Question

Costs in the short run versus in the long run

Ike’s Bikes is a major manufacturer of bicycles. Currently, the company produces bikes using only one factory. However, it is considering expanding production to two or even three factories. The following table shows the company’s short-run average total cost (SRATC) each month for various levels of production if it uses one, two, or three factories. (Note: Q equals the total quantity of bikes produced by all factories.)

Number of Factories	Average Total Cost
	(Dollars per bike)
	Q = 100	Q = 200	Q = 300	Q = 400	Q = 500	Q = 600
1	360	200	160	240	400	720
2	540	300	160	160	300	540
3	720	400	240	160	200	360

Suppose Ike’s Bikes is currently producing 100 bikes per month in its only factory. Its short-run average total cost isper bike.

Suppose Ike’s Bikes is expecting to produce 100 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using .

On the following graph, plot the three SRATC curves for Ike’s Bikes from the previous table. Specifically, use the green points (triangle symbol) to plot its SRATC curve if it operates one factory (SRATC1SRATC1); use the purple points (diamond symbol) to plot its SRATC curve if it operates two factories (SRATC2SRATC2); and use the orange points (square symbol) to plot its SRATC curve if it operates three factories (SRATC3SRATC3). Finally, plot the long-run average total cost (LRATC) curve for Ike’s Bikes using the blue points (circle symbol).

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

SRATC1SRATC2SRATC3LRATC0100200300400500600700800720640560480400320240160800AVERAGE TOTAL COST (Dollars per bike)QUANTITY OF OUTPUT (Bikes)

In the following table, indicate whether the long-run average cost curve exhibits economies of scale, constant returns to scale, or diseconomies of scale for each range of bike production.

Range	Economies of Scale	Constant Returns to Scale	Diseconomies of Scale
Fewer than 300 bikes per month
Between 300 and 400 bikes per month
More than 400 bikes per month

Answer 1

Short Run Total Cost is the cost when we assume that capital input is held fixed at a level of K1 and that in short run the firm is free to vary only its labor input because we assume that alterations in the level of capital input are infirnitely costly in the short run.

SC = VK1+WL

where S is short run cost with the level of capital input (K1) fixed.

and thus Short run average cost (SRATC) = SC/Q

Below figure show the connections between short run and long run average and marginal cost curves.Short run and long run average costs are equal at that output for which the fixed capital input is appropriate. At point Q ,SRATC = LRATC because K1 is used in producing Q1 at minimal cost.For movement away from Q1, short run average costs exceed long run average cost,thus reflecting the cost minimizing nature of the long run total cost curve.Also the MC passes through the low point of the AC curve.At Q1,long run average and marginal costs are equal. Associated with Q1,is a certain level of capital input (say k1), the short run average cost curve for this level of capital input is tangent to the AC curve at its minimum point.

Range

Fewer than than 300 bikes per month - Diseconomies of scale

Between 300 and 400 bikes per month - Constant Returns of scale

More than 400 bikes per month - Economies of scale