Exercise 2. Two plants
A firm has two plants, both with increasing marginal costs.Plant 1 is more efficient than plant 2. Specifically, the costfunction in plant 1 isc1(y1)=2y12, while thecost function in plant 2 isc2(y2)=3y22. Outputproduced in plant 1, y1, is identical to output producedin plant 2, y2. For any overall output levelY=y1+y2the firm wants to minimize costs.
- What is the marginal cost in plant 1? Find∂c1/∂y1.
- What is the marginal cost in plant 2? Find∂c2/∂y2.
- The firm needs to produce a total of Y=10 units. If it decidesto produce all of them in plant 1 (y1=100 andy2=0), what is the total cost?
- What is the optimal production level,y1*and y2*, that wouldminimize cost? What is the total cost now?
