Question

In: Economics

In the competitive market for soy beans, there are 520 identical farms, each farm having the...

In the competitive market for soy beans, there are 520 identical farms, each farm having the cost function. c(q) = .5q2 + 3q + 32 where q is the quantity of output in tons produced by each farm. mc(q) = q + 3. The market demand equation is Qd(p) = 4640 – 100p. • Find a firm’s individual supply equation. • What is the equation for the market supply? What is the equilibrium price and quantity in this market? • What is the q for each firm? • What are profits/losses for each firm? • Should each farm in the short-run stay in business? Explain your answer.

Solutions

Expert Solution

A firms individual supply function is the marginal cost function.

The a single firms supply function is,

P = q + 3

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There are 520 firms in the market.

So, Q = 520q, where Q = Market quantity and q = Each Firm's quantity

At equilibrium,

Price = Marginal Cost

P = MC

Thus we have,

P = q + 3

q = P - 3 -----------> Firm's individual Supply function

Now, we know that,

Q = 520*q

Q = 520*(P - 3)

Q = 520P - 1560 ----------> This the equation for market supply.

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At market equilibrium,

Demand = Supply

4640 - 100P = 520P - 1560

620P = 6200

P = 10 ------------------> Equilibrium Price

Setting P = 10 in the demand function,

Q = 4640 - 100P

Q = 4640 - 100*10

Q = 3640 ----------------> Equilibrium quantity

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We know that,

Q = 520q

520q = 3640

q = 7 -------------------> Each firm's quantity.

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The total cost for each firm at q = 7 is,

C = 0.5q² + 3q + 32

C = 0.5(7)^2 + 3*7 + 32

C = 77.5

Total Revenue = Price*Quantity of each firm

TR = 10*7 = 70

Profit = Total Revenue - Total Cost

Profit = 70 - 77.5 = - 7.5 ---------------> Loss of each firm

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In the presence of 520 firms, each firm incurs a loss of 7.5. Thus some of the firms will exit the market in the short run until firms start earning normal profit.

Rahul Sunny answered 2 weeks ago

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