Mathematical Principles of Economics - Essay Example

1 2 3 4 5 6 7 8 9 10 11 12 Q (Items/ Minute) Demand Schedule Price $/item TC TFC TVC MC ATC AFC AVC TR MR Monopoly Profit 0 22 10 10 - - - - - 0 - -10 1 20 12 10 2 2 12 10 2 20 20 8 2 18 15 10 5 3 7.5 5 2.5 36 16 11 3 16 19 10 9 4 6.33 3.33 3 48 12 29 4 14 24 10 14 5 6 2.5 3.5 56 8 32 5 12 30 10 20 6 6 2 4 60 4 30 6 10 37 10 27 7 6.17 1.67 4.5 60 0 23 7 8 45 10 35 8 6.43 1.43 5 56 -4 11 8 6 54 10 44 9 6.75 1.25 5.5 48 -8 -6 9 4 64 10 54 10 7.11 1.11 6 36 -12 -28 10 2 75 10 65 11 7.5 1 6.5 20 -16 -55 11 0 87 10 77 12 7.91 0.91 7 0 -20 -87 Q1b) Q1c) The relationship between the shape of the TC curve and MC curve is that the TC keeps on rising with the additions to output and similarly the cost of producing one extra unit i.e the MC also keeps on rising as more and more output is produced. The MC adds to the total cost of the firm and since MC is throughout increasing, it is adding more and more to the Total Cost of producing the output. Q2a) The short run equilibrium Price is $8 and Quantity is 7000 items per minute for 1000 identical firms. This is the equilibrium point because when the price is $8, MC is also $8. In perfect competition, equilibrium point is when P=MR=MC. P ($/item) 0 2 4 6 8 10 12 14 16 18 20 22 Qd (‘000 items/minute) 11 10 9 8 7 6 5 4 3 2 1 0 Qs (‘000 items/minute) 0 0 0 5 7 9 11 13 15 17 19 21 Q2b) The individual firm would make a profit. The profit is $11. The quantity where MR =MC is 7 items per minute. At this point the Price is $8 and the AC is$6.43. Profit is calculated by: Revenue –Cost (7*8)-(6.43*7) 56-45= $11 The firm will remain in the market in the short run because its AR is greater than its AVC. Q2c) The long run equilibrium Price is $12 and quantity is 5 items per minute. This is the equilibrium point because here the AC is at its minimum at $6. Q2d) In the long run, firms in perfect competition make no profit, no losses. They earn only normal profits where Revenue is equal to cost. Q2e) Initially the firms increased when the existing firms were earning supernormal profits i.e. when average revenue was greater than average cost. As more and more firms entered the industry the share of profit for each firm started getting less and less and may firms left the industry. Hence in the long run, there will be only enough firms in the market to break-even and a no profit, no loss situation. Q3) The profit maximizing price will be $14 and quantity will be 4 items per minute if the firm is a monopolist. This is the price and quantity because here the monopoly profit is the highest at $32. The monopoly profit is calculated by taking the difference between the TR and TC. The other approach by which we can prove that this is the profit maximizing price and quantity is MR>MC. At quantity 4 items per minute, MR is $8 and MC is $5. Beyond this point, increasing quantity will cause MR to be less than MC and the monopolist wont be maximizing profits. For instance if quantity is increased to 5 items per minute, MC will increase to $6 and MR will decrease to $4 and hence not a profit maximizing condition. Q4a) Arc elasticity of Demand Q/P* [(P1+P2)/2]/[(Q1+Q2)/2] Between Quantities 3 and 4 1/-2* 15/3.5 = -15/7 Q4b) Arc elasticity of Demand between Quantities 7 and 8 1/-2* 7/7.5 = -7/15 Q4c) Over the range of prices between $14 and $16 on average, a 1% reduction in price increases quantity demanded by 2.14%. Since elasticity is greater than 1 at this point, it means that consumers are highly responsive to a change in price and will quickly move to substitutes. Over the range of prices between $6 and $8 on average, a 1% reduction in price increases quantity demanded by 0.46%. Since elasticity is less than 1 at this point, it means price elasticity of demand is inelastic and the consumers are more or less indifferent to changes in price and will not move to substitutes. Q5) Price Elasticity of Splots 2.68 Cross Elasticity of Splots and Trogs -0.7 Cross Elasticity of Splots and Rivils -4.1 Cross Elasticity of Splots and Ults +1.9 The price elasticity of Splots at 2.68 shows that Splots has an elastic demand and that consumers are responsive to changes in price. This means that if price of Splots will rise, the quantity demanded will fall more than proportionately and the total revenue will fall. In the other case of falling prices for Splots, the quantity demanded will rise more than proportionately and the total revenue will rise. The cross elasticity of Splots and Trogs at –0.7 shows that if the price of Splots rises then the quantity demanded of Splots will decrease and demand for Trogs will also fall. The negative cross elasticity shows that Splots and Trogs are complementary goods i.e. the consumption of one good is affected by the price of the other. The cross elasticity of Splots and Rivils at –4.1 shows that if the price of Splots rises, quantity demanded for Rivils will fall and vice versa. Splots and Rivils are also complementary goods meaning they are jointly demanded and the price of one will have an effect on the other. The cross elasticity of Splots and Ults at +1.49 shows that if the price of Splots rises, consumers will switch to Ults and quantity demanded of Ults will increase. The positive cross elasticity of Splots and Ults shows that they are close substitutes and consumers are indifferent between both the goods. If price of one good rises, consumers will stop demanding that good and consume more of the other good. Cost, Revenue (Dollars/ Minute) 14 12 MC 10 8 P=MR=AR AC 6 4 2 0 1 2 3 4 5 6 7 8 9 10 11 Quantity (Items/Minute) Bibliography: Lipsey, Richard.G & Chrystal, K.Alec, Principle of Economics, 9th Edition. Read More