Cally uses labour (L) and capital (K) in her production process. The wage rate for one unit of labour is $10, while units of capital cost $20 per unit.
a. Graphically depict the isocost line for Cally's firm for a $12,000 expenditure by Cally on inputs. Draw a typical Cobb-Douglas isoquant for an output level to depict the optimal levels of L and K for quantity Qo and TCo = $12,000. Make sure all relevant points on your diagram are identified.
b. The provincial government has decided that a minimum hourly wage for labour should be of $12 per hour. In the short-run, with capital fixed at K, show graphically what happens to total cost when Cally continues to produce Qo and explain why.
c. Show the optimal factor mix the Cally will use in the long-run to produce Qo given the change in the wage rate, also explain your answer.