A firm that uses two inputs to produce output has the production function 3x1/3y1/3, where x is the amount of input 1 and y is the amount of input 2. The price of output is 1 and the prices of the inputs are wx and wy. The firm is constrained by the government to use exactly 1000 units of input 1.
a. How much of input 2 does it use?
b. What is the most that it is willing to bribe an inspector to allow it to use another unit of input 1?