IPAle is a new firm that produces craft beer. Let q be the number of bottles produced. Each worker is able to manufacture bottles according to the following production function: q= = 4e where the variable e represents the effort of the worker. For the worker, her personal cost of exerting effort is simply: Effort Cost = The worker receives from IPAle a salary w for each bottle produced (not a salary per unit of effort). The worker's utility equals her income minus her effort cost, and she chooses the effort that maximizes her utility. a) Find the worker's optimal effort choice for any given wage Assume the market price per bottle is $4. b) Find the worker's effort choice for a wage w = $2 per bottle and the firm's profits c) Find the worker's utility and the total surplus. That is the sum of the worker's utility and the firm's profits. Assume now that the worker owns the firm, she is self-employed. Now, instead of getting a wage, she directly obtains the profits from producing bottles. Keep the market price at $4 per bottle. d) Calculate the effort and the number of bottles produced. Is it bigger than before? Explain why e) Calculate the worker's utility. This is equal to the total surplus for the self-employed case