Consider tomato framing in the US, a highly competitive market. Assume the marke

Question

Consider tomato framing in the US, a highly competitive market. Assume the market is perfectly competitive, and that the market demand for tomatoes is given by Q- 120 - 10P and market supply is given by Q 842P a) Find the competitive equilibrium price and quantity of tomatoes in this market. b) Assume that one particular farmer, knows that his cost function is given by ca)1q 0.lq Find the farmer's profit-maximizing level of output, and calculate the profits he makes What if the price doubles? Now how much would the farmer want to produce to maximize profits?What are his profits now? c)

Explanation / Answer

Equilibrium price is reached where Qs=Qd

120-10P = 84+2P

12P = 36

P = 3

Equilibrium of firm at P=MC

MC = dTC/dQ = 1+0.2q

AC = C/q = 1/q+1+0.1q

1+0.2q = 3

0.2q = 2

q = 10

AC at q = 10 = C/q = 1/10+1+0.1*10 = 2.1

Profits = (P-AC)*Q

= (3-2.1)*10 = 9

If price doubles to 6

1+0.2q = 6

0.2q = 5

q = 5/0.2 = 25

AC at q = 25 = C/q = 1/25+1+0.1*25 = 3.54

Profits = (P-AC)*Q

Profits = (6-3.54)*25 = 61.5

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