Week 5 Tutorial Solutions.pdf

Week 5 Tutorial Questions Solutions (Ch3 & 4)

Week 5 Page 1

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

Number of

Widgets

Produced

MPN MRPN

(P = $ 5)

MRPN

(P = $ 10)

0 0 N/A N/A N/A

1 8 8 40 80

2 15 7 35 70

3 21 6 30 60

4 26 5 25 50

5 30 4 20 40

6 33 3 15 30

a. Find the MPN for each level of employment.

Answer: Refer to the above table.

b. 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?

Answer: (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 2

c. Graph the relationship between Acmes labour demand and the nominal wage. How does this graph differ from a labour demand curve? Graph

Acmes labour demand curve.

Answer: 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.

d. With the nominal wage fixed at $38, the price of widgets doubles from $5

each to $10 each. What happens to Acmes labour demand and production?

Answer: 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.

e. 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?

Answer: 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


Week 5 Page 3

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. A technological breakthrough raises a countrys 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.

Answer:

b. 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?)

Answer: In the initial situation, capital K1 and labour N

1produce output Y

1; when

productivity rises they produce output 1.1 Y1. Suppose that a small

increase in capital to K2 with labour left at N

1 produces output Y

2 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


Week 5 Page 4

(Y2 Y1) / (K2 K1); when productivity rises the new MPK is (1.1 Y21.1

Y1) / (K

2 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. Find an equation relating desired national saving Sd to r and Y.

Answer: Sd = Y C G = Y (360 200r + 0.1 Y) 120 = 480 + 200r + 0.9Y


Week 5 Page 5

b. 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.

Answer: (1) Using Eq: Y = Cd + I

d + 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 = I

d

480 + 200r + 0.9Y = 120 400r0.9Y = 600 600r

When Y = 600, r = 0.10.

So we can use either Y = Cd + I

d + G or S

d = I

d 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 S

d line from S

1 to S

2 in the following

figure. Setting Sd = I

d, 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 6

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.

Documents

Week 5 Tutorial Solutions.pdf