Consider the following technology: C(yi) = y3i − 8y2i + 36yi Many firms have access to...

Consider the following technology: C(y_i) = y³_i − 8y²_i + 36y_i

Many firms have access to this technology, in fact so many that there is not room for all to profitably operate in the industry. Market demand for the product is given by P = 2420 − Y

where Y is market quantity.

a. If these firms are price takers, and entry/exit is costless, what is the long run free entry equilibrium per-firm quantity produced by each firm in the industry? Explain.

b. Do you have enough information to determine the number of firms who operate in such a long run free entry equilibrium? If so what is the number and justify your solution. If not explain what other information you would need.

c. Is the price-taking behavioral assumption sensible for this industry?

Solutions

Expert Solution

According to the cost function, C(y) = y3 − 8y2 + 36y for a typical firm, the average cost is AC = C(y)/y = y2 - 8y + 36. Given that so many firms are there that there is not room for all to profitably operate in the industry. There seems to be a long run equilibrium established. Hence AC must be at its minimum in this market. Find minimum AC as dAC/dy = 0

2y = 8 or y* = 4.

Hence each firm in this market is producing 4 units and so the AC is minimum and is equal to AC = (4)^2 - 8*4 + 36 = 20. Price in the long run is equal to minimum of AC so price is also 20. Now that Market demand for the product is given by P = 2420 − Y , we find that total quantity demanded is 2420 - 20 = 2400 units. Since each firm produces 4 units, number of firms = 2400/4 = 600 firms.

a. If these firms are price takers, and entry/exit is costless, the long run free entry equilibrium per-firm quantity produced by each firm in the industry is 4 units.

b. We have enough information to determine the number of firms who operate in such a long run free entry equilibrium. There are 600 firms.

c. The price-taking behavioral assumption is not sensible for this industry because more or less some firms will gain market power overtime by developing further advanced and cost efficient technolgy to oust the competition and earn long term profits.

Rahul Sunny answered 1 year ago

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