Question

The graph below shows a firm's isoquants and isocosts. The firm is initially producing Q-20 with the cost minimizing combination of K and L, where Q is output, Kis capital and Lis labor. Suppose the owner decides to expand production to Q=40. However, he signed a lease on the capital necessary to produce Q=20, which he cannot get out of in the short run. Are the short run total costs of producing Q-40 smaller or larger than the long run total costs of producing Q=40? Briefly explain. 20 19 C=$120 18 17 16 15 C=$60 14 13 12 x 10 9 8 7 6 5 Q 40 4 3 Q-20 2

Answer 1

18 T? 16 IS C c + 6 c 22 9 11 C K 8 7 A 6. 5 4 240 3 2. 9=20 - 2. 3 4 9 10 12 13 14 15 16 17 18 - ㅋ 8 L

The cost minimizing combination of K and L to produce a given level of output Q occurs at point where the slope of isoquant is equal to slope of isocost line i.e isoquant is tangent to isocost line.

For Q= 20 cost is minimized at point A and for Q=40 cost is minimized at point E.

Initially firm is producing Q=20 at point A. The cost minimizing combination to produce Q=20 is 6 units of K and 3 units of L.

Now the firm wants to increase it's production to Q=40. To increase output in short run firm cannot increase K , it can only increase L. So in short run Q=40 will be produced at point B( 6K and 10L). Since point B lies above the isocost line C=$120, it means the cost to produce Q=40 in short run is greater than $120.

In long run firm can vary both K and L to increase it's production.To produce Q=40 in long run the cost is minimized at point E. So to produce Q=40 it will cost $120 in long run. Hence the short run cost of producing Q=40 is greater than long run cost of producing Q=40.