Second Year Economics Notes PDF

Preview

Summary

ECONOMICSSecond Year Economics, Maths and Staisics notes.[Document subitle]Proit Maximisaion To ind the irst order condiions we difereniate with respect to K and L. By muliplying the two FOC's by K and L respecively you get the second order condiion. By dividing the FOC by the SOC you get the capit...

Description

ECONOMICS Second Year Economics, Maths and Statistics notes.

[Document subtitle]

1|Page

Contents ECON 2 SEM1 LECTURE 2.......................................................................................................................5 FRANK & CARTWRIGHT CHAPTER 9.......................................................................................................9 ECON 2 SEM1 LECTURE 3.....................................................................................................................13 ECON 2 SEM1 LECTURE 4.....................................................................................................................14 FRANK & CARTWRIGHT CHAPTER 10...................................................................................................16 ECON 2 SEM1 LECTURE 5.....................................................................................................................19 FRANK & CARTWRIGHT CHAPTER 11...................................................................................................25 ECON 2 SEM1 LECTURE 6.....................................................................................................................30 ECON 2 SEM1 LECTURE 7.....................................................................................................................34 FRANK & CARTWRIGHT CHAPTER 12...................................................................................................39 ECON 2 SEM1 LECTURE 8.....................................................................................................................40 ECON 2 SEM1 LECTURE 10...................................................................................................................41 ECON 2 SEM1 LECTURE 11...................................................................................................................49 FRANK & CARTWRIGHT CHAPTER 14...................................................................................................52 ECON 2 SEM 1 LECTURE 12..................................................................................................................59 FRANK & CARTWRIGHT CHAPTER 15...................................................................................................66 ECON 2 SEM 1 LECTURE 13..................................................................................................................69 ECON 2 SEM 1 LECTURE 14..................................................................................................................74 FRANK & CARTWRIGHT CHAPTER 16...................................................................................................79 ECON 2 SEM 1 LECTURE 16..................................................................................................................84 FRANK & CARTWRIGHT CHAPTER 17...................................................................................................94 ECON 2 SEM 1 LECTURE 17................................................................................................................100 FRANK & CARTWRIGHT CHAPTER 18.................................................................................................103 ECON 2 SEM 1 REVISION TUTORIAL SHEET 1.....................................................................................113 ECON 2 SEM 1 REVISION TUTORIAL SHEET 2.....................................................................................117 ECON 2 SEM 1 REVISION TUTORIAL SHEET 3.....................................................................................122 ECON 2 SEM 1 REVISION TUTORIAL SHEET 4.....................................................................................127 ECON 2 SEM 1 REVISION TUTORIAL SHEET 6.....................................................................................133 ECON 2 SEM 1 REVISION TUTORIAL SHEET 7.....................................................................................137 ECON 2 SEM 1 REVISION TUTORIAL SHEET 8.....................................................................................142 ECON 2 SEM 1 REVISION TUTORIAL SHEET 9.....................................................................................146 MATHS Y2 LECTURE 2........................................................................................................................153 MATHS Y2 LECTURE 3........................................................................................................................156 MATHS Y2 LECTURE 4........................................................................................................................158 2|Page

MATHS Y2 LECTURE 5....................................................................................................................161 MATHS Y2 LECTURE 6........................................................................................................................163 MATHS Y2 LECTURE 7........................................................................................................................164 MATHS Y2 LECTURE 8........................................................................................................................165 MATHS Y2 LECTURE 9........................................................................................................................167 MATHS Y2 ADDITIONAL MATERIAL....................................................................................................173

3|Page

4|Page

ECON 2 SEM1 LECTURE 2 Tuesday, 22 September 2015 10:00

Production   

Isoquant: combination of K and L to produce the same level of output. The slope of this isoquant shows the marginal rate of technical substitution; 'how much K should decrease when L increases a little to keep the same Q'. Note that each point of the isoquant can have a different MRTS.

5|Page

Profit Maximisation







To find the first order conditions we differentiate with respect to K and L. By multiplying the two FOC's by K and L respectively you get the second order condition. By dividing the FOC by the SOC you get the capital-labour ratio when the firm is profit maximising. This tells us that alpha represents the relative importance of capital; i.e. when alpha increases the relative use of capital increases. When beta decreases the relative us of capital also increases. Beta represents the relative importance of labour in production. The capital-labour ratio is also dependent on the relative price of inputs; i.e. the ratio of alpha to beta. This can explain why production methods in the same economy can differ and some firms can be labour intensive while others are capital intensive.

6|Page



In the short run the firm can only choose L as K is fixed. This means there is a variable cost wL with w representing the wage level, this is set by the market and the firm has no control over it.

7|Page

8|Page

FRANK & CARTWRIGHT CHAPTER 9 Wednesday, 25 November 2015 10:14

9|Page

10 | P a g e

11 | P a g e

12 | P a g e

ECON 2 SEM1 LECTURE 3 Tuesday, 29 September 2015 09:55

Cost Minimisation:       



There are several types of average cost (cost per unit) Total cost (TC) = Fixed cost (FC = rK) + Variable Cost (VC = wL) This distinction is only relevant in the short run as all variables are variable in the long run. ATC = (FC+VC)/Q AFC = FC/Q Both these costs are large when Q is very small due to the high level of fixed cost. When beta is less than one there is increasing marginal cost and this therefore implies diminishing returns on the production function due to the decreasing marginal product of labour. Beta being less than one means that the slope of MC is increasing in Q. Average fixed costs falls as production increases while average variable costs increases as production increases. This leads to an ATC falling while MC is less than ATC, once MC crosses through ATC, ATC begins to rise. Costs are minimised when ATC = MC. NB: In the textbook MC is decreasing and then increasing - this is not Cobb-Douglas.

Long-run cost minimisation:         

'Optimal' combination of inputs K and L to produce Q Note that in the short run the choice is easy: more L to produce more Q. Step 1: Isocost line (A bundle of production combinations that all cost the same.) C = rK+wL K = -(w/r)L+c/r Step 2: Draw Isoquant to show combinations that all produce the same amount. Step 3: Overlay isocost lines onto the isoquant and find the point of tangency, this will be the point where costs are minimised. As Isocost lines move towards the left cost is reduced. When the firm minimises costs: -(MPL/MPK) = -(w/r), therefore MPL/MPK = w/r. If wages were to increase the curve would steeper because the cost of labour has risen. The curve becomes shallower if the cost of capital increases. These assumptions are made with K on the Y axis and L on the X axis. This helps to explain why an increase in the minimum wage is often bad for those on minimum wage. Although this analysis ignores the effects of the minimum wage on the quality and motivation of workers which could alter productivity.

13 | P a g e

ECON 2 SEM1 LECTURE 4 Friday, 2 October 2015 09:55

Competitive Market (Short-run): We will look out how buyers and sellers interact in the product market and the market outcome. The market outcome is the price, quantity and efficiency.  

 

Competitive market; many sellers - this means that each seller thinks his/her decisions do not affect the market outcome. Economic profit; the difference between total revenue and total costs, where total cost includes monetary (explicit) costs and opportunity costs (implicit) costs - associated with the resources used by the firm: π = pF(K,L) - (rK + wL). The first halve of the equation represents revenue, while the second halve represents cost. Implicit cost can be represented by r - it may be the interest the firm could earn be selling K and depositing the money at the bank. Accounting profit does not take account of these implicit costs ad is simply total revenue less monetary costs.

Perfect Competition: 

   

Firms sell a standardised product and we can assume that the goods produced by the firms are perfect substitutes for each other; Firms are price takers, this means each individual firm treats the market price of the product as given; Free entry and exit, firms will enter and stay in the market as long as they earn profits; firms and consumers have perfect information. Revenue can be written in terms of quantity: pF(K, L) = pQ. Marginal revenue = d(pQ)/dQ = p. This implies marginal revenue coincides with the market price. When a firm has influence on the market price p(Q) we have: MR = p(Q) + p' (Q)Q, where p'(Q) is the derivative of p(Q) with respect to Q. Profit maximisation with respect to Q in a competitive market: π = pQ - C(Q). The first order condition yields p - C'(Q) = 0, thus p = MC. This condition implies that each firm's supply curve coincides with marginal cost as long as the firm is in operation.

Shut-down condition:  



In a competitive market, a firm engages in production as long as p = MC > AVC. When p < ATC the firm makes a loss while operating since p < ATV - pQ < TC - revenue < total cost. Π = pQ - VC - FC. This means that even if the firm produces nothing it will still incur its fixed cost - therefore it is better to produce something in order to reduce this loss. When the price is higher than the firm’s variable cost it makes economic sense to produce something as this would reduce the size of the loss. If p < ATC but p > AVC, then the firm is making the loss lower, by producing rather than shutting down. Naturally if p > ATC at p = MC, then the firm makes a profit.

14 | P a g e

Market Equilibrium:  



Horizontally add up the supply curves of all firms in the market. We often use a linear supply function for simplicity. From each firm's viewpoint the demand curve is horizontal as they do not have any influence on the equilibrium price; no matter how much the firm produces they will not influence the market price. The firm will choose to produce where p = MC, when p > ATC the firm will make a profit and when p < ATC, the firm will make a loss.

15 | P a g e

FRANK & CARTWRIGHT CHAPTER 10 Wednesday, 25 November 2015 10:27

16 | P a g e

17 | P a g e

18 | P a g e

ECON 2 SEM1 LECTURE 5 Tuesday, 6 October 2015 10:04

Market Efficiency and Perfect Competition Resource allocation  



Scarce resources have to be allocated to increase social welfare. By buying the good it is implied that the resource has been allocated from the seller to you and that therefore the value of the good to you is higher than the value of the good to the seller; both are better off as a result of the transaction and this is efficiency. Below is a graph showing simple economic profit.

19 | P a g e



Below is a graph showing the producer surplus, i.e. the benefits to the producer of supplying the good.

20 | P a g e

21 | P a g e

22 | P a g e

23 | P a g e

 





Why doesn't the All England Club sell tickets at much higher prices? : Efficiency v 'fairness', but what is fairness? Consumer surplus does necessarily represent consumers' happiness: rich people may have a high willingness to pay even though they may only gain a little happiness from it. Poor people may have a lower willingness to pay despite the fact that attending may give them immense pleasure.

Competitive equilibrium will always maximise total surplus, any price above or below this may increase the surplus for one group but will lead to a deadweight loss and a reduction in total surplus. Competitive equilibrium can refer to short or long run scenarios; in the short run the number of firms is fixed and there are many firms following price taking behaviour, in the long run all factors are variable and there must be free entry and exit to the market.

24 | P a g e

FRANK & CARTWRIGHT CHAPTER 11 Wednesday, 25 November 2015 10:35

25 | P a g e

26 | P a g e

27 | P a g e

28 | P a g e

29 | P a g e

ECON 2 SEM1 LECTURE 6 Friday, 9 October 2015 10:02

Monopoly: π = p(Q)Q - C(Q) The key difference between this and competitive markets is that the monopolist is not a price taker, this is reflected by the fact that p is now a function of Q. Profit maximisation - first order condition yields: p'(Q)Q + p(Q) - C'(Q) = 0. Here the first half of the equation (p'(Q)Q + p(Q)) is marginal revenue while the second half (C'(Q)) is marginal cost. Note that for a large value of Q, marginal revenue is negative. Let the demand be Q = A-p, which means the price the monopolist can charge when supplying Q is p = A-Q. Revenue of the monopolist is therefore Q(A-Q), so marginal revenue, MR = A-2Q. We can confirm that MR is negative when Q > A/2. This is shown below. 30 | P a g e

31 | P a g e

Shut-down Condition Monopoly: A monopolist will shut down if average revenue < AVC for any Q. Average revenue is represented by the demand curve. This means the shut-down condition is equivalent to AVC being above the demand curve for any value of Q. Otherwise, the monopolist can make the loss lower by producing Q such that p(Q) > AVC, even if p(Q) < TVC. Remember: π = p(Q)Q - VC - FC. The shut-down condition for monopolists is shown on the graph below.

32 | P a g e

So should Monopoly always be avoided?  



Without monopoly profits firms may not have the incentive/ability to invest. The pharmaceutical industry is a prime example of this. For the consumer, perfect competition is ideal after the drug has been invented and the investment made - there will be no monopoly profits and consumer surplus will be maximised. However, if the firm knows that there will be no profit made the investment wouldn't be made in the first place so there would be no new drug. The government therefore encourages monopoly and innovation through patents and copyrights - these give the firm a monopoly in the market for a set period of time. 33 | P a g e



Ex-post, after innovation, perfect competition is the best outcome but ex-ante, before innovation, perfect competition kills any incentive to innovate. The government tries to balance the trade-off between these two by altering the length and breadth of the patent. The broader the patent and the longer it is effective the greater monopoly profits will be.

Factors that lead to monopoly:    

Economies of scale; i.e. high fixed cost and large minimum efficient scale. This is prevalent in industries that require networks/grids to distribute their product. Exclusive access to inputs; the government may limit access to raw materials, such as rare earth elements, to a small number of firms or to one firm. Government licences; this could apply to airports - the government may want to restrict the number of these in a certain area to ensure they are competitive globally etc. Network economies; the product becomes more viable as more people use it - social networking and online auction sites are prime examples of these.

Competitive Pressure in Monopoly: If the barriers to entry are low, then the threat of new entrants may cause the monopolist to charge lower prices and reduce profits to reduce the incentives of other firms looking to join the market. Looking at the number of firms in the market may not be enough to measure inefficiency caused. Economists prefer using the price-cost margin: (p(Q) - MC)/p(Q) to measure market power. In the context of competition policy, it is also known as the Lerner index.

ECON 2 SEM1 LECTURE 7 Tuesday, 13 October 2015 10:04

Monopoly (continued):

34 | P a g e

Government Interventions:  

 

In reality, many monopolies are regulated by the government to some extent; e.g. OFGEM for the energy market and the CAA for airports. In the past many monopolistic markets/industries have been owned by the government; e.g. railways, telecoms and aviation (BA). The health market is also currently state owned through the NHS, although private companies are allowed to operate. The government can grant exclusive contracts which create local monopolies - contractedout prisons with G4S. Antitrust Laws are enforced by the Competition and Markets Authority (CMA).

Price Discrimination: 

 



  

Identical or similar products can be sold at different prices; examples include magazines (subscribers and non-subscribers), public transport (children, students, adults, peak, off-peak) and books (paperbacks and hardbacks). Definition: pricing the same or a similar product at different levels. First-degree (perfect) price discrimination: Every consumer is charged the highest price they are willing to pay for each unit. There is therefore no consumer surplus, although this is technically efficient as total surplus is still maximised. Second-degree price discrimination: Consumer types (willingness to pay) unknown to the seller. This lead to self-selection by consumers (heavy & light users). Examples of this include mobile, water and electricity tariffs. Third-degree price discrimination: Selection by indicators (age, studentship membership, etc. They offer a different price for each market. What type of price discrimination is feasible is depe...