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Doctoral Program and Advanced Degree in Sustainable Energy Systems Doctoral Program in Mechanical Engineering Ecological Economics Week 3 Tiago Domingos Assistant Professor Environment and Energy Section Department of Mechanical Engineering Assignments • Preferences (exercise 4) x1 , x2 y1 , y2 iff x1 y1 – Convex definition: try to represent the indifference curves and understand the relationship between the extreme and average bundles. – Monotony definition: note that we assume that more is better, that is, that we are talking about goods, not bads. More precisely, if x1 , x2 is a bundle of goods and y1 , y2 is a bundle of goods with at least as much of both goods and more of one, then y1 , y2 x1 , x2 The second good is neutral… Assignments • Preferences (extra exercise) – Be aware that, Joana’s parents allow her to leave aside everything she dislikes eating!! • Choice (exercise 2) – You should explain the math... m 15 p x y 3 py x 2m 5 3 px x o 2m m If 5 0 there is a corner solution and y 3 px py – They are not complements. Y increases with px, there is a substitution. None of them is a bad…. Demand Effect on demand of a good Change in income Quantity demanded increases with income– normal goods. For some normal goods, the quantity demanded increases more than proportionally with income – luxury goods. For other normal goods, the quantity demanded increases less than proportionally with income – necessary goods. Quantity demanded decreases with an increase in income – inferior good (example: low quality food) Change in own price The quantity demanded for good 1 increases when its price decreases – ordinary good The quantity demanded for good 1 decreases with its price – Giffen good Change in the price of the other good The demand for good 1 increases when the price of good 2 increases – good 1 is a substitute for good 2 The demand for good 1 decreases when the price of good 2 increases – good 1 is a complement to good 2 Demand • Market demand – Individual demand x11 p1 , p2 , m1 population of consumers . n x1 p1 , p2 , mn . . – Market demand X 1 x1i p1 , p2 , m n i 1 Note: we sum the quantities, NOT the prices! Demand • Elasticity of demand – The price elasticity of demand, ɛ, is defined to be the percent change in quantity divided by the percent change in price. Elasticity is unit-free. 1 elastic demand dq q p dq and if 1 inelastic demand dp p q dp 1 unit elastic demand – Elasticity as the responsiveness of the quantity demanded to price. Demand • Income elasticity of demand – Is used to describe how the quantity demanded responds to a change in income. income elasticity – – – – % change in quantity % change in income Normal good: income elasticity of demand is positive Inferior good: income elasticity of demand is negative Luxury good: income elasticity of demand greater than 1 Necessary good: income elasticity of demand smaler than 1 Demand • Revenue – Revenue (R): the price of a good times the quantity sold of that good. R pq • Marginal Revenue MR dR dq – When |ɛ|=1, the marginal revenue curve is constant at zero. Point of maximum revenue. See Chapter 15 – Market demand: APPENDIX Technology • Production set – Combinations of inputs and output that are feasible patterns of production • Production function – Upper boundary of production set Technology • Returns to scale f x1 , x2 and 1 – Constant: f x1, x2 f x1 , x2 – Increasing: f x1, x2 f x1 , x2 – Decreasing: f x1, x2 f x1, x2 Profit maximization • Profits (π) – Revenues minus cost n m i 1 i 1 pi xi i xi • Maximization of profits max pf x1 , x2 1 x1 2 x2 x1 , x2 • In the long-run both factors are free to vary while in short-run some factors are fixed y * f x1* , x2* x p, 1 , 2 * 1 x2* p, 1 , 2 y * f p, 1 , 2 See Chapter 18 –Profit maximization: APPENDIX Cost minimization • Cost minimization problem – Minimize cost to produce some given level of output 1 x1 2 x2 min x1 , x2 s.t. f x1 , x2 y See Chapter 19 –Cost minimization: APPENDIX • Integrating cost minimization and profit maximization 1 x1 2 x2 min x1 , x2 C y, 1 , 2 s.t. f x1 , x2 y max pf x1 , x2 1 x1 2 x2 max py C y, 1 , 2 x1 , x2 y