Homework Prices&Markets
Task 1
1. Let’s find supply curve for a single firm assuming that the firm operates to maximize its profits. In this case the firm will produce the quantity at which its marginal cost (MC) equals the market price (P) (P>AVC).
MC=8Q=P or
Q=P/8
2. Since all 10 firms are identical, the industry supply curve will be:
Q=10(P/8)=5P/4
3. To find the short-run equilibrium price equate the industry supply with the demand:
5P/4=300-P
5P=1200-4P
9P=1200
P=1200/9=133,(3)≈133
So, the short-run equilibrium price will be $133. At this price the quantity supplied by all 10 firms will be about 167 units each firm will supply 16,7 units.
Task 2
1. In a short-run 10 firm supply about 167 units of product each and sell each unit for $133. In this condition the profit of a single firm by producing every unit is:
Profit=P - FR-ATC=133 – (4*16,7+144/16,7)=$57,57
2. Positive profit means that some other firms will enter the market until the economic profit of each single firm falls to zero. Assuming that each firm operates to maximize its profit (P=MC) and the quantity supplied equals the quantity demanded:
P= FR-ATC=4Q+144/Q and MC=P=8Q
4Q+144/Q=8Q
4Q2+144-8Q2=0
Q2=144/4=36
Q=6
P=$48
Thus, the long-run equilibrium price is $48. At this price a typical firm supplies 6 units.
The quantity demanded at this price is 252 units Number of operating firms in the market is 252/6=42. It means that 32 new firms entered the market.
Task 3
1. Let’s find the minimum market price of a unit, at which the potential entrants still will enter the market and will produce at their marginal cost:
P=FR-ATC and P=MC
16Q+144/Q=32Q
144=16Q2
Q=3
P=$96
2. Since the short-run equilibrium price for the market is $133, it makes sense for the potential entrants to enter the market. As soon as they start operating the quantity supplied will increase that will cause the market price to fall until it reaches new equilibrium of $96. At this price each incumbent firm
1. Let’s find supply curve for a single firm assuming that the firm operates to maximize its profits. In this case the firm will produce the quantity at which its marginal cost (MC) equals the market price (P) (P>AVC).
MC=8Q=P or
Q=P/8
2. Since all 10 firms are identical, the industry supply curve will be:
Q=10(P/8)=5P/4
3. To find the short-run equilibrium price equate the industry supply with the demand:
5P/4=300-P
5P=1200-4P
9P=1200
P=1200/9=133,(3)≈133
So, the short-run equilibrium price will be $133. At this price the quantity supplied by all 10 firms will be about 167 units each firm will supply 16,7 units.
Task 2
1. In a short-run 10 firm supply about 167 units of product each and sell each unit for $133. In this condition the profit of a single firm by producing every unit is:
Profit=P - FR-ATC=133 – (4*16,7+144/16,7)=$57,57
2. Positive profit means that some other firms will enter the market until the economic profit of each single firm falls to zero. Assuming that each firm operates to maximize its profit (P=MC) and the quantity supplied equals the quantity demanded:
P= FR-ATC=4Q+144/Q and MC=P=8Q
4Q+144/Q=8Q
4Q2+144-8Q2=0
Q2=144/4=36
Q=6
P=$48
Thus, the long-run equilibrium price is $48. At this price a typical firm supplies 6 units.
The quantity demanded at this price is 252 units Number of operating firms in the market is 252/6=42. It means that 32 new firms entered the market.
Task 3
1. Let’s find the minimum market price of a unit, at which the potential entrants still will enter the market and will produce at their marginal cost:
P=FR-ATC and P=MC
16Q+144/Q=32Q
144=16Q2
Q=3
P=$96
2. Since the short-run equilibrium price for the market is $133, it makes sense for the potential entrants to enter the market. As soon as they start operating the quantity supplied will increase that will cause the market price to fall until it reaches new equilibrium of $96. At this price each incumbent firm