Question

the only variable input a janitorial service uses to clean offices are workers who are paid a wage of $20 an hour, known as w. each worker is capable of cleaning 10 offices in one hour.

A) determine the average variable cost and marginal cost of cleaning one extra office

b) draw the diagram of the total cost, average variable cost, and marginal cost curves showing their relationships

c) how will these curves change with a lump sum franchise tax of $40?

Answer 1

A) The only variable input in this instance is the labor or worker with a wage or w of $20 per hour. Each individual worker is capable of cleaning 10 offices per hour. Therefore, the time taken by each worker to clean one office=1/10=0.1 hour. Hence, the marginal cost of cleaning one extra office=($20*0.1 hour)=$2. The hourly total variable cost of cleaning 10 offices=($20*10)=$200. Thus, the average variable cost of cleaning one more office=$200/10=$20.

B) Figure-1 in the document attached below illustrates the Average Variable Cost(AVC), Total Cost(TC), and Marginal Cost(MC) of cleaning offices. The y and the x axes in figure-1 represent the costs and number of offices respectively. Note that in figure-1, the TC curve starts from the origin with the assumption that there is initially no fixed cost of cleaning the offices and TC is, therefore, equal to the total variable cost or TVC. Now, note in figure-1 that when AVC is less than the MC the AVC tends to decrease until they are both equal at which point, the AVC is fixed. Now, when the MC is greater than AVC, with reference to figure-1, the AVC tends to increase subsequently. In this particular case, since the fixed cost of cleaning offices is 0, the changes in TVC directly affects or determines the changes in TC as well.

C) Now, if there is a lump sum fixed franchise tax of $40, then the fixed cost of office cleaning would be $40 and the TC of office cleaning would increase by $40 implying that the TC in figure-1 would now begin from $40 in the y-axes representing costs following the franchise tax imposition. From there onwards, the TC increases as TVC also increases as increasingly more offices are cleaned. However, TVC and AVC would not be affected as the lump sum fixed franchise tax is enforced which only increases the fixed cost of office cleaning.