Question

The market for study desks is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. All firms are identical in terms of their technological capabilities. Thus the cost function as given below for a representative firm can be assumed to be the cost function faced by each firm in the industry.

The total cost function for the representative firm is given by the following equation: TC = 2qs2+ 5qs+ 50

Suppose that the market demand is given by: P = 1025 - 2QD

Note: Q represents market values (of the entire industry) and q represents firm values. The two are different.

a) Determine the equation for average total cost for the firm (1 Mark)

b) What is the long-run equilibrium price in this market? (Hint: since the market supply is unknown at this point, it’s better not to think of trying to solve this problem using demand and supply equations. Instead you should think about this problem from the perspective for a firm)

c) What is the long-run output of each representative firm in this industry? (1 Mark)

d) When this industry is in long-run equilibrium, how many firms are in the industry?

e) How will the graph look like for the entire industry in the long run? (Mark the equilibrium industry price and quantity) (1 Mark)

f) How will the graph for the firm look like in the long run? (Mark the equilibrium price and quantity produced by the firm and mark any profit or loss being made by it)

Answer 1

Given:

Total cost function: TC = 2qs² + 5qs + 50

Market demand function: P = 1025 - 2QD

a.) The average total cost is the per-unit cost for a firm. That is, it is the total cost divided by the quantity level.

Putting the equation of total cost,

Therefore the average total cost equation is:

b.) In the long-run equilibrium in the market, the firm takes the price as given. And produces where the price is equal to the marginal cost. And in the long-run equilibrium, firms produce where the firm's average cost is equal to the marginal cost.

That is,

Firstly in perfect competition, the market price is determined where the market demand is equal to the market supply. Then firms take this price and produce where the price is equal to the marginal cost.  And at this point in the long-run equilibrium, firms are producing at their least average cost. So the average cost is equal to the price.

Therefore, In the long-run equilibrium

Therefore, finding a firm's marginal cost from the total cost function. A firm's marginal cost is the derivative of the firm's total cost.

Now, equation marginal cost and average total cost. we get each firm's long-run equilibrium output. And then putting the output into the marginal cost equation, we will get the price in the long-run equilibrium.

Therefore each produces 5 quantity in the long-run equilibrium, as we know that in the perfect competition, firms take the price and equate it to its marginal cost. So the market price is equal to the marginal cost.

Putting firm long equilibrium: qs = 5

Therefore, the market price in the long-run equilibrium is $25.

c.) The long-run equilibrium output of each firm is where the marginal cost is equal to the average cost. That is, the firms are producing at their least average cost in the long run.

Therefore, each firm's long-run equilibrium output is 5 units.

d.) The number of firms is determined by dividing the market quantity and each firm's quantity in the long-run equilibrium.

Therefore, we will find the market quantity by the market price we have determined above.

Market price: P =$25

Therefore, from the market demand function.

Therefore, the long-run industry equilibrium quantity is 500 units.

As we have already found out that the long run, each firm's equilibrium quantity is 5 units.

Therefore,

Therefore when this industry is in long run, there are 100 firms in the industry.

e.) Long-run industry equilibrium:

Description of the diagram:

D is the market demand curve and S is the market supply curve. The long-run equilibrium is determined where the market demand is equal to the market supply. Here, the market price is $25 and the market quantity is 500 units in the long-run equilibrium E.

f.) Individual firm in the long run:

Description of the diagram:

The individual firms take the price as given in perfect competition, and produce where the market price is equal to its marginal cost. And in the long-run equilibrium, the firms produce at its least cost. So the average cost curve touches the marginal cost at its least. Therefore, here in the long-run equilibrium, the firms produce 5 units of output at the market price of $25. Where the average cost touches the marginal cost curve and price line. The firm's long-run equilibrium point is e.

There is no economic profit made by the firms in the long-run, as firms are producing at their average cost. That is, firms are selling the goods at the price at which it produces. Therefore there is no economic profit earned by individual firms in the long run.