6. Suppose a price-taking producer of barrels for storing wine has the following total costs schedule:

Quantity Total Costs 0 20 1 30 2 42 3 55 4 75 5 100 6 130

a. Calculate marginal cost. If the price of a barrel in the market is $20, how many barrels will the firm produce?

b. Suppose the price in the market falls to $12 per barrel. How many barrels will this firm produce in order to maximize profits?

c. Suppose there is an improvement in technology that shifts total costs down by $8 at every level of production. How much will the firm produce and what will profits be at a price of $20 and at a price of $12?