Consider an economy that produces two goods, cars and shirts. Explain why if a tax is imposed on the consumption of cars but not on shirts, the economy will not exhibit product mix efficiency 

Explain what is meant by product mix efficiency and discuss the conditions under which the market will give us product mix efficiency. In your explanation of product mix efficiency, you should discuss what slopes are relevant for product mix efficiency and how they are relevant. While I expect to see the equation for product mix efficiency as part of your answer, you are also expected to explain the intuition behind the equation to demonstrate you understand the economics. (Note: this is often referred to as Pareto efficiency in a production economy).

You've been hired as an economic consultant to a price-taking firm that produces shirts. The firm already has a shirt factory, so it is operating in the short-run. The price of shirts is $5, the hourly wage is $12, and each shirt requires $1 worth of material. At the current level of output (20 workers and 70 shirts per hour), the firm is losing money: Its total cost exceeds its total revenue. The firm has experimented with different numbers of workers and discovered that 21 workers would produce 72 shirts; 15 workers would produce 60 shirts, and 16 workers would produce 63 shirts. Your job as a consultant is to tell the firm which of these four options to take, and explain and show your calculations as to why you selected an option.
1. Option 1: Shut down the unprofitable operation. Explain why giving numerical calculations.
2. Option 2: Continue to produce 70 shirts per hour. Explain why giving numerical calculations.
3. Option 3: Produce more shirts. Explain why giving numerical calculations.
4. Option 4: Produce fewer shirts. Explain why giving numerical calculations.