Tom owns a winery which produces red wines. He is a profit maximizing, pricetake

Question

Tom owns a winery which produces red wines. He is a profit maximizing, pricetaker. The market price for a bottle of red wine is $40. His costs are given by C = 0.1Q^2 + 20Q + 100 where Q represents the number of bottles.

a. How many bottles will he produce and what are his profits?

b. Assume the state now requires a $100 per year license for all wine producers. Assume the market price (here, the price of a bottle of red wine) remains at $40. How many bottles does Tom produce? What are his profits?

c. Suppose instead the state requires all wine producers to pay a $10 fee for each bottle. Again, assume the market price (here, the price of a bottle of red wine) remains at $40. How many bottles does Tom produce? What are his profits?

d. Is this firm in the long run or in the short run?

Explanation / Answer

Price for a bottle of red wine is $40.

TR = 40 Q and MR = 40

C = 0.1Q^2 + 20Q + 100

MC = 0.2Q + 20

At Equilibrium, MR = MC =>  0.2Q + 20 = 40

Q = 40-20 / .2 =>100

TR = 40 x 100 = 4000

C = 0.1(100)^2 + 20(100) + 100

1000+ 2000+100=> 3100

Profit = TR - TC => 4000 - 3100 => 900

b) Cost will increase by 100 but Marginal Cost will remain same and hence output but profit will decrease by $100

Q= 100 and Profit = 800

c)  $10 fee for each bottle will increase cost by $10Q

C = 0.1Q^2 + 20Q + 100 + 10 Q =>  0.1Q^2 + 30Q + 100

MC =  0.2Q + 30

At equilibrium,  0.2Q + 30 = 40

Q = 10/0.2 => 50

C = 0.1(50)^2 + 30(50) + 100 =>250 + 1500 + 100 => 1850

TR = 40 x 50 => 2500

Profit = 2500 - 1850 => 650

d. Short run because in Long run a price taker or perfectly competitve firm makes zero or normal profits.

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