Pset 0 - Test 1 - Ec202 Fall 21 - Solutions practice questions PDF

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Test 1 - Ec202 Fall 21 - Solutions practice questions...

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EC 202 – Fall 2021

Math review (“P-set #0”) The problems below are meant to remind you of some important skills you will use at some point this semester when working with the models. You must submit your answers on Blackboard and it will process it and then show you the solutions so you can check your work. (BU IT has to merge the Ec202 B and F sections together on Blackboard. Until that happens, probably on Tuesday 9/7 or Wednesday 9/8 you won’t be able to open or submit the assignment on Blackboard.)

1. This is a graph of total output (vertical) against units of labor employed (horizontal). When you make a graph in economics the slope can almost always be interpreted as a marginal [something]. He is it the marginal product of labor. Is the MPL increasing as L increases? a. yes b. no c. it depends

2. Consider this graph for the next two problems.

The relationships between some economic variables w, y and z and another economic variable, x, are shown in the graph above. Notice that the horizontal axis is labeled “x” since they are all functions of x but the vertical axis is not labeled. Does the vertical axis need a label in order for you to be able to understand the graph? Yes 3. What value of x minimizes w? 3 4. A common task when solving a model in this course is solving a system of linear equations like the one below. There is an interpretation, in words, for each equation but we’ll wait to learn about that later. The important thing right now is that you can solve this system. the equilibrium condition is What is the that solves this system? r = __2.5__ 5. (continuing from the previous question) What is the equilibrium value of ? In other words, for the value of in equilibrium, what is the associated value of ? 4.5 6. You’ll see lots of models where one variable is exogenous, and we won’t have a specific value to plug in for it. An example from the study of recessions is this model for GDP attributed to Keynes: where and . Plug in those expressions and solve for in terms of . You’ll get an equation in the form . What is for your final equation? (This is called a G multiplier.) 4 7. Sometimes we’ll need to work with exponents. Remind yourself about the rules for exponents and then determine the value of in . x=13

8. Remember that is the same as . What is the that solves ? (You can verify that works but I want you to find the other solution.) X=0.25 9. We will do a lot of plotting of equations on graphs and then do comparative statics by “shifting” the curves. This can be confusing because we often write the equation one way and then plot it with the axes “flipped” from what you would expect. Consider the equation . Suppose . Plot this equation on graph with on the vertical and on the horizontal. What is the intercept on the r axis? 4.5 10. The rule to remember about shifts of curves is “variables that are NOT on the axes can be shifters while variables on the axes are NEVER shifters.” For example, is in the equation above but is not on the axes so an increase of to will probably shift the curve. Get a new equation and graph the new curve. How did the curve shift? (There is more than one right answer.) [] up [] left [=] down [=] right 11. Sometimes you will have equations like and you are supposed to graph this on a graph with on the vertical and on the horizontal. This is equivalent to graphing an equation like on a normal x-y graph like you learned in algebra. What does look like on the graph? [] slopes up [] slopes down [] vertical line [=] horizontal line [] wavy like a sin wave 12. Let’s practice translating statements in words about the model into implications for the algebra and graphs. Suppose that investment is described by this equation: If someone said “due to higher business confidence there will be an increase in investment” they probably don’t mean that the numerical value of will go up. We don’t have a number for yet so how could we know if it increased? They probably meant “due to higher business confidence there will be more investment for any given r” or, in other words “more investment for any particular value of r.” That implies something about how the equation will change. Which equations below fit reflect an “increase in investment?” (check all that apply) []

[] [] []

13. Again consider the statement “due to higher business confidence there will be an increase in investment.” On a graph where r on is on the vertical and is on the horizontal, how would the curve “shift” due to higher business confidence? (check all that apply) [] shift right [] shift left [] shift up [] shift down 14. Suppose that I have 42 RMB and I have two options. i. I can just let it sit in the bank and accrue interest until 2030 when it will have grown into 46.39 RMB. ii. I can exchange the RMB for $s today at the current exchange rate of 7 RMB = $1, invest the $s in a project so I end up with $1.48 in 2030 for each $1 spent today, and then convert the $s back to RMB in 2030. The exchange rate in 2030 is expected to be 5 RMB per $1. 6 Which option is better? (For a short response question like this it is implied that you need to convince the reader you are right with an explanation.)

15. How many hours did this p-set take to complete? (Blackboard requires you give a numerical answer so “it took about 15 minutes” will be marked wrong. It will also mark unreasonable answers like 52 and -1 as wrong.)

It took about 30 minutes...