Week 5 Tutorial Questions Solutions (Ch3 & 4) Chapter 3: Q1: Macroeconomics P.100 Numerical Problems #3 Q2: Macroeconomics P.102 Analytical Problems #1 Chapter 4: Q3: Macroeconomics P.142 Numerical Problems #6 Q4: Macroeconomics P.143 Analytical Problems #5 Q1: Acme Widget, Inc. has the following production function: Number of Workers 0 1 2 3 4 5 6 a. Answer: b. Answer: Number of Widgets Produced 0 8 15 21 26 30 33 MPN MRPN (P = $ 5) MRPN (P = $ 10) N/A 8 7 6 5 4 3 N/A 40 35 30 25 20 15 N/A 80 70 60 50 40 30 Find the MPN for each level of employment. Refer to the above table. Acme can get $5 for each widget it produces. How many workers will it hire if the nominal wage is $38? If it is $27? If it is $22? (1) W = $38. Hire one worker, since MRPN ($40) is greater than W ($38) at N = 1. Do not hire two workers, since MRPN ($35) is less than W ($38) at N = 2. (2) W = $27. Hire three workers, since MRPN ($30) is greater than W ($27) at N = 3. Do not hire four workers, since MRPN ($25) is less than W ($27) at N = 4. (3) W = $22. Hire four workers, since MRPN ($25) is greater than W ($22) at N = 4. Do not hire five workers, since MRPN ($20) is less than W ($22) at N = 5. Week 5 Page 1 With the nominal wage fixed at $38 and the price of widgets fixed at $5. What happens to labour demand and production? If output doubles. Answer: Week 5 Graph the relationship between Acme’s labour demand and the nominal wage. So the increase in the price of the product increases the firm's labour demand and output. MPN doubles. What happens to Acme’s labour demand and production? P = $10. the firm should hire five workers. This graph is different from a labour demand curve because a labour demand curve shows the relationship between labour demand and the real wage. The table in part a shows the MRPN for each N. MRPN ($40) is greater than W ($38) at N = 5. How does this graph differ from a labour demand curve? Graph Acme’s labour demand curve. the introduction of a new automatic widget market doubles the number of widgets that workers can produce.Week 5 Tutorial Questions Solutions (Ch3 & 4) c. compared to 8 widgets in part (a) when the firm hired only one worker. Answer: e. Figure 1 plots the relationship between labour demand and the nominal wage. Answer: d. since MRPN ($30) is less than W($38) at N = 6. With five workers. Figure 2 shows the labour demand curve. With the nominal wage fixed at $38. The MPRN is the same as it was in part (d) when the price doubled. At W = $38. the price of widgets doubles from $5 each to $10 each. The firm shouldn't hire six workers. So labour demand is Page 2 . output is 30 widgets. so MPRN doubles. the choice is the same. Show how this change affects the graphs of both the production function relating output to capital and the production function relating output to labour. The marginal product of capital (MPK) in the initial situation is Page 3 . But the output produced by five workers now doubles to 60 widgets. whether P doubles or MPN doubles. Answer: Week 5 Show that a 10% increase in A also increases the MPK and the MPN by 10% at any level of capital and labour.1Y2 when productivity rises by 10%. a. What is the relationship between your answers to part (d) and part (e)? Explain. capital K1 and labour N1produce output Y1. when productivity rises they produce output 1. (Hint: What happens to ∆Y for any increase in capital ∆K or for any increase in labour ∆N?) In the initial situation. Answer: Since MRPN = P x MPN. f. then a doubling of either P or MPN leads to a doubling of MRPN.Week 5 Tutorial Questions Solutions (Ch3 & 4) the same as it was in part (d). Answer: b. Then it produces 1. Suppose that a small increase in capital to K2 with labour left at N1 produces output Y2 in the initial situation. Q2: A technological breakthrough raises a country’s total factor productivity A by 10%. Since labour demand is chosen by setting MRPN equal to W.1 Y1. Desired consumption and desired investment are Cd = 360 – 200r + 0.9Y Page 4 . Can a beneficial supply shock leave the MPK and MPN unaffected? Show graphically. Government purchases. are 120. Answer: Week 5 Find an equation relating desired national saving Sd to r and Y. leaving the slope unchanged. Q3: An economy has full-employment output of 600.Week 5 Tutorial Questions Solutions (Ch3 & 4) (Y2− Y1) / (K2– K1). it is possible for a beneficial productivity shock to leave the MPK and MPN unchanged. Answer: Yes. This could happen only if the shock was additive that is.10Y. Sd = Y – C – G = Y – (360 – 200r + 0. but did not affect its slope at any point.1 (Y2 − Y1) / (K2 − K1). a. and Id = 120 – 400r Where Y is output and r is the real interest rate. c. if it shifted the whole production function upward. So the new MPK is 10% higher than the old MPK. 3and 4 this is shown as a shift up in the production function.1 Y1) / (K2− K1) = 1.1 Y2−1. In Figs. when productivity rises the new MPK is (1.1 Y) – 120 = –480 + 200r + 0. G. you will show that the new MPN is 10% higher than the old MPN. so it holds for MPN as well. This argument is completely symmetric. If you substitute N for K everywhere and follow the same steps. Answer: Using both versions of the goods market equilibrium condition. Government purchases rise to 144.8).1 Y) – 144 = –504 + 200r + 0. (1) Using Eq: Y = Cd + Id + G Y = (360 + 200r + 0. this shows as a shift in the Sd line from S1 to S2 in the following figure. Y = 600.10.9Y = 600 – 600r At full employment. so r = 0. r = 0. (4.9 x 600) = 84.1Y So 0.1 Y) + (120 – 400r) +120 = 600 – 600r+ 0. we get:–504 + 200r+ 0. c.9Y.9Y = 120 – 400r0.9 × 600 = 600 – 600r. Week 5 Page 5 . desired saving becomes Sd = Y – Cd– G = Y – (360 – 200r + 0. So we can use either Y = Cd + Id + G or Sd = Id to get to the same result. we get r = 0. Assume that output equals full employment output. What happens to the market-clearing real interest rate? Answer: When G = 144. The market-clearing real interest rate increases from 10% to 14%.9Y = 624 At Y = 600.10. this is 600r = 624 – (0.7) and (4. (2) Using Eq: Sd = Id –480 + 200r + 0. Setting Sd = Id. Solving 0.9Y = 600 – 600r When Y = 600.14. find the real interest rate that clears the goods market. How does this increase change the equation describing desired national saving? Show the change graphically. Eqs.9Y = 120 – 400r600r + 0.Week 5 Tutorial Questions Solutions (Ch3 & 4) b. Sd is now 24 less for any given r and Y. so national saving (Sd = Y – Cd– G) declines at the initial real interest rate. with both current and future consumption declining.) Answer: When there is a temporary increase in government spending. consumers foresee future taxes. investment. the real interest rate is higher. focusing on effects on consumption. as shown in Fig. (Hint: The permanent increase in government purchases implies larger increases in current and future taxes. As a result.Week 5 Tutorial Questions Solutions (Ch3 & 4) Q4: “A permanent increase in government purchases has a larger effect than a temporary increase of the same amount. and the real interest rate for a fixed level of output. they will reduce their current and future consumption by about the same amount. consumption fails by more in the case of a permanent increase in government spending. So the saving curve in the saving-investment diagram does not shift. But if there is an equal increase in current and future government spending. and consumers try to smooth consumption. When there is a permanent increase in government spending. consumption declines. and there is no change in the real interest rate. consumers foresee future taxes as well. so investment declines by more. Thus current consumption does not fall by as much as the increase in G. 5. and that amount will be about the same amount as the increase in government spending. Thus the real interest rate increases and consumption and investment both fall. However. Since the saving curve shifts upward more in the case of a temporary increase in government spending. both currently and in the future. and the saving curve shifts to the left from S1 to S2.” Use the saving-investment diagram to evaluate this statement. Week 5 Page 6 .