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

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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.

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

We know that,

Q = 520q

520q = 3640

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

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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

-------------------------------------------------------------------------------------------------------------------------------------------------------------------------

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 7 months ago
Next > < Previous

Related Solutions

Iowa Soy Products buys soy beans and process them. Each ton of soy beans can be...
Iowa Soy Products buys soy beans and process them. Each ton of soy beans can be purchased for $300. At a cost of $200, each ton of soy beans is processed into 500 pounds of soy meal and 100 galons of soy oil. At the split off point, a pound of soy meal can be sold for $1.00 and soy oil can be sold for $4.00 per gallon. The joint products can be processed further. At an additional cost of...
Suppose that the perfectly competitive market for coffee beans is made up of identical firms with...
Suppose that the perfectly competitive market for coffee beans is made up of identical firms with long-run total cost functions given by T C = 2Q 3 − 24Q 2 + 80Q , where Q is 100,000 pounds of coffee beans. Assume that these cost functions are independent of the number of firms in the market and that firms may enter or exit the market freely. Market demand is Q = 100, 000 − 400P (a) Find the long-run equilibrium...
Iowa Soy Products (ISP) buys soy beans and processes them into other soy products. Each ton...
Iowa Soy Products (ISP) buys soy beans and processes them into other soy products. Each ton of soy beans can be converted for an additional $200 into 500 pounds of soy meal and 100 gallons of soy oil. A pound of soy meal can be sold at splitoff for $1 and soy oil can be sold in bulk for $4 per gallon. ISP can process the 500 pounds of soy meal into 600 pounds of soy cookies at an additional...
(8 marks) The market for wheat consists of 100 identical farms, each with the total and...
The market for wheat consists of 100 identical farms, each with the total and marginal cost functions shown: TC = 1,500 + 0.1q2 , MC = 0.2q, The corresponding supply function for a firm is, qs=5P where qs is measured in bushels per year for a firm. The market demand curve for wheat is QD = 24,000 – 100P, where Q is measured in bushels and P is the price per bushel. a. Determine the short-run equilibrium price and quantity...
Suppose the industry of all farms planting beans is now in a perfectly competitive longrun equilibrium,...
Suppose the industry of all farms planting beans is now in a perfectly competitive longrun equilibrium, and all farms have zero fixed cost for planting. Recent regulation in the market of fertilizers raises the price of bean fertilizer and therefore the marginal and average costs of all the farms in this industry. Note that marginal and average cost curves both experience a parallel shift up by the same amount. Please use a graphic tool to analyze the following changes to...
1. Suppose the industry of all farms planting beans is now in a perfectly competitive longrun...
1. Suppose the industry of all farms planting beans is now in a perfectly competitive longrun equilibrium, and all farms have zero fixed cost for planting. Recent regulation in the market of fertilizers raises the price of bean fertilizer and therefore the marginal and average costs of all the farms in this industry. Note that marginal and average cost curves both experience a parallel shift up by the same amount. Please use a graphic tool to analyze the following changes...
There are 300 purely competitive farms in the local dairy market. Of the 300 dairy farms,...
There are 300 purely competitive farms in the local dairy market. Of the 300 dairy farms, 298 have a cost structure that generates profits of $18 for every $300 invested.   A. What is the percentage rate of return for these 298 dairies? B. The other two dairies have a cost structure that generates profits of $26 for every $200 invested. What is their percentage rate of return? C. Assuming that the normal rate of profit in the economy is 10...
Assume a competitive market for computer hard drives. All firms in the market are identical each...
Assume a competitive market for computer hard drives. All firms in the market are identical each with cost function given by C(q) = 32 + 2q2 where q is measured in thousands of units per year. In this market, each firm will make zero profits when it produces _________ units.
Assuming the soy bean market in North Dakota is perfectly competitive and at the equilibrium, a...
Assuming the soy bean market in North Dakota is perfectly competitive and at the equilibrium, a large proportion is sold to buyers in China, use the supply and demand model to answer the following questions The Chinese government announced an increase in the tariff on the soy beans produced in the US. How does this policy affect the equilibrium of the soy bean market in North Dakota? How does it affect the welfare of farmers? If the US government announce...
Assume that a particular fruit is bought and sold in a perfectly competitive market. Each farm...
Assume that a particular fruit is bought and sold in a perfectly competitive market. Each farm is 1 acre in size and there are 120 acres on which this fruit is grown. On 80 of the lots, the AC = MC = $10 and each acre lot can produce a maximum of 20 units of fruit each year. On the other 40 acres AC = MC =25 and each acre lot can produce a maximum of 5 units of fruit...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT