Question

Suppose there is a perfectly competitive industry where all the firms are identical with

identical cost curves. Furthermore, suppose that a representative firm’s total cost is given by the equation

where is the quantity of output produced by the firm. You also know that the TC=200 +q^2+q where q is the quantity of output produced by the firm. You also know that the market demand for this product given by the equation P= 1000-2Q where Q is the market quantity. In addition, you are told that the market supply curve is given by the equation P=100 +Q

a. What is the equilibrium quantity and price in this market given this information?

b. What is the firm’s MC equation?

c. What is the firm’s profit maximizing level of production?

d. What is the total revenue?

e. What is the total cost?

f.What is the profit at this market equilibrium?

Answer 1

The answer is followingly . Suppose there is a perfectly competitive industry where all the firms are identical with
identical cost curves. Furthermore, suppose that a representative firm’s total cost is given
by the equation TC = 100 + q2
+ q where q is the quantity of output produced by the
firm. You also know that the market demand for this product is given by the equation P =
1000 – 2Q where Q is the market quantity. In addition you are told that the market supply
curve is given by the equation P = 100 + Q.
a. What is the equilibrium quantity and price in this market given this information?
To find the equilibrium set market demand equal to market supply: 1000 – 2Q =
100 + Q. Solving for Q, you get Q = 300. Plugging 300 back into either the
market demand curve or the market supply curve you get P = 400.
b. The firm’s MC equation based upon its TC equation is MC = 2q + 1. Given this
information and your answer in part (a), what is the firm’s profit maximizing level
of production, total revenue, total cost and profit at this market equilibrium? Is
this a short-run or long-run equilibrium? Explain your answer.
From part (a) you know the equilibrium market price is $400. You also know that
the firm profit maximizes by producing that level of output where MR = MC.
Since the equilibrium market price is the firm’s marginal revenue you know that
MR = $400. Setting MR = MC gives you 400 = 2q + 1, or q = 199.5. Thus, the
profit maximizing level of output for the firm is 199.5 units when the price is
$400 per unit. Using this information it is easy to find total revenue as the price
times the quantity: TR = ($400 per unit)(199.5 units) = $79,800. Total cost is
found by substituting q = 199.5 into the TC equation: TC = $40,099.75. Profit is
the difference between TR and TC: Profit = TR – TC = 79,800 – 40,099.75 =
$39,700.25. Since profit is not equal to zero this cannot be a long-run equilibrium
situation: it must be a short-run equilibrium situation.
c. Given your answer in part (b), what do you anticipate will happen in this market
in the long-run?
Since there is a positive economic profit in the short run, there should be entry of
firms in the long-run resulting in an increase in the market quantity, a decrease in
the market price, and firms in the industry earning zero economic profit.
d. In this market, what is the long-run equilibrium price and what is the long-run
equilibrium quantity for a representative firm to produce? Explain your answer.
The long-run equilibrium price is that price that results in the representative firm
earning zero economic profit. This will occur when MC = ATC for the
representative firm. ATC is just the TC equation divided by q. Thus, 2q + 1 =(100 + q2
+ q)/q. Solving for q, q = 10. Plugging 10 in for q into the ATC
equation yields the following: ATC = (100 + 102
+ 10)/10 = 21. So, when Price
equals MR = min ATC = MC = $21, this firm will break even. To see this
compute TR for the firm when it produces 10 units and sells each unit for $21: TR
= $210. Notice that this is the same as the firm’s TC: thus, the firm earns zero
economic profit.
e. Given the long-run equilibrium price you calculated in part (d), how many units
of this good are produced in this market?
To find this quantity you need to substitute $21 (the long-run equilibrium price)
into the market demand curve to determine the quantity that the market must
produce in order to be in long-run equilibrium. This quantity is equal to 489.5
unit.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 and marginal cost functions for the representative firm are given by
the following equations:
TC = 2qs
2
+ 5qs + 50
MC = 4qs + 5
Suppose that the market demand is given by:
PD = 1025 - 2QD
Note: Q represents market values and q represents firm values. The two are different.
a) Determine the equation for average total cost for the firm.
ATC for the firm is TC/q, so dividing the total cost equation above by q gives us:
ATC = 2qs + 5 + 50/qs
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. Specifically, a long run equilibrium occurs where ATC = MC =
Price)
In a long-run equilibrium, ATC equals Marginal Cost and profits equal zero. Setting
the two equations equal:
ATC = 2qs + 5 + 50/qs = 4qs + 5 = MC50/qs = 2qs
50 = 2qs
2
25 = qs
2
Take the square root of both sides and find:
5 = qs
However, the question wants us to find long run prices. We know that the firm
produces were Price = MR = MC, so if we can determine the firm’s MC, then we can
determine the equilibrium price in the market.
We know that:
MC = 4qs + 5
And solved for:
5 = qs
Substituting:
MC = 4(5) + 5 = 25
The equilibrium price in the market is 25.
c) What is the long-run output of each representative firm in this industry?
We solve for this in the previous part. 5 = qs
d) When this industry is in long-run equilibrium, how many firms are in the industry? (Hint:
firms are identically sized).
Now we should determine the market quantity Q from the market demand curve, given
that we know the market price is 25. Market demand is given as:
PD = 1025 - 2QD
And we know that market price = 25, so:
25 = 1025 - 2QD
1000 = 2QD
500 = QD
Since each firm is making 5 units (as we found in parts b and c), there must be 100
firms, since they are all identically sized.
Now suppose that the number of students increases such that the market demand curve for
study desks shifts out and is given by,
PD = 1525 - 2QD
e) In the short-run will a representative firm in this industry earn negative economic profits,positive economic profits, or zero economic profits? (Hint: You can solve this without
calculation.)
The demand curve has shifted to the right. Given what we learned earlier in the semester,
we should know that the market price will increase. If market prices are increasing, then
firms are earning higher marginal revenues than they earn in a long-run equilibrium. This
means that firms are earning positive economic profits.
f) In the long-run will a representative firm in this industry earn negative economic profits,
positive economic profits, or zero economic profits? (Hint: again, no calculation required)
In the long-run economic profits are always zero since there is free entry/exit in a perfectly
competitive market. Firms will either enter the industry until there are no possible profit
opportunities. If there are economic losses, firms will leave the industry until profits hit
zero.
g) What will be the new long-run equilibrium price in this industry?
The same as it was before, P = 25, because that is where zero-profits occur for firms.
h) At the new long-run equilibrium, what will be the output of each representative firm in
the industry?
Firm output will still be 5 as this is the quantity where ATC = MC, and long-run profits are
zero.
i) At the new long-run equilibrium, how many firms will be in the industry?
This will be different since there is a new demand curve. Specifically, there is a new
market demand. With the new market demand curve:
PD = 1525 - 2QD
We can substitute P = 25:
25 = 1525 - 2QD
1500 = 2QD
750 = QD
We can see that the new market demand is 750. Since each firm produces 5 units and firms
are all identical, there must be 750/5 or 150 firms.
Now, consider another scenario where technology advancement changes the cost functions of
each representative firm. The market demand is still the original one (before the increase in
the number of students). The new cost functions are:
TC = qs
2
+ 5qs + 36
MC = 2qs + 5
j) What will be the new equilibrium price? Is it higher or lower than the originalSimilar to part b), in a long-run equilibrium, ATC equals Marginal Cost and profits
equal zero. Setting the two equations equal:
ATC = qs + 5 + 36/qs = 2qs + 5 = MC
36/qs = qs
36 = qs
2
Take the square root of both sides and find:
6 = qs
However, the question wants us to find long run prices. We know that the firm
produces were Price = MR = MC, so if we can determine the firm’s MC, then we can
determine the equilibrium price in the market.
We know that:
MC = 2qs + 5
And solved for:
6 = qs
Substituting:
MC = 2(6) + 5 = 17
The equilibrium price in the market is 17.
The price is lower than before, and this makes sense because the technological
improvement has lowered the costs for the firm. With lower costs, the price is lower for
firms to have zero profits.
k) In the long-run given this technological advance, how many firms will there be in the
industry?
Now we should determine the market quantity Q from the market demand curve, given
that we know the market price is 17. Market demand is given as:
PD = 1025 - 2QD
And we know that market price = 17, so:
17 = 1025 - 2QD
1008 = 2QD
504 = QD
Since each firm is making 6 units (as we found in parts b and c), there must be 84 firms,
since they are all identically sized. (504/6 = 84)
Since each firm faces lower costs, more firms need to enter the industry to drive down
prices so that there are zero profits in the long run. We see the number of firms.