A firm utilizes two inputs, unskilled labor (L) and capital (K) to produce its product. The wage rate for one unit of labor is around $5, whereas the units of capital cost around $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 every day.
Q1. Assume that the federal government institutes a minimum wage for the unskilled labor of $10 per unit. In 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 latest isocost line related to this new cost in the similar graph as in part (b) and clearly label the intercepts.
Q2. Find out analytically the optimal level of inputs L** and K** which the firm will employ in the long run to produce Q0, given the minimum wage. Illustrate the cost related to this preference? Symbolize the new isocost and L** and K** in the similar graph as above.
Q3. How do you compare the original cost in (a) with the costs in (c) and (d)? Give the economic intuition behind such outcomes.