Grocery store case study

You will work in groups on this case study and turn it in as part of problem set 1. This is worth 5 points on problem set 1 and must be turned in along with problem set 1

Suppose I own a grocery store business. In each store, I need to decide the number of workers to employ. For simplicity, assume that the only costs are those I mention below.

Wages are $12 per hour.

Rental cost per hour of operation of the store is $10. I present this rental cost as a per-hour cost, but you must pay the entire monthly rent or none of it.

Below I show a chart that shows how hourly revenue changes depending on the number of workers I hire. I have included some empty columns in case you want to do calculations there, but you do not have to use that space.

Number of workers per hour	Total revenue per hour
0	0
1	30
2	43
3	53

What best describes the relationship between the number of workers and revenue

Increasing returns to scale

Constant marginal returns

Diminishing marginal returns

How many workers should I hire at my store? Explain.

Suppose you are considering opening additional stores.

In a realistic setting, the second store could have a higher or lower profit compared to the first store because there are conflicting forces.

With 2 stores, some of the fixed costs are spread out and I may enjoy economies of scale. This would make the second store add more profit than the first store did.

The second store is likely in a worse location than the first store. This is because I chose the best location for the first store so only the second best location is left over for the second store. The second store location could be worse because there are fewer customers, or it could be worse because there is higher rent.

To make the calculations easy, I assume that there are no economies of scale and that the second store location is worse than the first store location only because there is higher rent. This assumes that each store has identical demand from customers so the second and third stores follow the same worker - revenue chart shown above.

Per hour rental costs:

Per hour rental cost of first store: $10

Per hour rental cost of second store: $22

Per hour rental cost of third store: $25

Other than the rental cost of the store, each store is identical.

How many stores should I open? How many workers will I hire total? Explain.

Automatic checkout machines

Suppose automatic checkout machines are developed and I can rent one for $20 per hour. To simplify, I assume that you either rent 1 machine or you rent zero machines. In a more realistic setting, you would have to decided how many machines to rent in the same way as you decided how many workers to hire.

Without the machine, revenue is as before. With the machine, we have more revenue for a given level of labor. The chart below copies the information from the chart above and then also shows total revenue with the machine.

Number of machines	Number of workers	Total revenue per hour
0	0	0
0	1	30
0	2	43
0	3	53
1	0	35
1	1	48
1	2	58
1	3	66

To review, the costs are:

Workers are paid $12 per hour

Machines cost $20 per hour

First store rent costs $10 per hour

Second store rent costs $22 per hour

Third store rent costs $25 per hour.

All of the information in the above chart is identical at all 3 stores.

How many stores will I open? How many workers and machines will I have at each store? How many workers will I hire total? Explain your reasoning.

Suppose the cost of machines comes down to $15 per hour. This is a reduction in the cost of capital. With the lower cost of capital, how many stores will I open? How many workers and machines will I have at each store? How many workers will I hire total? Explain your reasoning.

Suppose the cost of machines comes down to $10 per hour. This is a reduction in the cost of capital. With the lower cost of capital, how many workers will I hire total. How many stores will I open? How many workers and machines will I have at each store?

When the cost of capital falls from $20 to $15 does the scale or substitution effect dominate?

When the cost of capital falls from $20 to $10 does the scale or substitution effect dominate? How many jobs are gained due to scale? How many are lost due to substitution?

Explain the scale effect in the context of this example.