Final answer:
The cost minimizing choice of K and L to produce 10 units of output is K=0 and L=9, with a total cost of 18.
Step-by-step explanation:
In this case, the production technology function is Y=min{K,L}, where Y represents the output, K represents the capital, and L represents the labor. Since we want to produce 10 units of output, we need to find the combination of K and L that minimizes the cost. To plot the isoquant at Y=10, we can use the table of workers and widgets provided.
Widgets (Q) 0.2 0.4 0.8 1 Workers (L) 1 2 3 3.25 4.4 5.2 6 7 8 9
From the table, we can see that to produce 0.2 units of output, 1 worker is needed. To produce 0.4 units, 2 workers are needed. To produce 0.8 units, 3 workers are needed. And to produce 1 unit, 3.25 workers are needed. This pattern continues for higher levels of output.
To minimize the cost, we need to choose the combination of K and L where the total cost is lowest. In this case, we need to find the combination of K and L that produces 10 units of output while minimizing cost. From the table, we can see that to produce 10 units, we would need 9 workers. However, we also need to consider the cost of capital, which is represented by R=3 (the price of capital). To calculate the cost, we multiply the quantity of capital (K) by the price of capital (R), and add it to the cost of labor, which is represented by W=2 (the level of wages).
So, the cost minimizing choice of K and L to produce 10 units of output is K=0 and L=9. The level of the cost would be 9*2 + 0*3 = 18.