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:
ASSIGNMENT – BMME5103 SEMESTER 2014 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 P 0 and quatity is Q 0. When I enter the market, the supply curve increase and shift to the right, the market now is equilibrium at the new point: P 1 < P 0 and new quantity equilibrium is Q 1 > Q 0. This result is entirely consistent with the law of supply and demand: When you participate in the market, as Pham Thi Hong Cuc Page 1 ASSIGNMENT – BMME5103 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. Pham Thi Hong Cuc Page 2 ASSIGNMENT – BMME5103 Question 2 Suppose the same firm’s cost function is C(q) = 4q 2 + 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) = 4q 2 + 16 a. Therefore, Variable cost is that part of total cost that depends on q (4q 2 ) 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. Pham Thi Hong Cuc Page 3 ASSIGNMENT – BMME5103 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 q 2 q 2 = 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. Pham Thi Hong Cuc Page 4 ASSIGNMENT – BMME5103 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: Q D = 6500 – 100P Market demand Q S = 1200P Market supply C(q) = 722 + q 2 /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: Q D = 6500 – 100P Q S = 1200P Q D = Q S 6500 – 100P = 1200P 1100P = 6500 P = 5 => Q = 6000. Pham Thi Hong Cuc Page 5 ASSIGNMENT – BMME5103 - 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 +500 2 /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 q 2 = 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. Pham Thi Hong Cuc Page 6 ASSIGNMENT – BMME5103 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 $15 were to be introduced. Calculate the consumer and producer surplus after its introduction. (3 marks) f. Who has benefited from the introduction of the price ceiling? (2 marks) [TOTAL: 15 MARKS] Answer: a. Sketch the demand and supply curves: We have: Q D = 70 – 2P Q S = -10 + 2P Pham Thi Hong Cuc Page 7 ASSIGNMENT – BMME5103 Supose P = 0 => Q D = 70, Q S = -10 Q D = 0 => P = 35 Q S = 0 => P = 5 Q D = Q S 70 – 2P = -10 + 2P 4P = 80 P = 20; Q D = Q S = 30 b. The Equilibrium price and quantity: Equilibrium price is 20$ 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 = $15 => the consumer and producer surplus: P = 15$ => Q S = 20 ; Q D = 20 => P D = 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 Pham Thi Hong Cuc Page 8 ASSIGNMENT – BMME5103 following payoffs matrix. Each firm must make its choice without knowing what the other has chosen. Firm I Big car Small car Big car II 1 = 400 II 1 = 800 II 2 = 400 II 2 = 1000 Firm 2 Small car II 1 = 1000 II 1 = 500 II 2 = 800 II 2 = 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. Pham Thi Hong Cuc Page 9 ASSIGNMENT – BMME5103 b. There are two Nash equilibrium for this game. Identify them. In a two player game, a Nash Equilibrium is a strategy profile S 1 ; S 2 such that, for each firm, S 1 is a best response to the other player’s equilibrium strategy S 2. 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; 1-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: u 1 = 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: u 1 = 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: u 1 ((big; (b; 1-b)) = 500 + 500 + b300 – b x 900 u 1 ((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. u 2 ((big; (B; 1-B)) = 500 + 500 + B300 – B x 900 u 2 ((small; (B; 1-B)) = 500 + B 300 Pham Thi Hong Cuc Page 10 [...]... (Qx1 + Qx2 ) = (120,000 – 105, 000) / (23 – 20) x (23 + 20) / (120,000 + 105,000) = (15,000 x 43) / 3 x 225,000 = 0.96 Because Exy = 0.96 < 1, close to 1 so the two brands of novels are close subsitutes Pham Thi Hong Cuc Page 13 ASSIGNMENT – BMME5103 c We have: QY1 = 130,000; QY2 = 120,000 Y1 = 310; Y2 = 290 EY = ∆ QY/ ∆ Y x (Y1 + Y2) / (QY1 + QY2 ) = (130,000 – 120,000) / (310 – 290) x (310 + 290)... equilibrium, yielding a payoff of (20, 30) There is no incentive for Pham Thi Hong Cuc Page 11 ASSIGNMENT – BMME5103 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... 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) Pham Thi Hong Cuc Page 12 ASSIGNMENT – BMME5103 Question 7 Bookworm and Easyread are both publishers of popular novels a Assume that demand for Bookworm novels is elastic - Explain the meaning of the underlined term - Outline one important.. .ASSIGNMENT – BMME5103 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,... average variable, average total and marginal cost (6 marks) b For the above data, over which output range do we observe diminishing returns? (4 marks) [TOTAL: 10 MARKS] Pham Thi Hong Cuc Page 14 ASSIGNMENT – BMME5103 Answer: a The output levels: L Q AP= Q/L 1 2 3 4 5 6 7 8 8 24 39 50 56 59 61 62 8 12 13 12.50 11.20 9.83 8.71 7.75 MP= ∆Q/∆L 8 16 15 11 6 3 2 1 TVC =10*L 10 20 30 40 50 60 70 80 TC= TVC