office hours: 8:00AM – 8:50AM tuesdays LUMS C85 ECON 102 Tutorial: Week 18 Ayesha Ali www.lancaster.ac.uk/postgrad/alia10/econ102.html a.ali11@lancaster.ac.uk office hours: 8:00AM – 8:50AM tuesdays LUMS C85

Today’s Outline Week 18 worksheet – Capital Markets: We’ll try to do some questions on the board today. Please make sure you review all of problems on your own and ask if you have any questions. If you’re unsure of any solutions here, please see Chapter 22 in your textbook – it provides detailed explanations and examples. Some notes about Friday’s Exam. If you didn’t get your exam last week, please collect it at the end of class.

Question 1(a) Data on before-tax income, taxes paid and consumption spending for the Simpson family in various years is given below. Y T C (Y-T) Before-tax income (€) Taxes paid (€) Consumption spending (€) Disposable Income 25,000 3,000 20,000 22,000 27,000 3,500 21,350 23,500 28,000 3,700 22,070 24,300 30,000 4,000 23,600 26,000 Y T C (Y-T) Before-tax income (€) Taxes paid (€) Consumption spending (€) Disposable Income 25,000 3,000 20,000 27,000 3,500 21,350 28,000 3,700 22,070 30,000 4,000 23,600 Before-tax income (€) Taxes paid (€) Consumption spending (€) 25,000 3,000 20,000 27,000 3,500 21,350 28,000 3,700 22,070 30,000 4,000 23,600 Graph the Simpsons’ consumption function and find their household’s marginal propensity to consume. First, how do we graph a consumption function? We put Disposable Income (Y-T) on the X-axis, Consumption Spending on the Y-axis. So, the first thing we can do here is find Disposable Income. The graph of the consumption function will be a straight line through these points. We write the consumption function as: 𝐶= 𝐶 +𝑐(𝑌−𝑇) where: 𝐶 is the y-intercept; it captures factors other than disposable income that affect C. 𝑐 is the MPC, or the slope of the consumption function. It is the amount by which consumption rises when disposable income rises. (𝑌−𝑇) is the disposable income.

Consumption spending (€) Question 1(a) Graph the Simpsons’ consumption function and find their household’s marginal propensity to consume. What is the marginal propensity to consume? We know that the MPC is the slope of our consumption function, so we can find it by taking the change in Consumption Spending divided by the change in Disposable Income. Before-tax income (€) Taxes paid (€) Consumption spending (€) Disposable Income 25,000 3,000 20,000 22,000 27,000 3,500 21,350 23,500 28,000 3,700 22,070 24,300 30,000 4,000 23,600 26,000 If disposable income increases from 22,000 to 23,500, a rise of 1500, consumption rises by 1350. Since 1350/1500 = 0.9, it looks like the MPC is 0.9. Can we write the Consumption Function out using the 𝐶= 𝐶 +𝑐(𝑌−𝑇) format? To do this, we need to find the intercept of the consumption function, 𝐶 . To find 𝐶 , we can plug into the equation any of the numerical combinations of consumption and disposable income given above. For example, if we set C = 20,000 and Y-T = 22,000, We get 20,000= 𝐶 +0.9(22,000), solving for 𝐶 , we get: 𝐶 =200. So the consumption function for the Simpson’s is C=200+0.9(𝑌−𝑇).

Question 1(b) How much would you expect the Simpsons to consume if their income was €32,000 and they paid taxes of €5,000? . From the consumption function derived in part (a), we can plug in Y = 32,000 and T = 5,000: C=200+0.9(𝑌−𝑇) C=200+0.9(32,000−5,000) C=200+0.9 27,000 C=24,500

Question 1(c) Homer Simpson wins a lottery prize. As a result, the Simpson family increases its consumption by €1,000 at each level of after-tax income. (‘Income’ does not include the prize money.) How does this change affect the graph of their consumption function? How does it affect their marginal propensity to consume? . The graph shifts upward by 1000 at each level of disposable income (the vertical intercept, 𝐶 , rises from 200 to 1200). The MPC is unaffected, because the increase in consumption is the same at each level of disposable income, so that the graph makes a parallel upward shift. So, the MPC, or the slope of the consumption function, does not change.

Question 2 Suppose the economy can be described as follows: consumption function is C = 1,000 + 0.75(Y  T), IP = 1,000, G = 500, NX = 0 and T = 600. Find short-run equilibrium output in this economy. In the Keynesian Cross, in equilibrium, output ,Y, equals planned aggregate expenditure PAE. Y = PAE or Y = C + I + G + NX Inserting values into this equation gives Y = 1,000 + 0.75(Y – 600) + 1,000 + 500 + 0 Solving this equation for Y yields equilibrium output Y = [1/(1-0.75)]*2,050 Y = 8,200

Question 3 For the economy described in Problem 2, where : consumption function is C = 1,000 + 0.75(Y  T), IP = 1,000, G = 500, NX = 0 and T = 600. And MPC = c = 0.75 Find the values of: The income-expenditure multiplier. The income expenditure multiplier = 1/(1-c), where c is the MPC. Inserting the value for c (= 0.75) from Problem 2 gives us 1/(1-0.75) = 4. b. The tax multiplier The tax multiplier = –c/(1-c). Inserting the value for c (=0.75) gives us -0.75/(1-0.75) = -3.

Question 4 For the economy described in Problem 3, where: consumption function is C = 1,000 + 0.75(Y  T), IP = 1,000, G = 500, NX = 0 and T = 600. The income-expenditure multiplier = 4 and the tax multiplier = -3. Find the change in equilibrium output if the government cuts net taxes by 10. We want to find the change in equilibrium output, ΔY, which result from a change in tax, ΔT. To do this, we can multiply the tax multiplier times the change in taxes, ΔT. So ΔY = [-c/(1-c)]ΔT In Q3, we calculated the tax multiplier = -c/(1-c) = -3, so we can plug that in here: ΔY = (-3)*(-10) ΔY = 30 So a cut in net taxes by 10 will raise equilibrium output by 30. Note: The taxes are reduced by 10. They are not reduced by 10%. So taxes go from 600 to 590.

Question 5 Problems 5 to 8 assume that the economy is described by the following equations: C = 1,800 + 0.6(Y  T), IP = 900, G = 1,500, NX = 100, T = 1,500, Y* = 9,000 Find the output gap in this economy. The output gap is: The difference between the economy’s potential output and its actual output at a point in time. We can write this as: Y*-Y. To find the output Y*-Y we need to calculate short-run equilibrium output Y. In equilibrium, output Y equals planned aggregate expenditure PAE, so Y = PAE Y = C + I + G + NX Inserting values into this equation gives Y = 1,800 + 0.6(Y – 1,500) + 900 + 1,500 + 100 Solving this equation for Y yields equilibrium output Y = [1/(1-0.6)]*3,400 = 8,500 So the output gap = Y*-Y = 9,000 - 8,500 = 500.

Question 6 Problems 5 to 8 assume that the economy is described by the following equations: C = 1,800 + 0.6(Y  T), IP = 900, G = 1,500, NX = 100, T = 1,500, Y* = 9,000 Find the effect on short-run equilibrium output of a decrease in planned investment from 900 to 800. So, we do the same thing steps as in Q5. Short-run equilibrium output is reduced to 8,250. IP = 800

Question 7 Problems 5 to 8 assume that the economy is described by the following equations: C = 1,800 + 0.6(Y  T), IP = 900, G = 1,500, NX = 100, T = 1,500, Y* = 9,000 Show the determination of short-run equilibrium output for this economy using the Keynesian cross diagram. Determination of Short-Run Equilibrium Output (Keynesian Cross Diagram) The line PAE = 3,400 + 0.6Y, referred to as the ‘expenditure line’, shows the relationship of PAE to output. The 45° line represents the short-run equilibrium condition Y = PAE. Short-run equilibrium output (8,500) is determined at the intersection of the two lines, point E. This type of diagram is known as a ‘Keynesian cross’.

Question 8 Problems 5 to 8 assume that the economy is described by the following equations: C = 1,800 + 0.6(Y  T), IP = 900, G = 1,500, NX = 100, T = 1,500, Y* = 9,000 If net exports are given by NX = 950  0.1Y find the value for short-run equilibrium output and the multiplier. This is just like Example 22.7 in the textbook (pgs. 588-590). To find the short-run equilibrium output, we can do the same steps as in Q5, setting Y = PAE. Y = C + I + G + NX Y = 1,800 + 0.6(Y  1,500) + 900 + 1,500 + 950 - .01(Y) Y = 0.5(Y) + 4,250 0.5(Y) = 4,250 Y = 4,250 (2) Y = 8,500 So, actually we have the same short-run equilibrium output as we did in Q5. To find the multiplier, in this case, we will get: 1/(1-c+m) where m is the marginal propensity to import. We get this because we know that Net Exports = Exports – Imports. And, that Imports are dependent on Income, so IM = mY, where m is the marginal propensity to import. Since c is 0.6 from Problem 6 and m is 0.1, the multiplier = 1/(1-c+m) = 1/(1 - 0.6 + 0.1) = 2. NX = 950  0.1Y

Question 8 Problems 5 to 8 assume that the economy is described by the following equations: C = 1,800 + 0.6(Y  T), IP = 900, G = 1,500, NX = 100, T = 1,500, Y* = 9,000 If net exports are given by NX = 950  0.1Y find the value for short-run equilibrium output and the multiplier. To find the short-run equilibrium output, we can do the same steps as in Q5, setting Y = PAE. Y = C + I + G + NX Y = 1,800 + 0.6(Y  1,500) + 900 + 1,500 + 950 - .01(Y) Y = 0.5(Y) + 4,250 0.5(Y) = 4,250 Y = 4,250 (2) Y = 8,500 So, actually we have the same short-run equilibrium output as we did in Q5. An alternative way to find the multiplier is to use the equation above. NX = 950  0.1Y 𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟= 1 1 − 𝑡ℎ𝑖𝑠 Y = 0.5(Y) + 4,250

Important Details about the Exam What to know: Check your timetable for Exam time and location. You will need to write my name on your Exam booklet, as well as your own. My name is Ayesha Ali. What to bring: Bring a pen/pencil & eraser. Bring your library card number. (You will not be allowed to turn in an exam without a library card number.) Bring a standard (non-programmable) calculator. Bring a paper English/Other Language dictionary if you need one. Electronic dictionaries will not be allowed.

Next Class Week 19 Worksheet - Money Markets Chapter 23 in the Textbook Please email me by Saturday if you’d like me to go over any Exam questions/solutions in class next week. Exam is on Friday this week – Tutors have 4 weeks to complete marking The office will probably take a week or two for processing So, if there are no problems at all, you should get your exam results back in roughly 5 weeks. Please be patient and work hard in the meantime. Good luck!