Solutions to End-of-Chapter End-of-Chapter Exercises Technology: An Economic Defnition 11.1 Learning Learning Objective: Defne technology and give examples o technological change.
Review Qestions 1.1
Technology is the process a firm uses to turn inputs into outputs of goods and services. Technological change is a change in the ability of a firm to produce a given level of output with a given quantity of inputs.
1.2
Technological change could be negative, for instance, when a natural disaster destroys factories, as happened as a result of the earthquake and tsunami that hit Japan in 2011, or when a firm hires lesse!perienced workers. "n these cases, the firm would produce a lower level of output with the same quantity of inputs.
!roblems and "pplications 1.3
#ou shou should ld disagree disagree with the statemen statementt because because firms can e!perience e!perience technologica technologicall change change in the produc productio tion n of e!isti e!isting ng produc products, ts, not $ust $ust in the introd introduct uction ion of new products. %!amples include the firm&s managers rearranging the flow of work on a factory floor or the layout of a retail store, thereby increasing production and sales, retraining workers, or installing faster or more reliable machinery or equipment.
1.4
'b(, 'c(, and 'd( are e!amples of positive technological change because they enable a firm to produce more output with the same quantity of inputs. )hoice ' a( describes a change in production costs that is the result of a change in the price of an input, not a change in technology. )hoice 'e( is not an e!ample of technological change because the same quantity of inputs is used to produce the same quantity of output.
1.5
#ou should disagree because the statement is incorrect. The firms can now produce more output 'greater sales( with fewer inputs 'fewer trucks(. Therefore, this is indeed an e!ample of technological change.
The Short Run and the Long Run in Economics 11.2 Learning Learning Objective: Distingish between the economic short rn and the economic long rn.
Review Qestions 2.1
"n the short run, at least one of the firm&s inputs is fi!ed, but in the long run, the firm can vary all of its inputs, adopt new technology, technology, and change the si*e of its physical plant. The amount of time that it takes to move from the short run to the long run varies from firm to firm.
2.2
+i!ed costs are costs that remain constant as output changes, and variable costs are costs that change as output changes. n e!ample of a fi!ed cost is the lease payment for a factory or retail store- an e!ample of a variable cost is the cost of raw materials.
2.3
%!plicit costs involve spending money. "mplicit costs are nonmonetary opportunity costs, such as the wages the owner of a firm could have earned if he or she worked for someone else.
2.4
The production function shows the relationship between the inputs employed by a firm and the ma!imum output it can produce with those inputs. The shortrun production functi function on holds holds consta constant nt fi!ed fi!ed input inputss 'such 'such as the num number ber of ovens ovens in Jill& Jill&ss pi**a pi**a restaurant in the e!ample in the chapter(.
!roblems and "pplications 2.6
age age costs are variable if firms increase the number of workers they hire as they increase output. "f a publishing company decides to increase the quantity produced of any book it publishes, it does not need to hire any more editors, designers, or other employees 'although the firm that actually prints the books may have to(. %ven if the publishing company decides to publish additional titles, it may not need to hire more editors or other employees because these employees usually work on several titles at the same time. /nly if the company intends to significantly increase the number of titles it publishes will it hire more employees employees.. Therefore Therefore,, publishi publishing ng companies companies typically typically consider consider their their wage costs to be fi!ed costs, rather than variable costs. +or many firms, the cost of utilities can be a mi!ture of fi!ed and variable costs. +or e!ample, a store may keep its lights on and its outdoor signs lighted day and night. The cost of the electricity to keep these lights on would, therefore, be a fi!ed cost because the cost does not vary with the quantity of the product sold. /n the other hand, if, for e!ample, the store sells photocopies, then the more copies it sells, the more it runs its copy machines, and the more electricity it uses. o that part of its electric bill is a variable cost
2.7
'a(, 'd(, and 'e( are fi!ed costs because they do not change as the quantity of pi**as produced increases- 'b( and 'c( are variable costs because they increase as the quantity of pi**as produced increases. The time period under consideration is important. "n the long run, all of these costs are variable.
11.3
The Marginal Product o Labor and the Average Product o Labor Learning Learning Objective: #nderstand the relationship between the marginal prodct o labor and the average prodct o labor.
Review Qestions 3.1
arginal product normally increases at first due to speciali*ation and division of labor, but it eventually decreases because of the law of diminishing returns. The amount of capital per worker declines as more labor is hired to work with a fi!ed amount of capital. Therefore, the marginal product of labor falls. hen the marginal product of labor is greater than the average product of labor, the average product of labor increases. hen the marginal product of labor is less than the average product of labor, the average product of labor decreases. The marginal product of labor is equal to the average product of labor when the average product of labor is at its ma!imum value. 3.2
The marginal product of labor initially increases, due to speciali*ation and division of labor, as the number of workers hired increases.
3.3
The law of diminishing returns is the principle that, at some point, adding more of a variable input 'for e!ample, labor( to the same amount of a fi!ed input 'such as capital( will cause the marginal product of the variable input to decline. This principle doesn&t apply in the long run because, in the long run, none of the inputs are fi!ed- all inputs can vary.
!roblems and "pplications 3.4
3.5
Quantity of Workers
Total Output
Marginal Produt of !a"or
#$erage Produt of !a"or
0
0
1
300
300
300
2
400
500
350
6
1,500
7 00
500
3
1,400
3 00
385
5
2,200
6 00
330
7
2,300
2 00
300
8
2,600
9100
624
3.6
The studen student& t&ss analy analysis sis is incorr incorrect ect.. The The data data in Table able 11.6 11.6 repres represent ent the effect effectss of speciali*ation and division of labor and the law of diminishing returns, rather than the varying quality of the workers.
3.%
s long as ally&s :; for a semester is below her cumulative :;, her cumulative :; will fall. The current semester&s :; is her marginal :;, while her cumulative :; is her average :;. %ven if her marginal :; goes up, her average :; will go down as long as her marginal :; is below her average :;.
3. 3.1&
a.
AP = Q/L < 23=3 < 7 pi**as per worker
< >Q=> L < '2? − 23(='5 − 3( < 3=1 < 3 pi**as per worker ". MP < . "f we add the marginal product of the second worker '7 pi**as( to the number of pi**as produced when 1 worker is hired '5 pi**as(, then the total number of pi**as produced when 2 workers are ar e hired is 7 pi**as @ 5 pi**as < 11 pi**as. pi**a s. d. The law of diminishing returns sets in when the marginal product of labor first starts to fall- so in this case, it sets in with the fourth worker hired 'where marginal product falls to 5(.
11.4
The Relationshi bet!een Short"Run Production and Short"Run #ost Learning Learning Objective: $xplain and illstrate the relationship between marginal cost and average total cost.
Review Qestions 4.1
verage total cost is total cost divided by the quantity of output produced- marginal cost is the change in a firm&s total cost from producing one more unit of a good or service.
4.2
"f the margina marginall produc productt of labor labor is rising rising,, it means means that that each each additi additiona onall worke workerr is contributing more additional output than the previous worker. s a result, the additional, or marginal, cost of output must be falling because the additional output takes fewer additional workers to produce. arginal product and marginal cost are mirror images of each otherA hen marginal product increases, marginal cost falls, and vice versa.
4.3
hen marginal cost is below average total cost, marginal cost pulls average total cost down, so we are on the downwardsloping section of the Bshaped average total cost curve. curve. hen hen outpu outputt e!pand e!pandss enough enough,, marg margina inall cost cost rises rises to equal equal and then then e!ceed e!ceed average total cost. hen marginal cost is above average total cost, marginal cost pulls average total cost up, so we are on the upwardsloping section of the Bshaped average total cost curve. Therefore, at the point where marginal cost equals average total cost, the average total cost curve stops sloping downward but hasn&t begun sloping upwardthat is, the average total cost curve is at its lowest point when the marginal cost curve equals 'or intersects( it.
!roblems and "pplications 4.5
#es. s long as marginal cost is below average total cost, average total cost will be decreasing, even if marginal cost is increasing.
4.6
total cost is also always always increasing. a. Co. "n this case, average total ". s each unit costs an additional 'marginal( cost of D5 to produce, average total cost will also be D5 for each unit. The average cost curve and the marginal cost curve will be a straight line parallel parallel to the quantity a!is a!is at D5. Cote that this this result depends on the the assumption stated at the beginning of the problem that the firm has no fi!ed costs.
4.7
a. Quantity
Quantity of 'opies
Total
#$erage Total
)i*ed
+aria"le
Marginal
of Workers
per (ay
'ost
'ost
'ost
'ost
'ost
0
0
D3 0
D0
D30
1
700
30
30
?0
D0.166
D0.078
2
1,100
30
?0
120
0.104
0.0?0
6
1,500
30
120
170
0.107
0.100
3
1,?00
30
170
200
0.111
0.166
5
2,000
30
200
230
0.120
0.200
7
2,100
30
230
2?0
0.166
0.300
". The average total cost curve is B shaped- it falls initially and then rises. 'Cote that in this e!ample, we only get the B shape for the average total cost curve if we compute average total cost to three decimal places. t two decimal places, the average total cost of producing 1,100, 1,500, and 1,?00 copies is D0.11- so the average total cost curve will will have have a flat flat sect sectio ion. n.(( The The marg margin inal al cost cost curv curve, e, on the the othe otherr hand hand,, rise risess continuously, continuously, rather than being B shaped.
4.%
verage total cost is total cost divided by total output. "n this case, average total cost for 10,000 pi**as is D50,000=10,000 < D5.00. arginal cost is the change in total cost divided by the change in output. "n this case, marginal cost from the additional pi**a is D11=1 < D11. s the graph shows, when average total cost is rising, marginal cost must be above averag averagee total total cost. cost. Theref Therefore ore,, Jill Jill is correc correctt to say that her marg margina inall cost cost mu must st be increasing.
4.,
verage total cost is total cost divided by total output. "n this case, average total cost is D85,002=20,001 < D6.85. arginal cost is the change in total cost divided by the change in output. "n this case, marginal cost is D2=1 < D2. s the graphs show, when average total cost is greater than marginal cost, marginal cost may be either increasing 'graph 'a( shown below( or decreasing 'graph 'b( shown below(. Therefore, Jill is wrong to say that her marginal cost EmustF be increasing because it may or may not be increasing. a. "n this case, Jill&s average total cost is above her marginal cost, and her marginal cost is increasing.
". "n this case, Jill&s average total cost is above her marginal cost, and her marginal cost is decreasing.
11.5
$rahing #ost #urves Learning Learning Objective: %raph average total cost& average variable cost& average fxed cost& and marginal cost.
Review Qestions 5.1
The marginal cost curve intersects the average variable cost curve and the average total cost curve at their minimum points.
5.2
The difference between average total cost and average variable cost is average fi!ed cost. verage fi!ed cost decreases as output increases, so the difference between average total cost and average variable cost must also continuously decrease. ATC = AVC AVC + AFC , so ATC − AVC AVC = AFC . s AFC continuously AVC . continuously decreases, so does ATC − AVC
!roblems and "pplications 5.3
Gariable cost < total cost 9 fi!ed cost. o, D60,000 H D10,000 < D20,000. a. Gariable ". AVC = VC/Q VC/Q < D20,000=10,000 < D2- AFC = FC/Q < D10,000=10,000 < D1.
and AFC falls falls as . The gap must get smaller as output rises because ATC = AVC AVC + AFC and output rises. o, the dollar difference between ATC and and AVC is is greater when the output of tennis balls is 10,000. D15 Total cost < ATC I Q < D60 I 1,000 < D60,000. Gariable cost < AVC I I Q < D20 I 1,000 < D20,000. +i!ed cost < Total cost 9 Gariable cost < D60,000 H D20,000 < D10,000.
5.7
a. ". . d.
5. 5.,
arginal cost, average variable cost, and average total cost will all increasea. average fi!ed cost is unaffected. ". arginal cost, average variable cost, and average total cost will all increase- average fi!ed cost is unaffected. verage fi!ed cost and average average total cost will decreasedecrease- marginal marginal cost and average average . verage variable cost will be unaffected. d. verage fi!ed cost and average total cost will increase- marginal cost and average variable cost will be unaffected.
11.6
#osts in the Long Run Learning Learning Objective: #nderstand how frms se the long'rn average cost crve in their planning.
Review Qestions 6.1
"n the short run, Total cost < Gariable cost @ +i!ed cost- but in the long run, Total cost < Gariable cost because there are no fi!ed costs in the long run.
6.2
inimum efficient scale is the lowest level of output at which all economies of scale have been e!hausted. "n other words, minimum efficient scale is where the longrun average cost curve stops sloping downward. "n the long run, firms that don&t reach minimum efficient scale will have higher average costs than competitors that do reach minimum efficient scale, so they will probably be driven out of business. 'owever, firms firms that $ustify selling at premium prices due to product differentiation can survive. The te!tbook discusses this last point in )hapter 16.(
6.3
%conomies of scale e!ist when a firm&s longrun average costs fall as the firm increases output. +irms may e!perience economies of scale becauseA '1( a firm&s technology technology may allow it to increase production with a smaller proportional increase in at least one input'2( both workers and managers can become more speciali*ed as output e!pands- '6( large firms may be able to purchase inputs at lower costs than smaller firms can- and '3( as a firm e!pands, it may be able to borrow money at a lower interest rate, thereby lowering its costs.
6.4
Kiseco Kiseconom nomies ies of scale scale e!ist e!ist when when a firm& firm&ss longr longrun un averag averagee costs costs rise rise as the firm increases output. Kiseconomies of scale eventually arise because managing a store or factory above a certain si*e is simply too complicated.
6.5
Lecause shortrun average cost includes at least one input that is fi!ed in quantity, it can never be less than longrun average cost 'where there are no fi!ed inputs or fi!ed costs(.
!roblems and "pplications 6.7
a.
Jill&s average total cost will be lower with a smaller restaurant.
". Jill&s average total cost will be lower with a larger restaurant. . s we can see in +igure 11.7 in the te!t, economies of scale often take the form of a larger store or restaurant allowing for lower average cost for a large quantity, but actually higher average average total cost for a small quantity. The larger restaurant may use larger ovens, more tables, or other capital that isn&t efficiently used if Jill is only able to sell a smaller quantity of pi**as.
