HW1_Sketch_Solutions_-_Fall_2022 (3)

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ECO 206Y1Y: Microeconomic Theory Prof. Freitas, University of Toronto Eco 206 HW1 , Sketch Solutions These are sketch solutions only. If you still have questions, please stop by office hours. Q1 Given two goods: nectarines and peaches. Income is $500. Nectarines are $5 a kilo for the first 50 kilos, $2.5 a kilo between 50 and 100 kilos, and $1 a kilo after. Peaches are $10 a kilo. Assume that one peach weighs the same as one nectarine. 1) What is the Opportunity Cost of an extra peach? 2) Draw your budget line (peaches on the x-axis and nectarines on the y-axis) and indicate how it will change when (a) the price of nectarines decreases by $2.5 for the first 50 kilos. (b) and your income decreases by $250. 3) Assume now that you have endowment income. Endowment is 20 kilos of nectarines and 20 kilos of peaches. For this part of the question, assume a constant price of $5 a kilo for nectarines and $10 a kilo for peaches. (a) What is the Opportunity Cost of an extra peach? How does this differ from part 1)? (b) Draw the budget line (peaches on the x-axis and nectarines on the y-axis) and show what happens if the price of nectarines increases by $5 a kilo. Solution: 1) The Opportunity Cost depends on where we calculate it. For points on the Budget Constraint where the quantity of nectarines is less than 50 kilos then the OC is 2 nectarines. Between 50 kilos and 100 kilos, the OC is 4 nectarines. After that it is 10 nectarines. 2a) 6KJGIHNMKJX ±QPONRQTX° 1KJIHYGWONSKJX ±QPONRQTX° ² ³ ´ ³ 9RQTUKJ ($"( µ¶ 9RQTUKJ ($"( µ·³ ·³³ ³ ·²¸ ²² 9RQTUKJ ($"( µ² 9RQTUKJ ($"( µ¶ 9RQTUKJ ($"( µ·³ 2b) 202209 1 of 3 HW1

ECO 206Y1Y: Microeconomic Theory Prof. Freitas, University of Toronto 6KJGIHNMKJX ±QPONRQTX° 1KJIHYGWONSKJX ±QPONRQTX° ² ³ ´ ³ µ³³ ³ µ²¶ ²² 9RQTUKJ ($"( ·² 9RQTUKJ ($"( ·¸ 9RQTUKJ ($"( ·² 3a) Opportunity Cost of an extra peach is 2 nectarines. 3b) 5JJFHHMMJJX ±PPNNQTX° 3JJHHYFWNNSJJX ±PPNNQTX° ! ² ³² ´² ´² µ² ³² 202209 2 of 3 HW1

ECO 206Y1Y: Microeconomic Theory Prof. Freitas, University of Toronto Q2 You work for a food bank. your goal is to increase the number of affordable bundles for the food bank. The only source of income for the food bank is donations. Would you recommend people make donations in cash or in-kind? Explain your reasoning using a clearly labeled Budget Constraints. Make sure to clearly label the axes and the Opportunity Cost. Solution: Here you had two hard choices to make- (1) your axes and (2) the type of income, endogenous or exogenous. They are both determined by the eventual goal you want to achieve. If you want to think about different types of in-kind donations only, e.g. canned goods vs. fresh produce or baby formula etc. Then you would choose two of them as your axes. Cash donations would be the income that could be spent on the two goods i.e. exogenous income. If you want to think about endogenous income your only possibility is a basket of goods on your axes, no cash possible. It isn’t really possible to think about both cash and in-kind donations as income with these axes. If you want to think about cash donations as one type of income the food bank gets along with in-kind donations, then it means you have to pick the composite good (i.e. cash) as one of your axes. The other axis would then have to be something you think of as another important form of donation e.g. canned goods (specific) or in-kind donations (more general). The benefit of it is that you can think about questions like two types of donations and the differences between them (e.g. inability to sell in-kind donations etc.) The cost is that you are limiting one axes to a good with a price of $1 which can’t be changed as it is the definition of the good. The most common answer for students working within this framework was to impose the additional restriction that in-kind donations could not be converted into the composite good but cash could be converted into in-kind goods. This would be similar to the problem set example. 202209 3 of 3 HW1

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