1. Ecological Economics Week 3 Tiago Domingos Assistant Professor Environment and Energy Section Department of Mechanical Engineering Doctoral Program and Advanced Degree in Sustainable Energy Systems Doctoral Program in Mechanical Engineering

2. Assignments Preferences (exercise 4) –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 is a bundle of goods and is a bundle of goods with at least as much of both goods and more of one, then The second good is neutral…

3. 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... –They are not complements. Y increases with px, there is a substitution. None of them is a bad….

4. Demand Effect on demand of a good Change in incomeQuantity 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 priceThe 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

5. Demand Market demand –Individual demand –Market demand Note: we sum the quantities, NOT the prices!

6. 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. –Elasticity as the responsiveness of the quantity demanded to price.

7. Demand Income elasticity of demand –Is used to describe how the quantity demanded responds to a 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

8. Demand Revenue –Revenue (R): the price of a good times the quantity sold of that good. Marginal Revenue –When | ɛ |=1, the marginal revenue curve is constant at zero. Point of maximum revenue. See Chapter 15 – Market demand: APPENDIX

9. Technology Production set –Combinations of inputs and output that are feasible patterns of production Production function –Upper boundary of production set

10. Technology Returns to scale –Constant: –Increasing: –Decreasing:

11. Profit maximization Profits (π) –Revenues minus cost Maximization of profits In the long-run both factors are free to vary while in short-run some factors are fixed See Chapter 18 –Profit maximization: APPENDIX

12. Cost minimization Cost minimization problem –Minimize cost to produce some given level of output Integrating cost minimization and profit maximization See Chapter 19 –Cost minimization: APPENDIX