ZF and Co. produces the genuine line of Adrian Austin Economist Action Figures (a wildly popular item). The firms daily production function is given by

q=KLq=KL

where q is the number of dolls produced, K is the level of capital (measured in machine hours) and L is the level of labor (measured in hours). The firm has two choices for capital. A small plant will give them enough space for 100 machine hours per day and a large plant will give them enough space for 400 machine hours per day. The cost of capital is $100/machine hour and the cost of labor is $25/hour.

The firm currently has a small plant.

1. How much labor does the firm need to produce 200 dolls per day?
2. What is the fixed cost of producing 200 dolls per day?
3. What is the variable cost of producing 200 dolls per day?
4. What is the total cost of producing 200 dolls per day?
5. In the long run if the firm wishes to continue producing 200 dolls per day, will it change the size of the plant? Why or why not?
6. For what range of output does the firm choose to have a small plant in the long run?