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Usman Hannan

May 03, 2011 Introduction - Economic activity transforms resources into goods and services (goods, for short) - The resource endowment of an economy Is all the resources (human and physical) available to an economy. - A list of everything that can be used to produce goods. - Resources are limited or scarce in supply- only a certain amount available for use in economy - Technology determines how resources can be used to produce goods. - It tells the different combinations of resources that can be used to produce a good. - Firms choose the technology/technique that is least costly. - Individual preferences tell firms what goods people would like to buy. - Institutions provide rules followed by all agents in the economy. o Eg. Competition laws, leaving deposits on rented goods, etc. - They regulate economic activity. - The social state of an economy is how goods are distributed in an economy, i.e. the outcome of economic activity - We try to predict the social state by using the method of equilibrium. - An equilibrium is a set of choices for individuals and a corresponding social state such the no individual can make themselves better off by making some other choice. - We use comparative statics for analysis- analyze the impact of a change in a model by comparing the original equilibrium to the new one that results from the change. - We can divide economics by 2 characteristics: o Positive economics= what actually happens in an economy, what is. o Normative economics=what should happen in an economy based on value judgments. - Policymaking usually involves both positive and normative analysis. - Normative considerations tell us what are desirable social states and what are not. - Pareto optimality o The Pareto criterion: there are two possible market outcomes, two market equally wealthy. Marking one market wealthier by not hurting other market o A social state is Pareto-optimal if no one can be made better off without making someone else worse off. - The comparative equilibrium is Pareto optimal. - In practice, it may be too hard for policy makers to rank social states under some circumstances - May use cost-benefit analysis instead. - If the net social benefit is greater in state A than state B, state a is better (prefer state) - In this course, we will focus on how firms make decisions about how much to produce, what combination of resources to use in production and how different market structures affect firm’s decision. May 5,2011 Chapter 6 Production and Cost: one variable input The production function - Assuming a frim produces one good,Y use 2 inputs - Let Y= quantity of good Y - (Z1, Z2) - One best function: Technically efficient (it maximizes the qty of output that can be produced from the given bundle of inputs) Fixed-proportions production function = the input are always used in a fixed ratio - Y = min(z1/150, z2/100) - Take the min of the two inputs Leontief production functions - 0.8 kg spaghetti/4= 0.2 (input 1) - 8 tomatoes/4 = 2 tomatoes(Z2) - 12/4= 3 scallops(Z3) - 4/4= 1 garlic clove (Z4) - The production fn is y=min(z1,z2,z3,z4) - Y=min (4.9/0,2, 60/2, 54/3, 30) - Therefore, y=18 servings maximum Variable- proportions production function = the input mix can vary e.g. a courier service - let y= courier service measured in km - z1 = driver’s time measured in hours - z2=gasoline measured in litres - km/litre of gas = 1200/s - y<=sz1 - y<=1200/s*z2 - to find out s* and y* - sz1=1200/s*z2 - s=(1200z2/z1)1/2, and substitute to y*= sz1, so that y*=(1200z2z1)1/2 Cobb-Douglas production function - y=Az1u*z2v - e.g. milkshakes - y<=sz1, y<=10/s*z2 Production costs - sunk cost: Unavoidable, non-recoverable costs. E.g. you spend money and you will not see it again - Avoidable costs: can be recovered (at least in part)e.g. resell and recoup his costs - Fixed costs: do not vary with output. E.g. loan payments, rent - Variable costs: change when output levels change. E.g. labour, raw material costs Cost minimization - This implies that profit is maximized when costs are minimized. - TC= w1z1 + w2z2 LR cost minimization problem - Min w1z1+ w2z2 - Y= F(z1,z2) SR cost minimization - SR, at least one input is fixed in quantity. Total production function, TP - Gives us the total output for any qty of the variable input given the fixed qty of the other inputs - TP(z1)=F(z1,z2) Marginal product of Z1, MP(Z1) - The slope of TP(z1) - Maximized at point c where MP(z1)=0 - MP (Z1)= 8F(Z1, Z2)/8Z1 The free-disposal assumption - If firm has more than the output-maximizing level of z1, it will decide to use exactly that amount and no more Diminishing MP - 8MP(Z1)/8Z1=0 - Fixed = short run - TP(z1)=z1, if z1 <=10 - Tp(z1)= 10, if z1> 10 Average product - AP (Z1)= TP(Z1)/Z1 - Max AP and AP=MP Note these 3 things: - When MP>AP, AP is rising - When MP < AP, AP is falling - When MP = AP, AP is at a maximum. For input 2, is fixed at z2, and price of variable input 1 is w1, the cost minimization problem is - Min(z1) w1z1 - St y = TP (Z1) - VC(y)= minimum variable cost of producing y units of output - E.g. VC when the courier has 48 litres of gas is VC (Y)= W1Z1*= W1Y2/57600 Average variable cost, AVC - AVC(Y)=VC(Y)/y The SR marginal cost, SMC(y), is the rate at which cost increases in the SR as output increases. - The slope of VC(y) - SMC(y)= VC’ (y)= DVC(y)/dy - SMC = AVC at min AVC 3 points - SMC< AVC, AVC decreases as y increases - When SMC> AVC, AVC increases as y increases. - When SMC= AVC, AVC is at a minimum Average cost - AVC(y’)= w1z1/y= w1/AP(z1’) - AVC of an input= price of the input/ average product of the input Marginal product and Marginal cost - ^Y=MP (Z1)*^Z1 SMC = Price of the input /MP of the input SMC= W1/MP(Z1) Other costs - Fixed Cost, FC - Given fixed input z 2 with a price of w 2 o FC = w z 2 2 - Average Fixed Cost, AFC o AFC (y) = FC / y - SR Total Cost, STC o STC (y) = VC (y) + FC - SR average Total cost, SAC o SAC (Y)=STC (Y)/Y o SAC(Y)= AVC(Y)+AFC(Y) Example: - A firm faces the production function y = z 12/z21/3 - z 2s fixed at 1 - The price of input 1 is $5 - The TP function is 2/3 TP(z )1= z 1 - The AP function is 2/3 AP(z 1 = z 1 z 1 = z -1/3 1 - The MP function is MP(z )1= d TP(z ) 1 d z1 = 2 z 1-1/3 - To find the VC function, TP is y = z 2/3so re-arranging, we get z = y 3/2 1 1 3/2 - VC(y) = w z 1 1 = w 1 - Since w = 5, VC(y) = 5y 3/2 1 - If the firm wants to produce 120 y, VC(120) = 5(120 ) = $6572.50 May 10, 2011 chapter 7, production and cost: many variable inputs In most real situations, firms have the ability to vary more than one input during the relevant time period. They can substitute more of one input for less of another. Production Isoquant: all the different combinations of inputs that yield the same level of total output. - E.g. our courier Marginal rate of Technical substitution, MRTS - The MRTS mesures the rate at which one input can be substituted for the other, with output remaining constant. - The MRTS is the absolute value of the slope of the isoquant. - It tells us the rate at which we must increase the qty of input 2 per unit decrease in qty of input 1. - Example: if MRTS = 2.5, if we decrease input 1 by 1, we must increase input 2 by 2.5. - Note that MRTS uses a marginal reduction in qty of input 1. - That is, since the slope is Dz / Dz , let Dz g 0. 2 1 1 Generally, it becomes progressively harder to substitute one input for another. You need more and more of input 2 to compensate for each unit decrease in input 1. MRTS gets smaller – diminishes – as we move from left to right along an isoquant. - So it means that the graph become more flatter and flatter. • When the qty of input 1 is decreased by Dz , th1 change in total output y is approximately the MP of input 1 multiplied by Dz 1 Dy = MP(z )1z 1 or Dz 1 Dy / MP(z ) 1 • The change in input 2, Dz , 2ust yield a corresponding change in output y Dy = MP(z )Dz2 2 or Dz 2 Dy / MP(z ) 2 *****MRTS=MP(Z1)/MP(Z2) Numerical example - A production function is given by y= F(z1,z2)=1
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