fixed cost at a new location where demand is unproven. But the recommendation is conditional: if the station's foot traffic is growing, Option A's second site may build a new customer base. The decision hinges on whether the constraint is capacity (favour B) or unmet latent demand elsewhere (favour A). A pure recall answer cannot resolve this-the trader must estimate the elasticity of the queue.