Question

Homework (Ch 13) 5. 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'shortcun average total cost (SRATC) each month for various levels of production if it was one, two or the factories. (Note: Q the total quantity of bikes produced by all factories.) uals Average Total Cost (Dollars per bike) Number of factories Q-100 Q = 200 200 Suppose Ike's Bikes is currently producing 500 bike per month in its only factory to sho w erge Suppose Ike Bikes is expecting to produce 500 bikes per month for several years. In this case, in the long run, it would choose to produce bikes using prakse SRATC On the following graph, plot the three SRATC cures for le's Bikes from the previous table. Specifically, we the green pobus (triangle symbol) to plotis SRATC erwe i factory (SRATCYw the purple points (diamond symbol) to ploris SRATC curve if it operate face (SRATC, and the Grande Po p if it operates the factories (SRATC). Finally, plor the long-run awerage total cos (LRATC) cure for Ike's Bites in the blue polas (circle symbol). atically Note: Plot your points in the order in which you would like them connected. Line segments will connect the points t

Answer 1

Currently the firm is operating in 1 factory producing 500 bikes. For Q = 500 and N=1, SRATC is $400. In case it produces 500 bikes in long run its cost is minimum when N= 3. Hence it should work with 3 factories. In the short run there are three possibilities. In case the firm uses only 1 factory, its short run ATC is given by SRATC1. When it uses 2 and 3 factories respectively, its short run ATCs are SRATC2 and SRATC3. To get Long run ATC, we need to add the minimum of all these three costs at a gives level of output. For example, when Q=200, SRATC1 is 200, SRATC2 is 300 and SRATC3 is 400. Out of these the minimum is 200 SO SRATC1 is tangent to LRATC at Q = 200. Below is the table and the graph plot for SRATCs and LRATC. Data plots are provided in the graph a table is more helpful. Also note that LRATC will cover all the minimum of SRATCs so it might not be visible but it lies below the SRATC.

Short run and long run costs 800 720 640 100 200 300 400 500 600 SRATCI SRATC2 SRATC3 (Factory (Factory (Factory LRATC = 1) = 2) = 3) 360 540 720 360 200 300 400 200 160 240 160 160 160 160 400 300 200 720 540 360 160 240 Costs 400 400 OS 360 400 360 360 300 300 240 200 160 160 200 Fewer than 300 bikes More than 400 bikes Between 300 and 400 bikes Economies of scale Diseconomies of scale Constant returns to scale 100 200 500 600 700 300 400 Quantity SRATC1 (Factory = 1) ---SRATC3 (Factory = 3) -SRATC2 (Factory = 2) --LRATC