Tutorial 1 Solutions v2 PDF

Preview

Summary

EC1002 TUTORIAL 1 WEEK 3EXERCISE 1. 5 HOW MUCH DIFFERENCE DOES A COUPLE OF DEGREES WARMER OR COLDER MAKE? (Ch 1 .5) Between 1300 and 1850 there were a number of exceptionally cold periods as you can see from Figure 1. Research this so-called ‘little ice age’ in Europe and answer the following. Descr...

Description

EC1002 TUTORIAL 1 WEEK 3 EXERCISE 1.5 HOW MUCH DIFFERENCE DOES A COUPLE OF DEGREES WARMER OR COLDER MAKE? (Ch 1.5) Between 1300 and 1850 there were a number of exceptionally cold periods as you can see from Figure 1.6b. Research this so-called ‘little ice age’ in Europe and answer the following.

•

•

Describe the effects of these exceptionally cold periods on the economies of these countries. Within a country or region, some groups of people were exceptionally hard hit by the climate change while others were less affected. Provide examples. How ‘extreme’ were these cold periods compared to the temperature increases since the mid-twentieth century and those projected for the future?

There is no single correct answer to this question – however there are many incorrect ones! In answering this question, you are expected to do independent research into the impact of the Little Ice Age in Europe. This research should allow you to comment on the impacts of the Little Ice Age on people’s lives, as well as how these impacts differed by geography, wealth, and other differences. The answer doesn’t need to be a comprehensive review of the topic, but should include some specific examples, such as: “The Little Ice Age resulted in much colder temperatures than usual in Britain. During this time ice skating was popular, as water bodies were regularly frozen solid, something that is no longer the case today. Agriculture suffered considerably: there were frequent famines and relatively high mortality.” The Little Ice Age was a temperature anomaly of much less than 2 degrees centigrade, yet had substantial effects in some areas, and on some people. This is a small change with respect to what is predicted to result due to climate change over the next 100 years. According to climateactiontracker.org, current policies are predicted to lead to a 2.8-3.2 degree warming by 2100.

EXERCISE 1.10 APPLES AND WHEAT (Ch 1.8) Consider the example of Greta and Carlos in Chapter 1.8. Suppose that market prices were such that 35 apples could be bought for 1 tonne of wheat. • If Greta sold 16 tonnes of wheat, would both she and Carlos still be better off? • What would happen if only 20 apples could be bought for the price of a tonne of wheat? To answer this question we need to refer back to Chapter 1.8. Recall Figure 1.9 where we see Greta and Carlos’ consumption choice a) under self-sufficiency and b) under trade. In constructing this example, the textbook assumed that the “market rate” at which Greta and Carlos can exchange is 40 apples for 1 wheat.

Part 1: trade 16 wheat at market price of 35 apples per wheat If Greta specializes in wheat and sells 16 wheat to Carlos, she will receive 16x35=560 apples in return. She now has 560 apples and 34 wheat. If we compare this to her self-sufficiency consumption (500 apples, 30 wheat), we see she is still better off for both goods. Carlos now bought 16 wheat for 560 apples; that leaves him with 1000-560 =460 apples. Under self-sufficiency, Carlos had 300 apples and 14 wheat; now he has 460 apples and 16 wheat. So they are both better off at these trade prices than they would be under self-sufficiency. Part 2: trade 16 wheat at market price of 20 apples per wheat If Greta specializes in wheat and sells 16 wheat to Carlos, she will receive 16x20=320 apples in return. She now has 320 apples and 34 wheat. If we compare this to her self-sufficiency consumption (500 apples, 30 wheat), we see she has many fewer apples, and slightly more wheat. We cannot tell for certain whether Greta is worse off with respect to her self sufficiency consumption (she has fewer apples, but more wheat), but we suspect she is worse off.* Carlos now bought 16 wheat for 320 apples; that leaves him with 1000-320 =680 apples. Under self-sufficiency, Carlos had 300 apples and 14 wheat; now he has 680 apples and 16 wheat. Carlos is still better off.

* This explanation goes beyond what is asked in the question, but to see why, follow the reasoning here. It is possible that her preferences are such that she prefers this bundle of goods to her self sufficient production, but there is also a good chance she does (she would have to really prefer wheat!). We know that Greta can “transform” wheat into apples at a rate of 1:25. Supposing she kept her self sufficient wheat consumption level of 30 wheat, she could then make 4 fewer wheat and 100 more apples, bringing her basket to (420 apples, 30 wheat). This is now strictly less than she could make

EXERCISE 3.2 PRODUCTION FUNCTIONS (Ch 3.1) • Draw a graph to show a production function that, unlike Alexei’s, becomes steeper as the input increases. • Can you think of an example of a production process that might have this shape? Why would the slope get steeper? • What can you say about the marginal and average products in this case? This description corresponds to what is known as a convex function. Many examples are possible: one simple one is y=x2 (see below). This question does not ask for an equation, so your illustrated graph simply must “become steeper as the input increases.”

You can think about anything that you get better at, the more you do it. For example, the initial stages of learning a language: input = hours studied, output = knowledge of the language (for example, the number of foreign words the students has learned). Learning a language involves a 'learning curve', so initially an extra hour of study will not improve the knowledge of the language by much (as an absolute beginner you have to learn how to read or pronounce the words). Once the basics of that language have been mastered, then every additional hour of study can improve knowledge by a greater amount. The marginal product is increasing: the slope of the production function is getting steeper. That means that each additional unit of input adds marginally more than the previous one: average product will also increase. Since each additional unit of input adds more than the previous one, marginal product will also be greater than average product.

EXERCISE 3.3 WHY INDIFFERENCE CURVES NEVER CROSS (Ch 3.2) In the diagram below, IC1 is an indifference curve joining all the combinations that give the same level of utility as A. Combination B is not on IC1.

• •

• •

Does combination B give higher or lower utility than combination A? How do you know? Draw a sketch of the diagram, and add another indifference curve, IC2, that goes through B and crosses IC1. Label the point at which they cross as C. Combinations B and C are both on IC2. What does that imply about their levels of utility? Combinations C and A are both on IC1. What does that imply about their levels of utility? According to your answers to (3) and (4), how do the levels of utility at combinations A and B compare? Now compare your answers to (1) and (5), and explain how you know that indifference curves can never cross.

Combination B gives a higher utility than combination A: B is above IC1. You can sketch IC2 in different ways, as long as it goes through B and crosses IC1: the example below has the indifference curves

crossing above point A, but they could also cross below it. Both combinations B and C provide the same utility because they are on the same indifference curve. Both combinations A and C have the same levels of utility because they are on the same indifference curve. Based on the answers to questions (3) and (4), combinations A and B must also have the same level of utility. This contradicts our first observation about A and B. However, the conclusion was wrong because the indifference curves IC1 and IC2, which represent two different levels of utility, were crossing each other. Since there cannot be a point on a higher-utility indifference curve that gives the same utility as a point on a lower-utility indifference curve, indifference curves cannot cross.

EXERCISE 3.4 YOUR MARGINAL RATE OF SUBSTITUTION (3.2) Imagine that you are offered a job at the end of your university course with a salary per hour (after taxes) of £12.50. Your future employer then says that you will work for 40 hours per week leaving you with 128 hours of free time per week. You tell a friend: ‘at that wage, 40 hours is exactly what I would like.’ •

• •

• •

Draw a diagram with free time on the horizontal axis and weekly pay on the vertical axis, and plot the combination of hours and the wage corresponding to your job offer, calling it A. Assume you need about 10 hours a day for sleeping and eating, so you may want to draw the horizontal axis with 70 hours at the origin. Now draw an indifference curve so that A represents the hours you would have chosen yourself. Now imagine you were offered another job requiring 45 hours of work per week. Use the indifference curve you have drawn to estimate the level of weekly pay that would make you indifferent between this and the original offer. Do the same for another job requiring 35 hours of work per week. What level of weekly pay would make you indifferent between this and the original offer? Use your diagram to estimate your marginal rate of substitution between pay and free time at A.

Points 1-4 are best illustrated with diagrams: please see the PDF. For point 5, refer to the first indifference curve you drew, which just touches the feasible frontier (in this case, a budget constraint) at A. We know that at this point (the tangency point) the slope of the indifference curve is equal to the slope of the feasible frontier. The slope of budget constraint is -wage, or -£12.50. The MRS at Point A is therefore £12.50. The worker is willing to give up one unit of free time in exchange for £12.50 at that point (or, similarly, the worker is willing to give up £12.50 in consumption in exchange for an additional hour of free time at that point)....