3. Greta starts an internet-based grocery delivery service. His employees must p

Question

3. Greta starts an internet-based grocery delivery service. His employees must perform one of three activities:

• Administrative work: Exactly 2 workers are necessary to perform the administrative work for the business to operate. The administrative workers do not generate revenue.
• Delivery: Each employee working as a driver can deliver up to 20 orders daily.
• Assembling orders: Each employee can prepare and pack up to 100 orders daily.

Suppose that each worker can work in exactly one capacity (so she cannot split her time between delivery or packing).

Greta’s short-run production function says how many orders can be completed by L employees. Describe Greta’s short-run production function. (Hint: how many orders can she complete when she has 3 employees? How many orders can she complete when she has 10 employees?) What are her returns to scale when she changes employment from 5 to 10 workers?

Explanation / Answer

Greta's short run production function is P = 10D + 50A, where D is the number of delivery employees and A is the number of assembling employees. Administrative employees do not factor into short-run production because they represent a fixed cost (does not vary with quantity produced). To produce 100 orders, Greta will need 1 assembler and 5 deliverers (6 workers). P=10*5+50*1 = 100 If Gretta has 10 deliverers and 2 assemblers (12 workers), she can produce 200 orders. P = 10*10+50*2 = 200 Greta experiences constant returns to scale because doubling the number of employees exactly doubles her production. If we want to express this in terms of L (total workers), we can write: P=(50/3)L This expression assumes that Greta allocates her workers efficiently (puts them in the right roles).

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