A Firm Produces Output According to the Following Function

Essay

A firm produces output according to the following function:
q = f (L,K)= L¹/² K¹/³
The cost of labor is $9 per hour and the rental cost of capital is $4 per hour.
a.With the given prices,use the Lagrangian method to compute the optimal (cost-minimizing)capital to labor ratio (K/L)for the firm.
b.Suppose the firm wishes to produce 72 units of output.How much capital and how much labor does the firm employ?
c.What is the total cost of producing 72 units of output?
d.Suppose that the firm suddenly decides to double the quantity of output but only has a day to complete the order.Therefore,in that time,the amount of capital is fixed but labor hours are not.How much will it cost to produce 144 units of output? How much would it cost if the firm could also vary capital? Compute as well as providing a graph (isocost/isoquant)illustrating the optimal bundles.