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SOLUTIONS TO EXERCISES
VERSION 2017 – REVISION A
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Microeconomics
Markets, Methods & Models
an Open Text
by Douglas Curtis and Ian Irvine
SOLUTIONS TO EXERCISES
VERSION 2017 – REVISION A
ADAPTABLE | ACCESSIBLE | AFFORDABLE
Creative Commons License (CC BY-NC-SA)
Table of Contents
Table of Contents iii
Solutions to exercises 1
iii
Thinkpods
7200 iPads
1000
6000
600
4000
1.3 By examining the opportunity cost in the region where the combinations are defined, and by assuming a linear trade-off between each set of combinations, it can be seen that the first combi- nation in the table is feasible, but not the second combination.
- See diagram.
- See diagram.
- The person with the lower wage.
$ Inc
Leisure
$
$
12
1.5 1. Louis has an advantage in cutting the grass while Carrie Anne should wash cars.
- If they each work a twelve-hour day, between them they can cut 12 lawns and wash 24 cars.
1.6 Following the method described in the text:
Cars
Lawns
24 C.A.
8
15
Louis
12
39
12 lawns, 24 cars
20
1.7 1. Carrie Anne’s lawn intercept is now 12 rather than 8.
- Yes, specialization still matters because C.A. is more efficient at cars.
- The new coordinates will be 39 on the vertical axis, 24 on the horizontal axis and the kink point is the same.
1.8 C.A.’s intercepts are now 30 cars and 15 lawns; Louis’ intercepts are 18.75 cars and 15 lawns; the economy-wide PPF car coordinate is thus 48.75, the lawn coordinate is 30, and the kink point is 15 lawns and 30 cars.
1.9 1. 220 cakes requires 55 workers, the remaining 45 workers can produce 135 shirts. Hence this combination lies inside the PPF described in Exercise 1.1.
- 98 workers.
- 2%.
The aggregate price index is the weighted average of the component price indexes with weights equal to shares in total expenditure. For Year 1 the aggregate index is ( 100 × 0. 10 + 100 × 0. 55 + 100 × 0. 35 ) = 100. For years 2 through 5 this methodology gives aggregate price indexes of 101, 108, 110, 114.
Nominal 100 111.54 126.92 126.92 119.23 115. Carrot price $ 2.6 2.9 3.3 3.3 3.1 3 CPI 110 112 115 117 120 124 CPI new base 100 101.82 104.55 106.36 109.09 112. Real carrot index 100 109.55 121.40 119.33 109.29 102.
2.6 The scatter diagram plots observed combinations of income and consumption as follows. For parts (c) and (d): the variables are positively related and the causation runs from income to con- sumption.
460 480 500 520 540 560 580
0
200
400
600
100
300
500
Income
Consumption
2.7 The percentage changes in income are:
Pct Inc 1.3 2.7 2.0 4.0 2.7 2.0 3. Pct Con 3.0 1.6 3.7 3.8 4.1 4.1 3.
2.8 The relationship given by the equation Y = 10 + 2 X when plotted has an intercept on the vertical (Y ) axis of 10 and the slope of the line is 2. The maximum value of Y (where X is 12) is
Y
X
10
Y = 10 + 2 X
(^4) Y = 10 − 0. 5 X
22
6
34
12
X 0 1 2 3 4 5 6 7 8 9 10 11 12
Y 10 12 14 16 18 20 22 24 26 28 30 32 34
2.9 The relationship Y = 10 − 0. 5 X has a Y intercept of 10 but there is now a negative slope equal to one half (− 0 .5). When X has a value of 12, Y has a value of 4. If you plot this in the diagram for Exercise 2.8 it is the dashed line sloping downward from 10 to 4 at X = 12.
2.10 1. The relationship is negative.
- The relationship is non-linear.
P
Cigarettes
Q
D 1 D
Pcig S
Q 1 Q 0
P
Chewing Tobacco
Q
D 1
D
Ptob S
Q 0 Q 1
3.4 The supply curve shifts down and parallel, the demand curve shifts up and parallel.
- Setting the new supply equal to the new demand: 10 + 2 Q = 76 − 4 Q implies 6Q = 66 and therefore Q = 11, P = 32.
3.5 The diagram shows that equilibrium quantity is 240, equilibrium price is $130, which are the values obtained from equating supply and demand. At a price of $120 the quantity demanded is 300 and the quantity supplied 210. Excess demand is therefore 90.
P
Q
170
D
50
S
130
240
120
210 300
3.6 1. At a price of $140 quantity demanded is 180 and quantity supplied is 270; excess supply is therefore 90.
- Total quotas of 180 will maintain a price of $140. This is obtained by substituting the price of $140 into the demand curve and solving for Q.
3.7 It must buy 90 units at a cost of $140 each. Hence it incurs a loss on each unit of $60, making for a total loss of $5,400.
3.8 1. The quantity axis intercepts are 84 and 126.
- The quantities demanded are 160, 110 and 60 respectively, on the market demand curve in the diagram. These values are obtained by solving the quantity demanded in each demand equation for a given price and summing the quantities.
P
Q
5
625
2
225
3.11 1. The equilibrium admission price is P = $21, T R = $630.
- The equilibrium price would now become $18 and T R = $648. Yes.
- The answer is no, because total revenue falls.
3.12 Wages are a cost of bringing lettuce to market. In the market diagram the supply curve for lettuce shifts upwards to reflect the increased costs. If demand is unchanged the price of lettuce rises from P 0 to P 1 and the quantity demanded falls from Q 0 to Q 1.
P
Q
D
S 0
S 1
P 0
Q 0
P 1
Q 1
Wage increase raises costs
SOLUTIONS TO EXERCISES FOR CHAPTER 4
4.1 1. The intercepts for this straight line demand curve are P = $14, Q = 1400.
- Total revenue is this product of price times quantity. Compute it!
- At P = $7, total revenue is $4,900.
- Elasticities, in descending order, are 0.22, 0.33, 0.47, 0.65, 0.87, 1.15.
- Elasticity becomes greater than one in magnitude at one point where total revenue is maxi- mized.
P
Q
14 ε > 1 at P > $
1400
ε = 1 at the mid-point of the demand curve: P = $7.
4.2 1. The supply curve is vertical at a quantity of 100.
- We are told − 0. 5 = %∆Q/%∆P. The percentage change of quantity is − 10 /95; therefore the percentage change in price must be: %∆P = −( 10 / 95 )/ − 0. 5 = 20 / 95 = 21%. The new price is therefore 0. 4 × 1. 21 = 0 .48.
(^050) 100 150 200 250
0
2
4
6
Quantity Demanded
Price of Movies
4.5 The supply curve is vertical at Q = 40. Substituting this quantity into the demand equation yields an equilibrium price of $40.
- The supply curve is vertical at Q = 40. Substituting this quantity into the demand equation yields an equilibrium price of $40.
- The supply elasticity is zero and the demand elasticity is − 5 .0. The latter is obtained by noting that ∆P/∆Q = − 0 .2, and P = $40 at Q = 40. Using the elasticity formula yields − 5 .0.
- Since the elasticity value exceeds unity he should reduce the price and install more seats if his objective is to generate more revenue.
- Above the price $24, which is the mid-point on the demand curve, demand is elastic.
P
Q
48
D
240
S = 40
40
4.6 1. There has been a 20% increase in price. Feeding this into the elasticity formula yields − 0. 6 = %∆Q/20%. Hence the percentage change (reduction) in quantity is 12%.
- Following the same reasoning as in part (a) the result is 24%.
- In the short run revenue rises since demand is inelastic (less than one in absolute value); in the long run it falls since demand is elastic (greater than one in absolute value).
4.7 1. It is elastic for magazines and inelastic for CDs and Cappuccinos.
- A reduction in magazines purchased and an increase in cappuccinos purchased. Magazines are complements and cappuccinos are substitutes for CDs.
- The demand curve for magazines shifts down in response to an increase in the price of CDs and it increases in response to an increase in the price of cappuccinos.
4.8 1. Reduce the price, because the elasticity is greater than one.
- Yes, it would reduce train ridership because the positive cross-price elasticity indicates that these goods are substitutes.
4.9 1. Plot the scatter.
- The scatter is a positively sloping group of points indicating a positive relationship.
- The elasticities estimated at mid values are 1.0, 0.64, 0.47, 0.52, 0.29 and 0.32. For ex- ample: the first pair of points yields a %∆P = 5 / 12 .5 and %∆Q = 8 , 000 / 20 , 000. Hence, %∆Q/%∆P = ( 8 , 000 / 20 , 000 )/( 5 / 12. 5 ) = 1 .0.
- They are normal goods because the income elasticity is positive.
4.10 1. All three supply curves intersect at P = $18 and Q = 8.
- The supply elasticities are 1.0, 1.125 and 1.5 respectively. These are obtained from substi- tuting the equilibrium P and Q values into Equation 4.1 Part (c) in the text, and noting that the slopes, ∆Q/∆P, from each equation are 2.25, 2, and 1.5.
- The elasticities are computed in the same way, once you have calculated the equilibrium quantity for each equation at this new price: 1.0, 1.2 and 2.0.
- The supply curve through the origin always has a value of unity.
- The new, tax-inclusive, supply curve is horizontal at P = $40 (not illustrated in the figure). The equilibrium price is $40 and the equilibrium quantity becomes 30. With 30 units sold, each generating a tax of $10, total tax revenue is $300.
- Since the equilibrium is on the lower half of a linear demand curve the demand is inelastic.
P
Q
100
D
50
P = 30
35
4.13 As illustrated in the text, we could equally shift the demand curve down by $10 to yield P = 90 − 2 Q. Equating this to P = 30 yields Q = 30 once again. The price of $30 here is what goes to the supplier; the buyer must pay this plus the tax – that is $40.
4.14 1. The supply and demand curves are illustrated below.
- Solving the demand equations for Q = 20 yields prices of $12 and $15 respectively.
- The consumer bears the entire tax burden.
P
Q
P = 2 + 0. 5 Q
P = 5 + 0. 5 Q
Q = 20
12
15
SOLUTIONS TO EXERCISES FOR CHAPTER 5
5.1 1. The step functions are similar to those in Figure 5.1. In ascending order, Margaret is the first supplier, Liam the second, etc. You must also order the demanders in descending order.
- Two: Margaret and Liam will supply, while Jones and Lafleur will purchase. The third highest demander (Murray) is willing to pay $6, while the third supplier is willing to supply only if the price is $9. Hence there is no third unit supplied.
- The equilibrium price will lie in the range $7.0-$7.5. So let us say it is $7. The consumer surplus of each buyer is therefore $1 and $0.5. The supplier surpluses are zero and $2.
- Two driveways will still be cleared. The highest value buyers are now willing to pay $ and $8. The third highest value buyer is willing to pay $7.0. But on the supply side the third supplier still supplies only if he gets $9. Therefore two units will be supplied. If the price remains at $7 (it could fall in the range between $7 and $8) the consumer surpluses are now $5 and $1, and the supplier surpluses remain the same.
5.2 1. The supply curve is horizontal at a price of $10. The demand curve price intercept is $34 and the quantity intercept is 34. The equilibrium quantity is 24.
- The new supply curve is P = 12. Substituting this price into the demand curve yields Q = 22.
- Tax revenue is $44: each of the 22 units sold yields $2. The deadweight loss is the standard triangular area in Figure 5.4. It is $2.
5.3 1. With a supply curve given by P = 10, the new demand curve yields an equilibrium quantity of 24 once again. The new demand curve is ‘flatter’ at the equilibrium than the original, indicating that it is more elastic.
- With a tax of $2 imposed the new equilibrium quantity is 21. Hence tax revenue is $42. The DWL is $3.
5.4 1. The supply curve goes through the origin and the demand curve is horizontal at W = $
- see diagram below.
- The equilibrium amount of labour supplied is 20 units. The supplier surplus is the area above the supply curve below the equilibrium price= $160.
- At a net wage of $12, labour supplied falls to 15. The downward shift in the wage reduces the quantity supplied. The new supplier surplus is the triangular area bounded by W = 12 and L = 15. Its value is therefore $90.