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
Week 5 Tutorial Questions Solutions (Ch3 & 4) c.
Answer:
d. Answer:
e.
Answer:
Week 5
Graph the relationship between Acme’s labour demand and the nominal wage. How does this graph differ from a labour demand curve? Graph Acme’s labour demand curve. Figure 1 plots the relationship between labour demand and the nominal wage. This graph is different from a labour demand curve because a labour demand curve shows the relationship between labour demand and the real wage. Figure 2 shows the labour demand curve.
With the nominal wage fixed at $38, the price of widgets doubles from $5 each to $10 each. What happens to Acme’s labour demand and production? P = $10. The table in part a shows the MRPN for each N. At W = $38, the firm should hire five workers. MRPN ($40) is greater than W ($38) at N = 5. The firm shouldn't hire six workers, since MRPN ($30) is less than W($38) at N = 6. With five workers, output is 30 widgets, compared to 8 widgets in part (a) when the firm hired only one worker. So the increase in the price of the product increases the firm's labour demand and output.
With the nominal wage fixed at $38 and the price of widgets fixed at $5, the introduction of a new automatic widget market doubles the number of widgets that workers can produce. What happens to labour demand and production? If output doubles, MPN doubles, so MPRN doubles. The MPRN is the same as it was in part (d) when the price doubled. So labour demand is Page 2
Week 5 Tutorial Questions Solutions (Ch3 & 4) the same as it was in part (d). But the output produced by five workers now doubles to 60 widgets.
f.
What is the relationship between your answers to part (d) and part (e)? Explain.
Answer:
Since MRPN = P x MPN, then a doubling of either P or MPN leads to a doubling of MRPN. Since labour demand is chosen by setting MRPN equal to W, the choice is the same, whether P doubles or MPN doubles.
Q2:
A technological breakthrough raises a country’s total factor productivity A by 10%. Show how this change affects the graphs of both the production function relating output to capital and the production function relating output to labour.
a.
Answer:
b.
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. (Hint: What happens to ∆Y for any increase in capital ∆K or for any increase in labour ∆N?) In the initial situation, capital K1 and labour N1produce output Y1; when productivity rises they produce output 1.1 Y1. Suppose that a small increase in capital to K2 with labour left at N1 produces output Y2 in the initial situation. Then it produces 1.1Y2 when productivity rises by 10%. The marginal product of capital (MPK) in the initial situation is Page 3
Week 5 Tutorial Questions Solutions (Ch3 & 4) (Y2− Y1) / (K2– K1); when productivity rises the new MPK is (1.1 Y2−1.1 Y1) / (K2− K1) = 1.1 (Y2 − Y1) / (K2 − K1). So the new MPK is 10% higher than the old MPK. This argument is completely symmetric, so it holds for MPN as well. If you substitute N for K everywhere and follow the same steps, you will show that the new MPN is 10% higher than the old MPN.
c.
Can a beneficial supply shock leave the MPK and MPN unaffected? Show graphically.
Answer:
Yes, it is possible for a beneficial productivity shock to leave the MPK and MPN unchanged. This could happen only if the shock was additive that is, if it shifted the whole production function upward, but did not affect its slope at any point. In Figs. 3and 4 this is shown as a shift up in the production function, leaving the slope unchanged.
Q3:
An economy has full-employment output of 600. Government purchases, G, are 120. Desired consumption and desired investment are Cd = 360 – 200r + 0.10Y, and Id = 120 – 400r Where Y is output and r is the real interest rate. a.
Answer: Week 5
Find an equation relating desired national saving Sd to r and Y. Sd = Y – C – G = Y – (360 – 200r + 0.1 Y) – 120 = –480 + 200r + 0.9Y Page 4
Week 5 Tutorial Questions Solutions (Ch3 & 4) b.
Answer:
Using both versions of the goods market equilibrium condition, Eqs. (4.7) and (4.8), find the real interest rate that clears the goods market. Assume that output equals full employment output. (1) Using Eq: Y = Cd + Id + G Y = (360 + 200r + 0.1 Y) + (120 – 400r) +120 = 600 – 600r+ 0.1Y So 0.9Y = 600 – 600r At full employment, Y = 600. Solving 0.9 × 600 = 600 – 600r, we get r = 0.10. (2) Using Eq: Sd = Id
–480 + 200r + 0.9Y = 120 – 400r0.9Y = 600 – 600r When Y = 600, r = 0.10. So we can use either Y = Cd + Id + G or Sd = Id to get to the same result.
c.
Government purchases rise to 144. How does this increase change the equation describing desired national saving? Show the change graphically. What happens to the market-clearing real interest rate?
Answer:
When G = 144, desired saving becomes Sd = Y – Cd– G = Y – (360 – 200r + 0.1 Y) – 144 = –504 + 200r + 0.9Y. Sd is now 24 less for any given r and Y; this shows as a shift in the Sd line from S1 to S2 in the following figure. Setting Sd = Id, we get:–504 + 200r+ 0.9Y = 120 – 400r600r + 0.9Y = 624 At Y = 600, this is 600r = 624 – (0.9 x 600) = 84, so r = 0.14. The market-clearing real interest rate increases from 10% to 14%.
Week 5
Page 5
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.” Use the saving-investment diagram to evaluate this statement, focusing on effects on consumption, investment, and the real interest rate for a fixed level of output. (Hint: The permanent increase in government purchases implies larger increases in current and future taxes.)
Answer:
When there is a temporary increase in government spending, consumers foresee future taxes. As a result, consumption declines, both currently and in the future. Thus current consumption does not fall by as much as the increase in G, so national saving (Sd = Y – Cd– G) declines at the initial real interest rate, and the saving curve shifts to the left from S1 to S2, as shown in Fig. 5. Thus the real interest rate increases and consumption and investment both fall.
When there is a permanent increase in government spending, consumers foresee future taxes as well, with both current and future consumption declining. But if there is an equal increase in current and future government spending, and consumers try to smooth consumption, they will reduce their current and future consumption by about the same amount, and that amount will be about the same amount as the increase in government spending. So the saving curve in the saving-investment diagram does not shift, and there is no change in the real interest rate. Since the saving curve shifts upward more in the case of a temporary increase in government spending, the real interest rate is higher, so investment declines by more. However, consumption fails by more in the case of a permanent increase in government spending.
Week 5
Page 6
