A firm uses two inputs, unskilled labor (L) and capital (K) to produce its product. The wage rate for one unit of labor is $5, while units of capital cost $20. The firm's production function per day is Q (L, K) =4LK, while the MPL=4K and the MPK=4L. The firm wants to keep a constant production of Q0=400 units of output per day.
- Suppose the federal government institutes a minimum wage for unskilled labor of $10 per unit. In the short run, with capital fixed at the level K*, how much would it cost the firm to hold the output constant at Q0? Draw the new isocost line associated to this new cost in the same graph as in part b) and clearly label the intercepts. [Hint: if capital is fixed at level K* and the firm still wants to produce Q0, the amount of labor L* will not change, only the isocost will change]
- Find analytically the optimal level of inputs L** and K** that the firm will use in the long run to produce Q0, given the minimum wage. What is the cost associated to this choice? Represent the new isocost and L** and K** in the same graph as above. [Hint: remember, in the long run the firm can change both capital and labor, but still wants to produce Q0]
How do you compare the original cost in a) with the costs in c) and d)? Give the economic intuition behind these results.