Derivation of iso-cost line.
A industry uses two inputs, unskilled labor (L) also capital (K) to produce its product. The wage rate for one unit of labor is $5, while units of capital cost $20. The industry's production function per day is Q (L, K) =4LK, while the MPL=4K also the MPK=4L. The industry wants to keep a constant production of Q0=400 units of output per day.
1. 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*, explain how much would it cost the industry 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) also clearly label the intercepts.
2. Find analytically the optimal level of inputs L** also K** which the industry will use in the long run to produce Q0, given the minimum wage. Illustrate what is the cost associated to this choice? Represent the new isocost also L** also K** in the same graph as above.
3. Explain how do you compare the original cost in a) with the costs in c) also d)? Give the economic intuition behind these results.