Assignment of managerial economics 2014, Question 1 Assume you own and operate a small coffee shop located in a busy shopping complex. You sell a range of hot and cold coffees, muffins and sandwiches. Question 2 Suppose the same firm’s cost function is C(q) = 4q2 + 16. Question 3 Suppose you are given the following information about a particular industry: Question 4 Suppose the demand and supply curves for good M are as follows:
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MANAGERIAL ECONOMICS – BMME5103
ASSIGNMENT (60%) Question 1
Assume you own and operate a small coffee shop located in a busy shopping complex You sell a range of hot and cold coffees, muffins and sandwiches
a Using the concepts of demand and supply substitutability, discuss and attempt to define the market in which your business operates.(3 marks)
b Product differentiation is seen to be an important part of your competitive strategy Explain what is meant by the term product differentiation, giving examples that could apply to your market
(3 marks)
c Provide and explain two factors that will affect the demand and supply for the hot coffee
Do these factors make a change in demand and supply? Give reasons for your answer
(4 marks)
[TOTAL: 10 MARKS] Answer:
a Before my small coffee shop enters into the market, the market is equilibrium at the price
is P0 and quatity is Q0.
When I enter the market, the supply curve increase and shift to the right, the market now is equilibrium at the new point: P1 < P0 and new quantity equilibrium is Q1 > Q0 This result is entirely consistent with the law of supply and demand: When you participate in the market, as
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supply increases output if prices remain at the old, the buyer also purchased the old equilibrium level of output, while this merchandise will be redundant, it was inevitable that you would have
to sell at lower prices than the original equilibrium price
b The term product differentiation:
One of strategies can help the company success in their business that is a differentiation, the business can limit their competition as low as possible.Product differentiation is a marketing strategy businesses use to gain an edge over their competitors In industries where multiple competitors produce similar products, managers will try to make their product unique in some way so that it stands out from the pack Sometimes this is done by pursuing a low-cost strategy, and while that is a legitimate marketing strategy, it is different from product
differentiation Product differentiation means that some feature, physical attribute, or
substantive difference exists between a product and all other possible alternatives
c Two factors that will affect the demand and supply for the hot coffee They are price of
hot coffee and the price of substitute product is cool coffee
- Price of hot coffee: Price makes increase the quatity of supply and decrease the quantity
of demand; and vice varsa
- Price of substitute product: When the price of substitute product is increase to make the demand of hot coffee increase, so the price of hot coffee also increases and quality of demand also increase and vice versa
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Suppose the same firm’s cost function is C(q) = 4q2 + 16
a Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost (Hint: Marginal cost is given by MC = 8q)
(3 marks)
b Show AC, MC, AVC on a graph
(3 marks)
c Find the output that minimizes AC
(3 marks)
d At what range of prices will the firm produce a positive output
(2 marks)
e At what range of prices will the firm earn a negative profit?
(2 marks)
f At what range of prices will the firm earn a positive profit?
(2 marks)
[TOTAL: 15 MARKS] Answer:
We have: C (q) = 4q2 + 16
a Therefore, Variable cost is that part of total cost that depends on q (4q2 ) and fixed cost is
that part of total cost that does not depend on q (16)
VC = 4q 2
FC = 16
AC = TC/q = 4q + 16/q AVC = VC/q = 4q AFC = FC/q = 16/q
b Show AC, MC, AVC, on a graph:
AC is u-shaped Ac is relatively large at first because the firm is not able to spread the fixed cost over very many units of output As output increases, AFC will fall relatively rapidle AC will increase at some point because the AFC will become very small and AVC is increasing as q increases AVC will increase because of diminishing returns to the variable factor labor MC and AVC are linear, and both pass through the origin
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AVC is everywhere below AC MC is everywhere above AVC If the average is rising, then the marginal must be above the average MC will fit AC at its minimum point
c The output that minimizes average cost:
We have when MC = AC, the average cost will be minimum
AC = 4q + 16/q = 8q =MC
16/q = 4q
16 = 4 q2
q2 = 4 => q = 2
d The firm will produce a positive output at what range of prices:
The firm will supply positive levels of output as long as P = MC > AVC, or as long as t firm is covering its variable costs of production In this cse, MC is everywhere above AVC so the firm will supply positive output at any positive price
(P = MC => P = 4q + 16/q
With q = 2 => p = 16)
e When the firm earn a negative profit:
The firm will earn negative profit when P = MC < AC, or at any price below minimum average cost In part d, we found that AC = 16 Therefore, the firm will earn negative profit if P <16
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f When the firm will earn a positive profit:
In part e, we found that the firm will earn negative profit at any price below 16 P<16 Therefore, the firm will earns positive profit as long as P >16
Question 3
Suppose you are given the following information about a particular industry:
QD = 6500 – 100P Market demand
QS = 1200P Market supply C(q) = 722 + q2/200 Firm total cost function MC(q) = 2q/200 Firm marginal cost function Assume that all firms are identical and that the market is characterized by the pure competition
a Find the equilibrium price, the equilibrium quantity, the output supplied by the firm, and the profit of each firm
(5 marks)
b Would you expect to see entry into or exit from the industry in the long run? Explain What effect will entry or exit have on market equilibrium?
(5 marks)
c What is the lowest price at which each firm would sell its output in the long run? Is profit positive, negative, or zero at this price? Explain
(3 marks)
d What is the lowest price at which each firm would sell its output in the short run? Is profit positive, negative, or zero at this price? Explain
(2 marks)
[TOTAL: 15 MARKS] Answer:
a The equilirium price, quantity, output supplied by the firm and the profit of the firm:
The equilibrium when market supply equal to market demand
We have: QD = 6500 – 100P
QS = 1200P
QD = QS
6500 – 100P = 1200P
1100P = 6500
P = 5 => Q = 6000
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- To find the output for the firm, we set P = MC
With P = 5
MC (q) = 2q/200
P = MC
2q/200 = 5
q = 500
- Profit of the firm is TR minus TC
π = TR – TC
π = pq – C (q) = 5 (500) – (722 +5002/200) = 528 Because the total output in the market Q = 6000, and the firm out put is q = 500, so 6000/500 =
12 firms in the industry
b Would you expect to see entry into or exist from the industry in the long run? Explain
What effect will entry or exist have on market equilibrium?
In long run, when the market also bring profits to firms, entry will continues to P = MC = AC
As firms enter the supply curve for industry will shift down and to the right and the equilibrium price will fall, firms will be lost the fixed cost Then, having firms can not stand anymore and quit to the market
c What is the lowest price at which each firm would sell its output in the long run? Is profit
posititve, negative, or zero at this price? Explain
In the long run, the firm will not sell for a price that is below minimum average cost At any price below minimum average cost, profit is negative and the firm is better off selling its fixed resources and producing zero output To find the minimum average cost, set MC = AC and solve for q:
2q/ 200 = 722/q + q/200
q/200 = 722/ q
q2 = 722 x 200
q = 380
AC (q) = 3.8 Therefore, the firm will not sell for any price less than 3.8 in the long run
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d What is the lowest price at which each firm would sell its output in the short run? Is profit
postive, negative, or zero at this price? Explain
The firm will sell for any positive price, because at any positive price marginal cost will be above AVC (AVC = q/2000) Profit is negative as long as price is below minimum AC, or as long as price is below 3.8
Question 4
Suppose the demand and supply curves for good M are as follows:
QD = 70 - 2P
QS = -10 + 2P where P is price per kg measured in dollars and Q is quantity measured in ‘000kgs
a Sketch the demand and supply curves
(2 marks)
b Determine the equilibrium price and quantity
(2 marks)
c Calculate the value of the consumer and producer surplus at the equilibrium price
(3 marks)
d Explain why governments may introduce a price ceiling
(3 marks)
e Suppose a price ceiling of $15 were to be introduced Calculate the consumer and
producer surplus after its introduction
(3 marks)
f Who has benefited from the introduction of the price ceiling?
(2 marks)
[TOTAL: 15 MARKS]
Answer:
a Sketch the demand and supply curves:
We have: QD = 70 – 2P
QS = -10 + 2P
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Supose P = 0 => QD = 70, QS = -10
QD = 0 => P = 35
QS = 0 => P = 5
QD = QS 70 – 2P = -10 + 2P
4P = 80
P = 20; QD = QS = 30
b The Equilibrium price and quantity:
Equilibrium price is 20$
Equilibrium quantity is 30,000 kgs
c Consumer and producer surplus at the equilibrium price:
Consumer surplus = (35 - 20) x 30,000 x ½ = 225,000$
Producer surplus = (20 – 5) x 30,000 x ½ = 225,000$
d Governments may introduce a price ceiling because:
- To keep the price down to an acceptable level
- During wartime price controls may be imposed on essential items such as: petrol, rice etc
- To help the poor and the disadvantaged
e Suppose P = $15 => the consumer and producer surplus:
P = 15$ => QS = 20 ; QD = 20 => PD = 25$
Consumer surplus = ½ x [ (35-15) + (25 -15) ] x 20,000 = 300,000$
Producer surplus = (15 -5) x 20,000 x ½ = 100,000 $
f Because consumer surplus > producer surplus, consumer have benefit when introduce
ceiling price is $15
Question 5
Firm 1 and firm 2 are automobile producers Each has the option of producing either a big or a small car The payoffs to each of the four possible combinations of choices are as given the
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following payoffs matrix Each firm must make its choice without knowing what the other has chosen
Firm I
Big car Small car Big car II1 = 400 II1 = 800
II2 = 400 II2 = 1000
Firm 2
Small car II1 = 1000 II1 = 500
II2 = 800 II2 = 500
a Does either firm have a dominant strategy?
(2 marks)
b There are two Nash equilibrium for this game Identify them
(3 marks)
[TOTAL: 5 MARKS]
Answer:
a Does either firm have a dominant strategy?
A dominant strategy is the best response to the all strategies of all other players In the game above neither Firm 1 nor Firm 2 have a dominant strategy In the table below the underlined value are the choices that a _rm would make, given the other _rm has already chosen the associated car size
As can be seen in the table above, each firm would prefer to be producing the opposite sized car as the other firm
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b There are two Nash equilibrium for this game Identify them
In a two player game, a Nash Equilibrium is a strategy profile S1 ; S2 such that, for each firm, S1
is a best response to the other player’s equilibrium strategy S2 Again, looking at the underlined choices above, we can see that this game has two pure strategies Nash Equilibrium, namely Firm
1 chooses big car, Firm 2 chooses small car and Firm 1 chooses small car, Firm 2 chooses big car
Addtitionally, since games almost always have an old number of Nash Equilibrium, we should suspect that there is also mixed strategy equilibrium We can find this equilidrium by calculating the expected payoff for each firm Let the strategies for each firm be given by (B; B) and (b; 1-b) for Firm 1 and Firm 2 respectively where B is the probability that Firm 1 chooses big car and
b is the probability that Firm 2 chooses big car Then the expected payoff for Firm 1 can be written as:
u1 = B x b x 400 + B (1-b) 1000 + (1-B) (1-b) 500 + (1-B) b 800
= 500 + B 500 + b300 – B x b x 900 And the expected payoff for Firm 2 can be written as:
u1 = B x b x 400 + B (1-b) 800 + (1-B) (1-b) 500 + (1-B) b 1000
= 500 + B 500 + b300 – B x b x 900
Then, we can use these result to _nd the
mixed equilibrium If the second _rm is
playing the mixed strategy (b; 1-b), we can
find the utility of Firm1 on building a big
or small car respectively as:
u1 ((big; (b; 1-b)) = 500 + 500 + b300 – b x 900
u1 ((small; (b; 1-b)) = 500 + b 300
For this strategy to be in equilibrium these two
equations must be equal Then, we find by
solving for b that b = 5/9 Now, we do the same for Firm 2
u2 ((big; (B; 1-B)) = 500 + 500 + B300 – B x 900
u2 ((small; (B; 1-B)) = 500 + B 300
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Again, setting these equal, we fin that B = 5/9 Then, our mixed Nash Equilibrium is that both firms build big cars with probability 5/9 The following graph shows the three mixed equilibria, two of which (E1 and E2) are the special cases of pure strategy equilibria
Question 6
Two major networks are competing for viewer ratings in the 8:00 -9:00pm and 9:00-10:00pm slots on a given weeknight Each has two shows to fill this time period and is juggling its lineup Each can choose to put its “bigger” show first or to place it second in the 9:00-10:00pm slot The combination of decisions leads to the following “rating points” results:
Network 1
Network 2 First Second First 20, 30 18, 18
Second 15, 15 30, 10
a.Find the Nash equilibria for this game, assuming that both networks make their decisions at the same time
(4 marks)
b If each network is risk - averse and uses a maximin strategy, what will be the resulting equilibrium?
(4 marks)
c.What will be the equilibrium if Network 1 makes its selection first? If Network 2 goes first?
(4 marks)
d Suppose the network managers meet to coordinate schedules and Network 1 promises to schedule its big show first Is this promise credible? What would be the likely outcome?
(2 marks)
[TOTAL: 15 MARKS] Answer:
a The Nash equilibria for this game, assuming that both networks make their decisions at
the same time:
A Nash equilibria exists when neither party has an incentive to alter its strategy, taking the other’s strategy as given By inspecting each of the four combinations, we find that (Second, First) is the only Nash equilibrium, yielding a payoff of (20, 30) There is no incentive for
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either party to change from this outcome If we pick First for Firm 1 and Second for Firm 2, Firm 2 has an incentive to switch to First, in which case Firm 1 is better switching to Second
b If each network is risk – averse and uses a maximin strategy, what will be the resulting
equilibrium?
This conservative strategy of minimizing the maximum loss focuses on limiting the extent of the worst possible outcome, to the exclusion of possible good outcomes If Network 1 plays First, the worst payoff is 15 If Network 2 plays First, the worst payoff is 15 If Network 2 plays Second, the worst payoff is 10 Under maximin, Network 2 plays First The maximin equilibrium is (Second, First) with a payoff of (20; 30) (This is a dominat strategy)
c What will be the equilibrium if Network 1 makes its selection first? If Network 2 goes
first?
- If network 1 plays first, network 2 will also play first, yielding 15 for Network 1
- If Network 1 plays Second, Network 2 will play first, yielding 20 for Network1
Therefore, if it has the first move, Network 1 will play Second, and the resulting equilibrium will
be (Second, First)
- If Network 2 plays First, Network 1 will play Second, yielding 30 for Network 2
- If Network 2 plays Second, Network 1 will play First, yielding 10 for Network 2
If it has the first move, Network 2 will play First, and the euilibrium will be again (Second, First)
d Suppose the network managers meet to coordinate schedules and Network 1 promises to
schedule its big show first Is this promise credible? What would be the likely outcome?
A move is credible if, one declared, there is no incentive to change If Network 1 goes first, then Network 2 will also want to go first which gives them both 15 In this case, once Network 1 knows that Network 2 also want to go first, Network 1 will wants to change its strategy to
Second The promise in this case to schedule the bigger show first is not credible Network 2 will schedule its bigger show First since this is a dominat strategy and the coordinated outcome if likely to be (Second, First)