Question

The Great Table Co uses labor hours and lathe machine hours to produce tables. Making a table requires at least two labor hours and at least one lathe hour. Also, the total number of hours must be six in any combination. (I.E., 5 labor hours and 1 lathe hour suffice to produce a TABLE, just as 4 and 2, 3 and 3, and so on. But 5 lathe and 1 labor hour are insufficient, as it takes a minimum of 2 labor hours.) The production process exhibits constant returns to scale. a) What do the isoquants of the Great Table Co (firm) look like? Draw in isoquants for four tables and for six tables. b) Suppose labor cost $10 per hour and lathe time costs $15 per hour. What combination of inputs would the firm use to produce six tables? c) At these input prices, derive the total and marginal cost of the firm.

Answer 1

a) Isoquant is the graph showing different combinations of inputs that are required to produce a fixed number of output. In this case, the isoquant to produce 1 table woudl have a total of 6 hours between labor and lathe, so long as labor is at least 2 and lathe is at least 1 hour. So the iso quant will be:

Labor, Lathe

2, 4

3, 3

4, 2

5, 1

We can similarly do for 4 and 6 tables. Pls see graph below (labor hours on horizontal axis and lathe hours on vertical axis)

b) Since labor hour costs less than lathe hour, the firm woudl like to employ as much of labor as possible. Hence for one table, it will go with the last combination (5 hours of labor and 1 hour of lathe) from answer a). And for six tables it will be five times as much, i.e., 30 hours of labor and 6 hours of lathe

c) the total cost woudl be:

30*10 + 6*15 = 300+90 = $390

Marginal cost will be equal to teh cost of one chair, ie, 5*10+1*15 = 50+15 = $390