Final Exam Practice questions
if Mr. Dent Carr's total costs were 5s^2 + 50s + 20, then if he repairs 10 cars, his average variable costs will be a.$100. b.$102. c.$150. d.$200. e.$75.
A TC=5s^2 + 50s + 20 VC= 5s^2 + 50s AVC= VC/s AVS= 5s^2 + 50s /s AVC = 5s+50 s=10 AVC= 5s+50 AVC 5(10)+50 AVC=100
The marginal cost curve of a firm is MC = 6y. Total variable costs to produce 10 units of output are a. $120. b. $300. c. $80. d. $400. e. $26.
B MC= 6y variable cost = integral of 6y= 3y^2 total variable cost to produce 10 unity 3y^2=3(10)^2=300
If a profit-maximizing competitive firm has constant returns to scale, then its long-run profits must be zero.
T?
The cost function C(y) = 10 + 3y has marginal cost less than average cost for all levels of output.
T c(y)=10+3y MC=3 AC=TC/y=(10+3y)/(y)=10/y+3 AC>MC for all values of y
A firm produces Ping-Pong balls using two inputs. When input prices are ($15, $7) the firm uses the input bundle (17, 71). When the input prices are ($12, $24) the firm uses the bundle (77, 4). The amount of output is the same in both cases. Is this behavior consistent with WACM? a. Yes. b. No. c. It depends on the level of the fixed costs. d. We have to know the price of the output before we can test WACM. e. It depends on the ratio of variable to fixed costs.
A ws*Ls + rs*Ks is less than or equal to ws*Lt + rs*Kt And, wtLt +wtKt is less than equal to wtLs + wtKs wsLs +rsKs = [(17*15)+(71*7] = 255+497 = 752 wsLt + rsKt = [(17*12)+(71*24)] = 204+1704=1908 wtLt +wtKt = (4)(12)+(4)(24)=144 wtLs + wtKs = (4)(15)+(4)(7) = 88
On a tropical island there are 100 potential boat builders, numbered 1 through 100. Each can build up to20 boats a year, but anyone who goes into the boatbuilding business has to pay a fixed cost of $19.Marginal costs differ from person to person. Where y denotes the number of boats built per year, boat builder 1 has a total cost function c(y) = 19 + y. Boat builder 2 has a total cost function c(y) = 19 + 2y, and more generally, for each i, from 1 to 100, boat builder i has a cost function c(y) = 19 + iy. If the price of boats is 25,how many boats will be built per year? a.480 b.120 c.60 d.720 e.Any number between 500 and 520 is possible.
A AC= c/y=(19 + iy)/y=19/y+i 19/y+I<=25 19/(20)+i<=25 i<=24 24*20=480
A firm has the short-run total cost function c(y) = 4y^2 + 100. At what quantity of output is short-run average cost minimized? a. 5 b. 2 c. 25 d. 0.40 e. None of the above.
A AC=c/y where y is the output produced AC= c/y= (4y^2 + 100)/y= 4y+100/y to minimize AC we take first order derivative of the AC function dAC/dy= 4 -100/y^2 4 -100/y^2=0 5=y at Y=5 we take second derivative of AC function to ascertain whether AC is minimized d(dAC/dy)= -200/y^3 -200/(5)^3= 1.6 showing that AC is minimized at Y=5
An orange grower has discovered a process for producing oranges that requires two inputs. The production function is Q = min{2x1, x2}, where x1 and x2 are the amounts of inputs 1 and 2 that he uses. The prices of these two inputs are w1 = $5 and w2 = $10, respectively. The minimum cost of producing 160 units is therefore a.$2,000. b.$2,400. c.$800. d.$8,000. e.$1,600.
A Q = min{2x1, x2} Cost is minimized when 2x1 = x2 160 = min{2x1, x2} 2x1 = 160 x1 = 80 x2 = 2x1 = 160 Total cost= w1x1+w2x2 TC = (5)(80)+(10)(160) TC= 2000
A competitive firm has a long-run total cost function c(y) = 3y^2 + 675 for y > 0 and c(0) = 0. Its long-run supply function is described as a.y = p/6 if p > 90, y = 0 if p < 90. b.y = p/3 if p > 88, y = 0 if p < 88. c.y = p/3 if p > 93, y = 0 if p < 99. d.y = p/6 if p > 93, y = 0 if p < 93. e.y = p/3 if p > 95, y = 0 if p < 85.
A c(y) = 3y^2 + 675 AC=c/y=(3y^2 + 675)/y=3y+675/y 3y+675/y=0 3y=-675/y 3y^2=675 y^2=225 y=15 3(15)+675/(15)=45+45=90 MC=6y=p y=p/6 a.y = p/6 if p > 90, y = 0 if p < 90.
the production function is f(L, M) = 4L^(1/2) M^(1/2), where L is the number of units of labor and M is the number of machines used. If the cost of labor is $100 per unit and the cost of machines is $16 per unit, then the total cost of producing 7 units of output will be a.$140. b.$406. c.$112. d.$280. e.None of the above.
A cost is minimized where MRTS = W/R= 100/16 MRTS= MPL/MPM= (dQ/dL)(dQ/dM) (4(1/2)L^((1/2)-1)M^(1/2))/ (4(1/2)M^((1/2)-1)L^(1/2) = (2L^(-1/2)M^(1/2))/ (2M^(-1/2)L^(1/2) =M/L M/L = 100/16 M=100L/16 Q=4L^(1/2) M^(1/2) 7=4L^(1/2) M^(1/2) 7=4L^(1/2) (100L/16)^(1/2) L=0.7 M=100L/16 M=100(.7)/16 M=4.375 cost = wL + rM cost = (100)(.7)+(16)(4.38) cost = 140
the production function is given by f(x) = 4x^1/2. If the price of the commodity produced is $100 per unit and the cost of the input is $15 per unit, how much profit will the firm make if it maximize profits? a.$2,666.67 b.$1,331.33 c.$5,337.33 d.$2,651.67 e.$1,336.33
A the production is given as f(x)= 4x^(1/2) the price of production is $100 per unit and price of input is $15 per unit the profit function of the firm is as follows pi= TR-TC TR is the total revenue that us earned by selling q units at $100 per unit. Thus TR becomes 400q^1/2 TC is the total cost of production so TC becomes 15q to calculate the level of output at which the output is maximized, calculate the first derivative of the profit function and equate it to zero pi= 400q^1/2-15q dpi/dq=((200)/(q^1/2)) - 15 ((200)/(q^1/2)) - 15 =0 q=1600/9 thus the output level at which profit maximized is 1600/9 units substitute this value of q into the profit function pi= 400q^1/2-15q 400(1600/9)^(1/2) -15 (1600/9)= 2666.67
A firm produces one output using one input. When the cost of the input was $3 and the price of the output was $3, the firm used 6 units of input to produce 18 units of output. Later, when the cost of the input was $7 and the price of the output was $4, the firm used 5 units of input to produce 20 units of output. This behavior a. is consistent with WAPM. b. is not consistent with WAPM. c. is impossible no matter what the firm is trying to do. d. suggests the presence of increasing returns to scale. e. suggests the presence of decreasing returns to scale.
B (3)(18)-(3)(6)=36 (4)(20)-(7)(5) = 45 is not consistent with WAPM.
During the height of the pet rock craze in the 1970s, the price elasticity of demand was estimated to be 1.20. Since pet rocks have a marginal cost of zero, a profit-maximizing seller of pet rocks would a.increase prices. b.decrease prices. c.leave prices unchanged. d.need more-detailed market information before making any pricing changes. e.diversify into selling Karen Carpenter LPs.
B If the price elasticity is more than 1 it means the demand is price elastic i.e. if the price change by 100% the demand will change more than 100%. The marginal cost is already zero i.e. the monopolist will have no extra cost no matter how much they produce. So, the higher he sells the higher profit he makes. To sell more he has to reduce the price and increase the quantity. It will increase his profit. decrease price
Philip owns and operates a gas station. Philip works 40 hours a week managing the station but doesn't draw a salary. He could earn $700 a week doing the same work for Terrance. The station owes the bank $100,000 and Philip has invested $100,000 of his own money. If Philip's accounting profits are $1,000 per week while the interest on his bank debt is $400 per week, the business's economic profits are a.$0 per week. b.−$100 per week. c.$600 per week. d.$300 per week. e.$1,000 per week.
B Philip is operating his own gas station he could have earned $700 a week working as gas station manager for terrance so by working his own, Philip is forgoing a salary of $700 the foregone alarm is an implicit cost for Philip economic profit = accounting profit - opportunity cost EP= 1000- (700+400) EP = -100
A firm has the production function Q = X^(1/2) X. In the short run it must use exactly 35 units of factor 2. The price of factor 1 is $105 per unit and the price of factor 2 is $3 per unit. The firm's short-run marginal cost function is a. MC(Q) = 105Q-1/2. b. MC(Q) = 6Q/35. c. MC(Q) = 105 + 105Q2. d. MC(Q) = 3Q. e. MC(Q) = 35Q-1/2.
B Q = X^(1/2) X amount of x2= 35 price of x1= 105 price of x2= 3 Q = X^(1/2) X Q = X^(1/2) 35 Q =35 X^(1/2) X^(1/2) =Q/35 x=Q^2/35^2 sc=p1x1+p2x2 sc=(105)(Q^2/35^2)+(3)(35) sc= 3Q^2/35 +105 take the derivative 6Q/35+0
The bicycle industry is made up of 100 firms with the long-run cost curve c(y) = 2 + (y^2/2) and 60 firms with the long-run cost curve c(y) = y2/10. No new firms can enter the industry. What is the long-run industry supply curve at prices greater than $2? a.y = 420p. b.y = 400p. c.y = 200p. d.y = 300p. e.y = 435p.
B TC for 100 firms: TC= 2 + (y^2/2) MC=dTC/dy MC=y 100MC=100y y=100p TC for 60 firms: TC=y^2/10. MC=dTC/dy MC= y/5 60MC=60y/5 5*60*MC=60y 300MC=60y y=300p y=y1+y2 y=100+300=400
the cheese business in Lake Fon-du-lac, Wisconsin, is a competitive industry. All cheese manufacturers have the cost function C = Q^2 + 9, while demand for cheese in the town is given by Qd = 120 − P. The long-run equilibrium number of firms in this industry is a.120. b.38. c.19. d.34. e.39.
B TC=Q^2 + 9 ATC=TC/q=(Q^2 + 9)/Q=q+9/q dTC/dq=1-9/q^2 1-9/q^2=0 1=9/q^2 q^2=0 q=3 ATC=q+9/q ATC= (3)+9/(3) ATC=6 Qd = 120 − P 120-6=114 114/3=38
Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 2s^2 + 50. If the price he receives for repairing a car is $8, then in the long run, how many cars will he fix per week if he maximize profits? a.2 b.0 c.4 d.3 e.6
B c(s) = 2s^2 + 50 DC(S)/DS=4S P=MC 8=4s s=2 profit=TR-TC =(2)(8)-(2(2^2+50)) =-92 since he is loosing profit he will exit the market making the answer 0
A competitive firm's production function is f(x1, x2) = 6x^1/2 + 8x^1/2. The price of factor 1 is $1 and the price of factor 2 is $4. The price of output is $8. What is the profit-maximizing quantity of output? a. 416 b. 208 c. 204 d. 419 e. 196
B find the profit function in terms of the two factor of production P=TR-TC P= 8(6x^1/ 1+ 8x^1/2 ) -(1x+4x) p=48x^1/2+64x^1/2-x+4x find the optimal quantity of X1 dp/dx1=0 (24/x^.5) -1 =0 x1 = 576 find the optimal quantity of X2 dp/dx2=0 32/x^1/2 -4 =0 x2 = 64 find the optimal level f output q= 6x^1/2 + 8x^1/2 q= 6(576)^1/2 + 8(64)^1/2 q= 208
the production function is given by F(L) = 6L^2/3. Suppose that the cost per unit of labor is $8 and the price of output is 4, how many units of labor will the firm hire? a.16 b.8 c.4 d.24 e.None of the above.
B production function F(L)=6L^2/3 Marginal Product of Labor = dF(L)=dL MPL = 4L^(-1/3) to obtain the number of labors hired equate MPL = W/P 4L^(-1/3) = 8/4 4L^(-1/3) = 2 L^(-1/3) = 1/2 L=8
A competitive firm is choosing an output level to maximize its profits in the short run. Which of the following is not necessarily true? (Assume that marginal cost is not constant and is well defined at all levels of output.) a.Marginal cost is at least as large as average variable cost. b.Total revenues are at least as large as total costs. c.Price is at least as large as average variable cost. d.Price equals marginal cost. e.The marginal cost curve is rising.
B the competitive firm can make losses in the short run, so that total revenues can be less than total costs. the requirement is that total revenues should at least be as large as total variable costs therefore, Total revenues are at least as large as total costs.
A firm has the production function Q = KL, where K is the amount of capital and L is the amount of labor it uses as inputs. The cost per unit of capital is a rental fee r and the cost per unit of labor is a wage w. The conditional labor demand function L(Q, w, r) is a.Qwr. b.the square root of Qr/w. c.Qw/r. d.the square root of Qw/r. e.Q/wr.
B the firm problem is to: min l,k w1x1+w2x2 stq=kl the solution myst satisfy MPl/MPk=wl/wk and q=kl from the first condition we get k/l =w/r from which we can isolate =lw/r then plugging k into the production function we find q=(lw/r)(l), and isolating l we get: (qr/lw)^(1/2)
Suppose that Dent Carr's long-run total cost of repairing s cars per week is c(s) = 3s^2 + 75. If the price he receives for repairing a car is $18, then in the long run, how many cars will he fix per week if he maximizes profits? a.3 b.0 c.6 d.4.50 e.9
B the firm produces at MC=P TC=3s^2 + 75 MC=dTC/ds=6s 6s=18 s=3 TC=3s^2 + 75 TC=3(3)^2 + 75 TC=102 TR=PQ TR=18(3)=54 profit= TR-TC profit = 54-102 profit = -48 the firm is going to leave the market and therefore the answer is 0
Mr. Dent Carr's total costs are 2s^2 + 45s + 30. If he repairs 15 cars, his average variable costs will be a.$77. b.$75. c.$150. d.$105. e.$52.50.
B total cost function=2s^2 + 45s + 30 variable cost function = 2s^2 + 45s therefore at number of cars repaired: 15 total variable cost= 2s^2 + 45s =2(15)^2 + 45(15)= 1125 average variable cost: total variable cost/y=1125/15=75
when Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 − N/200 bushels of corn. If the price of corn is $1 per bushel and the price of fertilizer is $.40 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits? a.64 b.120 c.248 d.240 e.200
B we know in order too maximize profit, value of Marginal product of fertilizers = marginal cost of fertilizers thus value of MP of fertilizers = price *MPL .40= 1(1-N/200) .40=1-N/200 N/200= .60 N= 120
As assistant vice president in charge of production for a computer firm, you are asked to calculate the cost of producing 170 computers. The production function is q = min{x, y} where x and y are the amounts of two factors used. The price of x is $18 and the price of y is $10. What is your answer? a. $2,580 b. $4,760 c. $8,460 d. $6,180 e. None of the above.
B y = min(x1,x2) x1= y and x2 = y 170 = x1 and x2 = 170 Cost = (18)(170)+(10)(170) cost = 4760
Suppose that Nadine in Problem 1 has a production function 3x1 + x2. If the factor prices are $3 for factor 1 and $3 for factor 2, how much will it cost her to produce 80 units of output? a.$960 b.$80 c.$240 d.$600 e.$160
B X1 and X2 are perfect substitutes so firm will use only that input which has higher productivity ad lower price. in this case price of both inputs is the same but productivity of X1 is higher so he will produce 80 units of output using X1 y=3x1 + x2 y=3x1 80=3x1 x1= 26.66 26.66 * 3 =80
A firm has a long-run cost function, C(q) = 8q^2 + 288. In the long run, this firm will supply a positive amount of output, as long as the price is greater than a.$200. b.$192. c.$96. d.$48. e.$101.
C C(q) = 8q^2 + 288 AC=c/q=(8q^2 + 288)/q=8q+288/q take the derivative 8-288/q^2 8-288/q^2=0 8=288/q^2 8q^2=288 q^2=36 q=6 AC=8q+288/q AC= 8(6)+288/(6) AC= 96
In the reclining chair industry (which is perfectly competitive), two different technologies of production exist. These technologies exhibit the following total cost functions: C1(Q) = 1,000 + 600Q − 40Q2 + Q3 C2(Q) = 200 + 145Q− 10Q2 + Q3 Due to foreign competition, the market price of reclining chairs has fallen to $190. In the short run, firms using technology 1 a. and firms using technology 2 will remain in business. b.will remain in business and firms using technology 2 will shut down. c.will shut down and firms using technology 2 will remain in business. d.and firms using technology 2 will shut down. e.More information is needed to make a judgment.
C C1(Q) = 1,000 + 600Q − 40Q2 + Q3 C2(Q) = 200 + 145Q− 10Q2 + Q3 the variable costs will be as follows VC1(Q)=600Q − 40Q2 + Q3 VC2(Q)= 145Q− 10Q2 + Q3 AVC1(Q)=VC1/Q=600 − 40Q + Q2 AVC2(Q)= VC2/Q=145− 10Q + Q2 d(AVC1)/dQ= − 40 + 2Q q=20 d(AVC2)/dQ= − 10 + 2Q q=5 C1(20) = 1,000 + 600(20) − 40(20)2 + (20)3=5000 C2(5) = 200 + 145Q− 10Q2 + Q3= 800 revenue 1= pq revenue 1=(190)(5000)=950,000 revenue 2= pq revenue 2=(190)(800)=152,000 lower revenue than minimum AVC means that at any point below minimum of AVC the firm will shut down
the production function is f(x1, x2) = x1^(1/2)x2^(1/2). If the price of factor 1 is $4 and the price of factor 2 is $6, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? a.x1 = x2. b.x1 = 0.67x2. c.x1 = 1.50x2. d.We can't tell without knowing the price of output. e.x1 = 6x2.
C f(x1, x2) = (x1x2)^(1/2) MRS = (MU x1)/(MU x2)= (x2/x1) MRS= Px1/ Px2 (X2/X1) = 4/6 (X2/X1) = 2/3 x1= 3/2X2 = 1.5X2
A competitive firm uses a single input x to produce its output y. The firm's production function is given by y = x^3/2 for quantities of x between 0 and 4. For quantities of a greater than 4, the firm's output is y = 4 + x. If the price of the output y is $1 and the price of the input x is $3, how much x should the firm use to maximize its profit? a. 16/9 b. 4 c. 0 d. 4/9 e. 9/2
C firms production function is y = x^3/2. 0<x<4 y=4+x. x>4 Py= 1 Px=3 pi = Py-cx = (1)(x^3/2) - 3x dpi/dx= 3/2X^(1/2)-3 3/2X^(1/2)-3 =0 x=4 profit = (1)(x^3/2) - 3x profit = (1)(4^3/2) - 3(4) profit =-4 the firm should not produce anything as they will be loosing money
A firm has a short-run cost function c(y) = 3y + 11 for y > 0 and c(0) = 8. The firm's quasi-fixed costs are a. $8. b. $11. c. $3. d. $7. e. They are not possible to determine from this information.
C quasi fixed cost = C(y=0)-c(0) quasi fixed cost= (3(0)+11)-8=3
A profit-maximizing competitive firm uses just one input, x. Its production function is q = 4x^1/2. The price of output is $28 and the factor price is $7. The amount of the factor that the firm demands is a. 8. b. 16. c. 64. d. 60. e. None of the above.
C the firm will demand at MRPL = wages production function: q = 4x^1/2 MPL = dq/dx= 2x^(-1/2) MRP=MPL*P MRP = 2x^(-1/2) *28 MRP = 56x^(-.5) 56x^(-.5) =7 x=64
A competitive firm uses two inputs, x and y. Total output is the square root of x times the square root of y. The price of x is $17 and the price of y is $11. The company minimizes its costs per unit of output and spends $517 on x. How much does it spend on y? a. $766 b. $480 c. $655 d. $517 e. None of the above.
D Q = x^1/2y^1/2 For profit maximization: MPx/MPy = Px/Py Px = 17 and Py = 11 MPx = dQ/dx = .5(y^(1/2)/x^(1/2)) MPy = .5(x^(1/2)/y^(1/2)) y/x = 17/11 x=517/17=30.41 y=17/11*30.41=47 amount spent on y = 47*11=517
An industry has 100 firms. These firms have identical production functions. In the short run, each firm has fixed costs of $200. There are two variable factors in the short run and output is given by y = (min{x1, 3x2})1/2. The cost of factor 1 is $5 per unit and the cost of factor 2 is $4 per unit. In the short run, the industry supply curve is given by a.Q = 100p/10. b.the part of the line Q = 50(min{5, 12}) for which pQ > 200/Q. c.Q = 575p1/2. d.Q = 100p/12.67. e.None of the above.
D 100 firms y = (min{x1, 3x2})1/2 FC=200 x=5 w=4 k=y^2, 4L=y^2, L=y^2/(4) TC= wL+xk+FC TC= (4)(y^2/(4))+(5)(y^2)+200 TC= 6y^2+200 MC=dTC/dy=12y p=12y y=p/12 100(p/12)
The snow removal business in East Icicle, Minnesota,is a competitive industry. All snowplow operators have the cost function C = Q^2 + 4, where Q is the number of driveways cleared. Demand for snow removal in the town is given by Qd = 120 − P. The long-run equilibrium number of firms in this industry is a.120. b.29. c.56. d.58. e.59.
D C = Q2 + 4 AC=C/Q=Q2 + 4/Q=Q+4/Q d(AC)/Dq=1-4/Q^2 1-4/Q^2=0 1=4/Q^2 Q^2=4 Q=2 minimum AC= Q+4/Q= 2+4/2=4 Qd= 120 − P=120-4=116 Qd=xQ 116=x(2) x=58
A firm has the long-run cost function C(Q) = 4Q^2 + 64. In the long run, it will supply a positive amount of output, so long as the price is greater than a. $64. b.$72. c.$16. d.$32. e.$37.
D C(Q) = 4Q^2 + 64 ATC=C/q ATC=(4Q^2 + 64)Q=4Q+64/Q take first derivative 4-64/Q^2 4-64/Q^2=0 4Q^2=64 Q=4 ATC=4Q+64/Q ATC=4(4)+64/(4) ATC=16+16 ATC=32
A firm has the long-run cost function C(q) = 3q^2 + 27.In the long run, it will supply a positive amount of output, so long as the price is greater than a.$36. b.$44. c.$9. d.$18. e.$23.
D C(q) = 3q^2 + 27 AC=c/q=(3q^2 + 27)/q= 3q+27/q dAC/dq=3-27/q^2 3-27/q^2=0 3=27/q^2 3q^2=27 q^2=9 q=3 ATC=3q+27/q ATC= 3(3)+27/(3) ATC=18
The following relationship must hold between the average total cost (ATC) curve and the marginal cost curve (MC): a. If MC is rising, ATC must be rising. b. If MC is rising, ATC must be greater than MC. c. If MC is rising, ATC must be less than MC. d. If ATC is rising, MC must be greater than ATC. e. If ATC is rising, MC must be less than ATC.
D If ATC is rising, MC must be greater than ATC.
A profit-maximizing firm continues to operate even though it is losing money. It sells its product at a price of $100. a.Average total cost is less than $100. b.Average fixed cost is less than $100. c.Marginal cost is increasing. d.Average variable cost is less than $100. e.Marginal cost is decreasing.
D If the firm is incurring loss and even it is operating , then the firm market price is Below ATC and above AVC d.Average variable cost is less than $100.
If output is produced according to Q = 4L + 6K, the price of K is $24, and the price of L is $20, then the cost-minimizing combination of K and L capable of producing 72 units of output is a.L = 9 and K = 6. b.L = 20 and K = 24. c.L = 18 and K = 12. d.L = 0 and K = 12. e.L = 18 and K = 0.
D at equilibrium the slope of the isoquant is equal to the price ratio of the inputs: MPl/MPk=w/k assuming w=20 and k=24 w/k = 20/24=5/6 the equation of the isoquant is: Q = 4L + 6K MPl=4 MPk=6 MPl/MPk=4/6 MPl/MPk<w/k 4/6<5/6 Q = 4L + 6K 72= 4L + 6K k=12 L=0
The production function is f (L, M) = 5L^1/2 M^1/2, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is $9 per unit and the cost of using machines is $64 per machine, then the total cost of producing 12 units of output is a.$438. b.$108. c.$576. d.$115.20. e.$57.60.
D f (L, M) = 5L^1/2 M^1/2 MPL/MPM = cost of labor / cost of machine df(L,M)/dl=mpl = 2.5m^1/2. /l^1/2 df(L,M)/dm=mpm = 2.5L^1/2. /m^1/2 MPL/MPM = (2.5m^1/2. /l^1/2 ) / (2.5L^1/2. /m^1/2 ) =m/l=mpl/mpm m/l=9/64 m=9/64l f (L, M) = 5L^1/2 M^1/2 12= 5L^1/2 (9/64l)^1/2 L=6.4 m=9/64l m=(9/64)(6.4) m=0.9 total cost = (labor) (cost of labor) + (machine)(cost of machine) TC= (6.4)(9)+(.9)(64) TC=115.20
A competitive firm produces output using three fixed factors and one variable factor. The firm's short-run production function is q = 305x − 2x^2, where x is the amount of variable factor used. The price of the output is $2 per unit and the price of the variable factor is $10 per unit. In the short run, how many units of x should the firm use? a.37 b.150 c.21 d.75 e.None of the above.
D firm's short run production function is q= 305X - 2x^2 x= variable factor firms profit function is given by pi = pq-10x pi= 2(305X - 2x^2) -10x pi= 2(305X - 2x^2) -10x pi = 610x - 4x^2-10x pi = 600x - 4x^2 dpi/dx= 600-8x 600-8x=0 600=8x x=75
A competitive firm produces its output according to the production function y = min{x3, 1000}. Let p be the price of output, and let the price of input x be $1. The profit maximizing output for this firm is a.1,000 if p > 1 and 0 otherwise. b.10 for all p. c.1,000 for all p. d.0 if p < 1/100 and 1,000 otherwise. e.None of the above.
D profit = px^3-x where x^3<= 1000, which means x<=10 profit = p(10)^3-10 profit = 1000p-10 1000p-10=0 p=1/100 if p=1/101 (which is <1/100) profit <0
suppose that a new alloy is invented which uses copper and zinc in fixed proportions where 1 unit of output requires 3 units of copper and 3 units of zinc for each unit of alloy produced. If no other inputs are needed, the price of copper is $3, and the price of zinc is $3, what is the average cost per unit when 4,000 units of the alloy are produced? a.$9.50 b.$1,000 c.$1 d.$18 e.$9,500
D total cost of 1 unit of New alloy = (price of copper)(units of copper) + (price of zinc)(units of zinc) total cost of 1 unit of New alloy = (3)(3) + (3)(3)=18 total unit produced = 4000 total cost = 18(4000) = 72000 average cost = total cost / units produced AC= 72000/4000=18
A firm has fixed costs of $4,000. Its short-run production function is y = 4x^1/2, where x is the amount of variable factor it uses. The price of the variable factor is $4,000 per unit. Where y is the amount of output, the short-run total cost function is a. 4,000/y + 4,000. b. 8,000y. c. 4,000 + 4,000y. d. 4,000 + 250y2. e. 4,000 + 0.25y2.
D total cost= fixed cost +variable cost y = 4x^1/2 x=.0625y since 1 unit of the variable factor costs 4000, then x units cost 4000x dollars 4000x = 4000 (.0625y) =250y VC= 250y fixed cost = 4000 total cost= fixed cost +variable cost TC= 4000+ 250y
Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) = 4L^(1/2)M^(1/2) must use 4 machines. If the cost of labor is $10 per unit and the cost of machines is $6 per unit, the short-run total cost of producing 64 units of output is a. $512. b. $384. c. $640. d. $1,328. e. $664.
E Q=4L^(1/2)M^(1/2) Q=64 M=4 64=4L^(1/2)(4)^(1/2) L=64 total cost = Lw+Kr total cost = (64)(10)+(6)(4) total cost = 664
Florence's Restaurant estimates that its total costs of providing Q meals per month is given by TC = 8,000 + 5Q. If Florence charges $9 per meal, what is its break even level of output? a.4,000 meals b.571.43 meals c.888.89 meals d.1,600 meals e.2,000 meals
E TC = 8,000 + 5Q total fixed cost =8000 variable cost per unit =5 break even sales point =TFC/(p-v) p=unit sale price=9 v= unit variable cost= 5 break even sales point =8000/(9-5) break even sales point =2000
If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400, then in the short run, if the market price of output is $24, a profit-maximizing firm will a. not produce at all, since marginal costs are increasing. b. produce as much output as possible since there are constant returns to scale. c. produce up to the point where average costs equal $24. d. produce a level of output where marginal revenue equals marginal costs. e. produce exactly 400 units.
E the firm maximizes profit when price = marginal cost then at the market price of 24, the firm will produce exactly 400 units
A firm with the cost function c(y) = 20y2 + 500 has a U-shaped cost curve.
F
The marginal cost curve passes through the minimum point of the average fixed cost curve.
F
The total cost function c(w1, w2, y) expresses the cost per unit of output as a function of input prices and output.
F
If the value of the marginal product of factor x increases as the quantity of x increases and the value of the marginal product of x is equal to the wage rate, then the profit-maximizing amount of x is being used.
F Let us consider X as labour. A firm will hire labours only until the marginal product of x equals the wage rate. Beyond which the firm May incur losses. It is also given that, the value of marginal product of factor X increases as the quantity of X increases. But we know that firm will not earn profits if it hires more labour (X) as marginal revenue will start to fall when wages rise. Hence the firm is not using the profit maximizing amount of X.
The area under the marginal cost curve measures total fixed costs.
F The area under the marginal cost measures the variable cost
Two firms have the same technology and must pay the same wages for labor. They have identical factories, but firm 1 paid a higher price for its factory than firm 2 did. If they are both profit maximizers and have upward-sloping marginal cost curves, then we would expect firm 1 to have a higher output than firm 2.
F When firm is in profit maximising equilibrium, price marginal product of labor is equal to wage rate.If firm 1 has higher price but wages are same then its output will be less than firm 2.
Price equals marginal cost is a sufficient condition for profit maximization.
F profit maximizing condition is where MR=MC
If the production function is f (x1, x2) = min{x1, x2}, then the cost function is c(w1, w2, y) = min{w1, w2}y.
F when the production function is of perfect complaint inputs than the cost function is linear here x1=x2=y, where y =f(x1, x2) now c= w1x1+w2x2 so c= y(w1+x1)
It is possible to have an industry in which all firms make zero economic profits in long-run equilibrium.
T When there is economic profit there is entry of new firms and when there is loss there is exit of firms.Firms in a perfectly competitive industry will earn zero economic profit in the long run if price is less than cost and many firms will leave the industry.
If there are increasing returns to scale, then average costs are a decreasing function of output.
T if the production function has decreasing returns to scale then the average cost of production increases if the production function has increasing returns to scale then average cost of production decreases so average decrease in case of increasing returns to scale so this statement is true
The short-run industry supply curve can be found by horizontally summing the short-run supply curves of all the individual firms in the industry.
T the industry supply curve is a sum of 3each quantity supplied of the individual firms at each price and the quantity is non the horizontal axis so the sum is a horizontal sum of individual firms for the industry
