1. ECON 102 Tutorial: Week 22 Shane Murphy www.lancaster.ac.uk/postgrad/murphys4/econ15 s.murphy5@lancaster.ac.uk

2. Question 1 Given the macroeconomic system: IS schedule: r = 8 - 0.006 Y LM schedule: r = - 3 + 0.003 Y Determine equilibrium values for national income and the interest rate r = 8 - 0.006 Y r = - 3 + 0.003 Y 0 = 11 - 0.009 Y Y = 11/0.009 =1222.2 r = 8 - 0.006 (1222.222) = 0.667

3. Question 1 Provide brief explanations of the IS schedule and the LM schedule: When interest rates go down, the cost of borrowing money goes down, so people borrow more. When people borrow more they have more cash to spend, therefore the amount of things people buy depends on the interest rate. Thats the IS part. As interest rates decreases, output increases in the goods market. It slopes downwards. When people are rich, they want to hold more money in their wallet instead of in the bank, which decreases the amount of money in the bank. When banks have less money in them, the interest rate at which the banks make loans (interest rate is the cost of borrowing remember) increases. So when income is high, interest rates are high. Thats the LM part. It slopes upwards. The IS/LM model puts these two lines together on the same graph. And shows how one interest rate puts both the IS side and the LM side in balance.

4. Question 2 Write down the equation of the IS schedule. S = Y- (100 + 0.6 Y) = 0.4Y - 100 J = I + G = 500 - 40 r + 200 S = J 0.4Y - 100 = 500 - 40 r 40 r = 800 - 0.4 Y r = 20 - 0.01 Y C = 100 + 0.6 Y I = 500 - 40 r G = 200 L t = 0.4 Y L a = 200 - 50 r Ms = 600 Y = C + I + G Md = L t + L a Md = Ms

5. Question 2 Write down the equation of the LM schedule. L = 0.4 Y + 200 - 50 r Ms = 600 L = M 0.4 Y + 200 - 50 r = 600 - 50 r = 400 - 0.4 Y 50 r = - 400 + 0.4 Y r = - 8 + 0.008 Y C = 100 + 0.6 Y I = 500 - 40 r G = 200 L t = 0.4 Y L a = 200 - 50 r Ms = 600 Y = C + I + G Md = L t + L a Md = Ms

6. Question 2 Calculate the equilibrium levels of national income and the interest rate. r = 20 - 0.01 Y r = - 8 + 0.008 Y 0 = 28 - 0.018 Y Y = 28/0.018 = 1555.55 r = 20 - 0.01 (1555.55) = 20 - 15.555 r = 4.44 C = 100 + 0.6 Y I = 500 - 40 r G = 200 L t = 0.4 Y L a = 200 - 50 r Ms = 600 Y = C + I + G Md = L t + L a Md = Ms

7. Question 3 Write down the equation of the IS schedule. Y = C + I + G Y = 40 + 0.8 Yd + 200 - 20 r + 400 Y = 40 + 0.8(1 - 0.1) + 200 - 20 r + 400 Y = 640 + 0.72 Y - 20 r 20 r = 640 + 0.72 Y - Y 20 r = 640 - 0.28 Y r = 32 - 0.014 Y C = 40 + 0.8 Yd I = 200 - 20 r G = 400 t = 0.1 Yd = (1 - t) Y Lt = 0.3 Y La = 600 - 120 r Ms = 300 Y = C + I + G Md = Lt + La Md = Ms

8. Question 3 Write down the equation of the LM schedule. Md = Ms L t + L a = Ms 0.3 Y + 600 - 120 r = 300 120 r = 300 + 0.3 Y r = 2.5 + (0.3/120) Y r = 2.5 + 0.0025 Y C = 40 + 0.8 Yd I = 200 - 20 r G = 400 t = 0.1 Yd = (1 - t) Y Lt = 0.3 Y La = 600 - 120 r Ms = 300 Y = C + I + G Md = Lt + La Md = Ms

9. Question 3 Calculate the equilibrium levels of national income and the interest rate. r = 32 - 0.014 Y r = 2.5 + 0.0025 Y 0 = 29.5 - 0.0165Y 0.0165 Y = 29.5 Y = 1787.88 C = 40 + 0.8 Yd I = 200 - 20 r G = 400 t = 0.1 Yd = (1 - t) Y Lt = 0.3 Y La = 600 - 120 r Ms = 300 Y = C + I + G Md = Lt + La Md = Ms

10. Question 3 Calculate the impact upon equilibrium when money in circulation is increased to 450. IS schedule: r = 32 - 0.014 (1863.6) LM schedule: r = 1.25 + 0.0025 (1863.6) r = 5.91 Y = 1863.6

12. Practice Past Exam Questions (And Questions from Last Year’s Tutorials) Please Note: Solutions are not given to tutors for these questions. The solutions I’ve prepared are only suggestions only – I cannot guarantee they are correct.

13. UK National Debt comprises: (a) the sum of trade deficits over past years (b) sterling currency notes and coins in circulation, plus commercial bank deposits (c) outstanding loans to the state, excluding sterling currency notes and coins in circulation (d) outstanding loans to the state, including sterling currency notes and coins in circulation 2012 Exam Q32

14. Problem From Last Year You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: M D = 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; and the real money supply is £850 billion. Find the equilibrium interest rate (r) and the equilibrium income (Y). This problem from last year is very similar to Q7, but is written up as a word problem. See if you can solve it and check your answers against mine in the following slides.

15. Problem From Last Year You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: M D = 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; and the real money supply is £850 billion. Find the equations of the IS curve In the product market, equilibrium occurs when Y = C + I and so: C = 100 + 0.75Y I = 500 -10r We can plug these in to Y = C + I Y = 100 + 0.75Y + 500 – 10r 0.25Y = 600 -10r Y = 2400 – 40rThis is equation of the IS curve. Note: The coefficient on r is negative here because the lower the interst rate, the cheaper it is to invest, so investment will increase. There is an inverse relationship between the two. 2013/2014 Week 18

16. Problem From Last Year You are given the following information about an economy: autonomous consumption is £100 billion; autonomous investment is £500 billion; the marginal propensity to consume is 0.75; the coefficient on interest in the marginal efficiency of investment function is 10; the demand for money function takes the form: M D = 0.5Y – 15r, where Y is the economy's real output and r is the interest rate expressed as a percentage; the real money supply is £850 billion. Find the equations of the LM curve. In the money market, equilibrium occurs when M D = M S and so: M D = M S 0.5Y – 15r = 850 0.5Y = 850 + 15r Y = 1700 + 30rThis is the equation of the LM curve. 2013/2014 Week 18

17. Problem From Last Year In part (a) we found: IS curve: Y = 2400 – 40r LM curve: Y =1700 + 30r What are the equilibrium income and rate of interest in the economy given the information above? To find the equilibrium, set IS equal to LM: IS = LM 2400 – 40r = 1700 + 30r 70r = 700 r = 10% This is the equilibrium interest rate. To find the equilibrium income, we can plug this value of r into either expression for Y and obtain Y = £2,000 billion. 2013/2014 Week 18

18. IS Curve is Equilibrium in the Goods Market To solve for the IS curve set Output (Y) equal to Expenditure (C+I+G). I is usually a function of interest rate (r). To the up and right of the IS-curve, output is greater than Expenditure, while to the bottom and left of the IS-Curve, Output is less than Expenditure. To shift the IS curve to the right, we need to increase Expenditure (usually, I or G). Likewise, to shift IS to the left, we would need to decrease Expenditure. 2013/2014 Week 18

19. LM Curve is Equilibrium in the Money Market To solve for the LM-curve set Money Supply (Ms) equal to Money Demand (Md). Money Supply is usually constant and Money Demand is usually a function increasing in output (Y) and decreasing in interest rates (r). To shift the LM curve to the right, we need to increase Money Supply or decrease Money Demand (this could be done through increasing interest rates). Likewise, to shift LM to the left, we would need to decrease Money Supply or increase Money Demand (again, by using interest rates). 2013/2014 Week 18