ECON 315 CSU Fullerton
Short answer: Assume that the firm for which you work faces a demand function given by: P =20 - 2Q and a total cost function: 𝑇𝐶 = 100 + 8𝑄^2 - 100𝑄 a. Find the profit maximizing level of output b. What price should you charge once you determine the quantity that maximizes your profits? c. How much are the profits at the profit-maximizing level of output?
A. Profit= TR-TC This means Profit=p*Q-TC Profit= (20 - 2𝑄)𝑄 - (100 + 8𝑄^2 - 100𝑄). After simplifying the profit function, we have: 𝑃𝑟𝑜𝑓𝑖𝑡 = 20𝑄 - 2𝑄^2 - 100 - 8𝑄^2 + 100𝑄 = -10𝑄^2 + 120𝑄 - 100. To optimize the profit, we take the first order derivative of the the profit function with respect to Q: -20𝑄 + 120 = 0 → 𝑄 = 6 b. P=20-2Q= 20-2*6 Price=8 c. 𝑃𝑟𝑜𝑓𝑖𝑡 = (20 - 2𝑄)𝑄 - (100 + 8𝑄2 - 100𝑄) = (20 - 2 ∗ 6) ∗ 6 - (100 + 8 ∗ 62 - 100 ∗ 6) = 48 - (100 + 288 - 600) = 48 + 212 = Profit=260
Horizontal Integration
Absorption into a single firm of several firms involved in the same level of production and sharing resources at that level
Refer to the above picture: At Joey's Lawncutting Service, a lawn mower cannot cut grass without a laborer. A laborer cannot cut grass without a lawn mower. Which graph in the above figure best represents the isoquants for Joey's Lawncutting Service when units of capital per day is on the vertical axis and units of labor per day is on the horizontal axis? a. Graph A b. Graph B c. Graph C d. Graph D
Answer: A This is a fixed-proportion example: one lawnmower is paired with one laborer, exactly.
Suppose that there are two industries, A and B. There are five firms in industry A with sales at $5 million, $2 million, $1 million, $1 million, and $1 million, respectively. There are four firms in industry B with equal sales of $2.5 million for each firm. The HHI for industry A is: a. 3,200. b. 2,800. c. 1,800. d. 2,500.
Answer: A. 𝑆r= 5 + 2 + 1 + 1 + 1 = 10 million. We can get 𝐻𝐻𝐼 = 10,000 ∗ ∑si/st= 10,000 [(5/10)^2 + (2/10)^2 + (1/10)^2 + (1/10)^2 + (1/10)^2] = 10,000[0.25 + 0.4 + 0.1 + 0.1 + 0.1] = 10,000 ∗ 0.32 = 3200.
An electronics company takes over one of its original suppliers in a merger. This is an example of: a. vertical integration. b. horizontal integration. c. cointegration. d. conglomerate integration.
Answer: A. After vertical integration, various stages in the production of a single product are carried out in a single firm.
Isoquants are normally drawn with a convex shape because inputs are a. Not perfectly substitutable b. Perfectly substitutable c. Perfect complements d. Perfect complements
Answer: A. If inputs are perfectly substitutable, isoquants would be straight downward sloping lines (we studied this as a special case when drawing isoquants). In general, isoquants are convex to the origin (and not straight lines), because usually Labor and Capital are not perfect substitutes of each-other and the ratio with which one can substitute the other varies from point to point along the isoquant.
If the last unit of input increases total product we know that the marginal product is: a. positive. b. negative. c. zero. d. indeterminate.
Answer: A. If the last unit of input contributes positively to output (it increases total output), this means that the marginal product of this input is positive. A positive MP means that the last (additional) input increases output.
The chemical industry has a Lerner index of 0.67. Based on this information, a firm with marginal cost of $10 should charge a price of: a. $30.3 b. $14.93 c. $6.7 d. $3.3
Answer: A. Lerner index: 𝐿 = (𝑃−𝑀𝐶)/P=.67 As the markup factor is given as 1/(1-L) The markup factor would be 1/(1-.67) = 3.03. Since MC is $10, and Price is [1/(1-L)]MC 3.03*10= 30.30
In which of the following production functions are inputs perfect substitutes? a. Linear b. L-shaped (Leontieff) c. Perfectly elastic d. Convex
Answer: A. Linear isoquants capture perfect substitutability between two inputs.
Isoquants that are downward-sloping straight lines imply that the inputs a. are perfect substitutes. b. are imperfect substitutes c. cannot be used together. d. must be used together in varying proportions.
Answer: A. Linear isoquants represent cases when L and K are perfectly substitutable. The MRTS is constant throughout the line/isoquant: unlike convex isoquants, in linear isoquants the MRTS does not depend on the amount of L and K that we have, since the productivities of L and K are constant regardless of the number of labor employed or the number of machines purchased.
Curve D is increasing because of a. diminishing marginal product. b. increasing marginal product. c. the fact that increasing marginal product follows decreasing marginal product. d. the fact that decreasing marginal product follows increasing marginal product.
Answer: A. MC is the amount by which TC increases due to an ADDITINAL unit of Q. MC is upward sloping when each additional unit of output (Q) gets costlier and costlier to produce. This is so, because of diminishing MPL: each additional worker has lower productivity than the preceding ones.
Curve D represents which type of cost curve? a. marginal cost b. average total cost c. average variable cost d. average fixed cost
Answer: A. The MC curve ALWAYS hits the ATC curve at its lowest point. From the graph, it seems that curve D is the MC curve since it crosses the U-shaped curve at its lowest point.
If the last unit of input increases total product we know that the marginal product is: a. Positive b. Negative c. Zero d. Indeterminate
Answer: A.. If output is increasing, this means that the marginal product of an input is positive because it added to output.
Curve C represents which type of cost curve? a. marginal cost b. average total cost c. Variable cost d. average fixed cost
Answer: ATC is usually U-shaped. So, curve C is the ATC curve.
Refer to the Table The marginal product and the average product for the third worker are: a. 𝑀𝑃𝐿=8; 𝐴𝑃𝐿 =6 b. 𝑀𝑃𝐿=6; 𝐴𝑃𝐿 =8 c. 𝑀𝑃l=8; 𝐴𝑃𝐿=8 d. 𝑀𝑃𝐿=7; 𝐴𝑃𝐿 =7
Answer: B
Curve A is always declining because of a. diminishing marginal product. b. dividing fixed costs by higher and higher levels of output. c. the fact that increasing marginal product follows decreasing marginal product. d. the fact that decreasing marginal product follows increasing marginal product.
Answer: B. AFC is downward sloping because as Q increases and FC stays fixed, the ratio declines as Q increases.
An isoquant represents levels of capital and labor that a. have constant marginal productivity. b. yield the same level of output c. incur the same total cost. d. All of the above.
Answer: B. An isoquant represents combinations of L and K that produce the same level of output. If we move up and down the isoquant, the quantity produced does not change, but the amount of L and K do change. The reason why we move up and down an isoquant is to produce the same level of output at a cost-minimizing fashion. For example, if L becomes relatively more expensive, to produce the same level of output, we move upwards along the isoquant, reducing labor and replacing it with capital.
The marginal product of an input is defined as a. change in average output attributable to the last unit of an input b. change in total output attributable to the last unit of an input. c. change in total input attributable to the last unit of an output d. change in average output attributable to the last unit of an output.
Answer: B. By definition. the marginal product of an input is the contribution to output (change in total output), that occurs once we add the LAST unit of input (so it's the output Q attributed to the last (additional) input).
The production function is 𝑄 = 𝐾^0.5𝐿^0.5. In the short-run, the firm sells its output at a price of $10 per unit, and can hire labor at a wage of $5 per unit. Capital is fixed at 25 units. The amount of labor that minimizes costs is: a. L=1 b. L = 25 c. L = 10 d. None is correct
Answer: B. Cost-Minimizing (Profit maximizing) with one input (or in the short-run if K is fixed): 𝑃 ∗ 𝑀𝑃𝐿 = 𝑤. Since 𝑀𝑃𝐿 = 0.5𝐾^(0.5) 𝐿^(−0.5) = .5 ∗ 25^(0.5)*𝐿^(−0.5) = .5 ∗ 5𝐿^(−0.5), plug this equation into the short-run miximizing condition. Thus, 𝑃 ∗ 𝑀𝑃𝐿 = 𝑤 → 10 ∗ .5 ∗ 5𝐿−0.5 = 25, we get 25/𝐿^0.5 = 5. Thus L=25
Which of the following statements best summarizes the law of diminishing marginal returns? a. In the short run, as more labor is hired, output diminishes. b. In the short run, as more labor is hired, output increases at a diminishing rate. c. In the short run, the amount of labor a firm will hire diminishes as output increases. As more labor is hired, the length of time that defines the short run diminishes.
Answer: B. Diminishing marginal returns (another term for diminishing marginal product) means that when more of an input is used (in this case labor), output increases but at a diminishing rate. This is so because each additional worker gives us fewer and fewer units of output compared to the previous workers.
If capital is fixed, but a firm varies labor a. the firm stays on the same isoquant. b. the firm moves to a new isoquant. c. the firm might move to a new isoquant, depending on how much labor is added. d. the firm's output will be dependent on the marginal rate of technical substitution.
Answer: B. If capital is fixed, this means that for us to produce the current level of output (to be in the current isoquant), there is a certain level of labor we need to hire. If we vary that amount of labor, we would move to a new isoquant: if L increases, with the same level of K we should move to a higher isoquant (produce more output) and if L decreases, with the same level of K, we should move to a lower isoquant (produce less output).
If the wage rate increases, what will happen to the isocost line? a) It will shift outward. b) It will become steeper. c) It will become flatter. d) It will shift inward (parallel to itself).
Answer: B. If the wage rate increases, this means that the horizontal intercept (which determines the maximum amount of labor that we can purchase if we spend all budget on labor) is now a smaller number. On the other hand, the increase in the wage rate has no impact on the amount of capital if we spend all the money on capital. So the vertical intercept stays the same, while the horizontal intercept got smaller; the isocost line has now become steeper.
If MRTS < w/r you should: a) hire more labor and less capital b) hire less labor and more capital c) hire less labor and less capital d) hire more labor and more capital
Answer: B. If 𝑀𝑃𝐿 /𝑀𝑃𝑘 < 𝑤/𝑟 → 𝑀𝑃𝐿 /𝑤 < 𝑀𝑃𝑘 /𝑟his means that the productivity of labor relative to its cost is less than the productivity of Capital relative to its cost. We have hired too much labor and too few units of capital. Based on this analysis, the rational thing to do is to decrease L and increase K. As you decrease L, 𝑀𝑃𝑘 increases, and as you increase K ,𝑀𝑃𝑘 decreases, so the ratio 𝑀𝑃𝐿 /𝑤 increases while 𝑀𝑃𝑘 /𝑟 decreases. You keep subtracting L and adding K until the two ratios are equal to each other.
Which of the following is NOT a property of isoquants? a. They do not cross. b. The closer they are to the origin, the higher the level of output. c. They have a downward slope. d. They are generally convex to the origin.
Answer: B. In general, isoquants do not cross, are downward sloping and convex to the origin. The closer they are to the origin, the lower the level of output. High levels of output are characterized by more L and more K, which means that the farthest away we are from the origin, the higher the level of output is.
The tobacco industry has a Lerner index of 0.76. Based on this information, compute the optimal markup factor. a. 4.17 times price b. 4.17 times marginal cost c. 0.24 times price d. There is not sufficient information to determine the optimal markup factor.
Answer: B. Lerner index: 𝐿 = (𝑃−𝑀𝐶)/P = 0.76 As the markup factor is given as 1/(1-L) The markup factor would be 1/(1-.76) = 4.17
If you are running a winery and you need one bottle for every 750ml of wine, then your production function a. is inefficient. b. is considered "fixed-proportion." c. will have a diminishing marginal rate of technical substitution. d. has downward-sloping, straight line isoquants.
Answer: B. Since each 750 ml of wine needs a wine bottle, this seems to be a fixed- proportion example. Wine and bottles cannot substitute at all in the production function, you need to use them in this exact proportion: 1 bottle of wine for 750 ml of wine.
A company is using 10 units of capital, each unit costing 40. The firm's average variable cost is 𝐴𝑉𝐶 = 2 + 0.5𝑄2 The total cost is: a. 𝑇𝐶(𝑄) = 402 + 0.5𝑄3 b. 𝑇𝐶(𝑄) = 400 + 2𝑄 + 0.5𝑄3 c. 𝑇𝐶(𝑄) = 402 + 1.5𝑄3 d. None is correct
Answer: B. TC=VC+FC. Since 𝐴𝑉𝐶 = 2 + 0.5𝑄^2 =VC/Q, so 𝑉𝐶 = 2𝑄 + 0.5𝑄^3. Also FC=10*40=400, therefore 𝑇𝐶(𝑄) = 400 + 2𝑄 + 0.5𝑄^3.
A firm produces output according to a production function: F(L,K) =4K +8L. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? a. L=2;K=4 b. L=0;K=8 c. K=4;L=0 d. K=1;L=6
Answer: B. The production function in this case is linear (inputs are perfectly substitutable), which means that the firm can substitute Labor for Capital (or vice versa) at a constant rate throughout the isoquant. We know that 𝑀𝑃𝐿 = 8 and 𝑀𝑃𝐾 = 4. Using the tangency condition, we have: 𝑀𝑃𝐿 /𝑤 = 8/60 < 𝑀𝑃𝐾/𝑟 = 4/20 Normally we would say we have hired too much labor - to get to the tangency condition and restore the equilibrium we would fire labor and hire more capital until the two sides of the equation are equal. The issue in this case is that the productivity of labor and capital does not change (they are constant) throughout the isoquant: no matter how much labor we have, its productivity is $MP_{L}$8 and capital productivity is $MP_{K}=4. This means the two ratios in the tangency condition WILL NEVER be equal. This means that we have a corner solution: either we hire all labor or hire all capital, whichever is more productive relative to its cost. In this case, capital is more productive relative to its cost, so we produce Q =32 using only capital ( K = 8 ) and no labor.
Given the production function q = 4LK, what is the marginal product of labor when capital is fixed at 25? a. 4K b. 100 c. 100K d. 100L
Answer: B. To find the 𝑀𝑃l we need to take the derivate of the production function with respect to labor and substitute for K=25 (since K is fixed in the short-run). MP = = 4K. Substituting K=25, we get, MP = 4K = 4 ∗ 25 = 100
If a firm hires one worker and eliminates four units of capital, and hires one more worker and replaces three more units of capital, keeping output constant, then a. workers and capital are perfect substitutes. b. the firm is operating inefficiently because capital is more efficient than workers. c. the firm is experiencing a diminishing marginal rate of technical substitution. d. there are decreasing returns to scale.
Answer: C The firm is replacing capital with labor, which means we are moving downward along the isoquant. As we do so, one labor seems to replace fewer and fewer capital (the first worker replaced 4 machines, while the second worker replaced only 3). This means that MPL is diminishing (while MPK is increasing). This means that MRTS, which is the ratio of MPL over MPK is diminishing.
With capital on the vertical axis and labor on the horizontal axis, vertical isoquants imply that a. capital and labor are perfect substitutes. b. capital and labor must be used together in a fixed proportion. c. capital is not productive. d. labor is not productive.
Answer: C This is a case of a special isoquant. If the isoquant is a vertical line, all output is produced by L and capital is a useless (non-productive) input.
Lectures in microeconomics can be delivered either by an instructor (labor) or a movie (capital) or any combination of both. Each minute of the instructor's time delivers the same amount of information as a minute of the movie. Which graph in the above figure best represents the isoquants for lectures in microeconomics when units of capital per day is on the vertical axis and units of labor per day is on the horizontal axis? a. Graph A b. Graph B c. Graph C d. Graph D
Answer: C This is an "either or" scenario: a lecturer can be delivered from instructor or from a video. Instructors and videos are perfectly substitutable in this case since each minute of instruction delivers the same information as each minute in the movie.
1. Suppose the production function is given by: 𝐹(𝐿, 𝐾) = min {2𝐿, 3𝐾}. Suppose that you have employed L=4 and K=9 units of inputs. What is the marginal product of the fourth worker? What is the average product of labor?
Answer: C.
A firm produces according to the following production function: 𝐹(𝑘, 𝐿) = 𝐿0.7𝐾0.3. The price of capital is $3 and the wage rate is $7. What is the optimal combination of labor and capital to produce 100 units of output? a. L=50 and K=50 b. L=100 and K=50 c. L=100 and K=100 d. L=10 and K=10
Answer: C. At cost minimization point, we have 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 𝑤/𝑟. 𝑀𝑃𝐿 /𝑀𝑃𝑘 = [(0.7𝐿-0.3𝐾^0.3) /(0.3𝐿^0.7𝐾^-0.7]) = (7K/3L) = 7/3. Thus K=L Plug this into the production function, we have 100 =𝐿^0.7*𝐾^0.3 → 𝐿^0.7*𝐿^0.3 = 100 → L=100 and K=100
A production function a. defines the minimum amount of output that can be produced with inputs K and L. b. defines the average amount of output that can be produced with inputs such as K and L. c. represents the technology available for turning inputs into output. d. is determined only by the expenditures on R&D.
Answer: C. By definition the production function represents the method (technology) through which inputs (L and K) are turned into output.
Jennifer is the only employee of her sole proprietorship. She is entertaining the idea of hiring an additional employee. She knows that on her own she can produce 100 units per day. Jennifer figures that Applicant A will help her produce 175 units per day whereas Applicant B will help her produce 155 units per day. Which of the following statements is MOST accurate? a. Applicant B has a marginal product of 75 units. b. Applicant B has an average product of 77.5 units. c. Applicant A has a marginal product of 75 units. d. Applicant A has an average product of 87.5 units.
Answer: C. By definition, the 𝑀𝑃𝐿 is the productivity of the last/extra/additional worker. If she hires Applicant A, Jennifer will be able to produce 175 units of output. She produces 100 by herself so Applicant A productivity must be: 𝑀𝑃 = Ll𝑄 = 175−100 = 75.
A firm is producing in the short run with output given by: 𝑄 = 10𝐿 - 0.25𝐿2. The firm hires labor at wage rate of $16 and sells the good for P=$8 . How many workers does the firm hire? a. L=24 b. L=96 c. L=16 d. L=8
Answer: C. Cost-Minimizing (Profit maximizing) with one input (or in the short-run if K is fixed): 𝑃 ∗ 𝑀𝑃𝐿 = 𝑤. 𝑀𝑃𝐿= 10-0.5L. Plug this into the short-run maximizing condition: 𝑃 ∗ (10 - 0.5𝐿) = 𝑤. Thus, 8 ∗ (10 - 0.5𝐿) = 16, we have L=16.
For the cost function 𝑇𝐶(𝑄) = 1000 + 14𝑄 + 9𝑄^2 + 3𝑄^3 what is the marginal cost of producing the fourth unit of output? + a. $42 b. $295 c. $230 d. $116
Answer: C. Marginal Cost is the derivative of the Total Cost function. 𝑀𝐶(𝑄) = 14 + 18𝑄 + 9𝑄2. When Q = 4 , we have: 𝑀𝐶(𝑄) = 14 + 18𝑄 + 9𝑄2 = 230
12. Total product begins to fall when: a. Marginal product is maximized b. Marginal product begins to decline c. Marginal product is negative d. Marginal product is positive but declining
Answer: C. Output begins to decline when if you add more input, total output (Q) is diminished. This means that the last unit of input has to have a negative MP (negative productivity), since it destroys total output
The industry elasticity of demand for gadgets is -2, while the elasticity of demand for an individual gadget manufacturer's product is -10. Based on the Rothschild approach to measuring market power, we conclude that: a. the Herfindahl index for this industry is 5. b. the Herfindahl index for this industry is 0.2. c. there is no monopoly power in this industry. d. there is significant monopoly power in this industry.
Answer: C. Rothschild index is given as 𝑅=Et/Ef, -2/-10 = 0.2. Since R<1, , the individual firm's quantity demanded is more sensitive to a price increase than is the industry as a whole. This firm does not face a demand curve that has the same sensitivity to price as the market demand curve, thus we know there is no monopoly power.
The shape of a production function which is as follows: The 𝑀𝑃𝐿 associated with this function is: a. Increasing b. Decreasing c. Constant d. Undefined
Answer: C. The MPPL is the slope of the production function. From the graph, the production function is a linear function, so its slope is constant. This means that 𝑀𝑃𝐿 will be a horizontal line (with a slope of zero).
If we move downward along an isoquant, the MRTS : a. stays constant b. increases. c. decreases. d. varies irregularly.
Answer: C. The MRTS is the negative of the slope of the isoquant (or the absolute value of the isoquant). As we move downward along the isoquant, its slope decreases (it gets flatter), which means that we need more and more L to replace 1 unit of Capital (K). In other words, as we move downward along the isoquant, Labor gets less and less productive, while Capital becomes more and more productive. This is so because as we move downward the curve, we have a lot more labor and very little capital; diminishing marginal productivity of an input (diminishing returns) says that the more we have of one input, the less productive that input is.
A firm produces output according to a production function: F(L,K) =min{4K,8L}.If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost- minimizing input mix for producing 8 units of output? a. L=8;K=8 b. L=2;K=1 c. K=2;L=1 d. K=2;L=2
Answer: C. This example is a case of no input substitution: L and K have to be used in exact proportions. In a sense, labor is twice as productive as Capital - in fact we need K=2 and L=1 to produce 8 units of output. Since this production function is L-shaped, it has no MRTS (MRTS does not exist). In fact, we cannot even use the tangency condition because to produce 8 units of output we need EXACTLY 2 units of Capital and 1 unit of Labor, regardless of their costs.
If a good is produced only by manual labor, the graph of the isoquant will be: a. L-shaped (Leontieff) b. Perfectly horizontal c. Perfectly vertical d. Convex to the origin
Answer: C. This isoquant falls under "special cases." Particularly, it seems that Capital here is a useless input, and labor is the only useful input for production. The graph of this isoquant is a perfectly vertical line.
An industry consists of six firms with annual sales of $300, $500, $400, $700, $600, and $600. What is the industry's C4? a. 0.58 b. 0.62 c. 0.74 d. 0.77
Answer: D = 300 + 400 + 500 + 600 + 600 + 700 = 3100. So 𝐶4 = (𝑆1+𝑆2+𝑆3+𝑆4)/Sr =(700+600+600+500)/ 3100 = 0.77
The marginal cost curve: a. Lies always below the average total cost curve (ATC) b. Lies always above the average variable cost curve (AVC) c. Intersects the ATC and AVC at their maximum points d. Intersects the ATC and AVC at their minimum points
Answer: D Marginal cost always goes through the lowest point of ATC and AVC. We gave an intuition for this in the lecture and we proved/showed this in examples.
Suppose the production function is given by: 𝐹(𝐿, 𝐾) = 4𝐿 + 2𝐾. Suppose that you have employed L=4 and K=9 units of inputs. What is the marginal product of the fourth worker? What is the average product of labor? a. 𝑀𝑃𝐿 = 2; 𝐴𝑃𝐿 = 10 b. 𝑀𝑃𝐿 = 4; 𝐴𝑃𝐿 = 6 c. 𝑀𝑃𝐿 = 2; 𝐴𝑃𝐿 = 8.5 d. 𝑀𝑃𝐿 = 4; 𝐴𝑃𝐿 = 8.5
Answer: D.
Curve A represents which type of cost curve? a. marginal cost b. average total cost c. average variable cost d. average fixed cost
Answer: D. AFC is always downward sloping because as Q increases AFC decreases. Curve A is the AFC curve.
For the cost function 𝑇𝐶(𝑄) = 200 + 3𝑄 + 8𝑄2 + 4𝑄3 , what is the average fixed cost of producing six units of output? a. 18.31 b. 212.61 c. 42.12 d. 33.33
Answer: D. AFC= FC/Q. From the TC function we know FC =200. Thus, AFC =200/6=33.33
With respect to production, the short run is best defined as a time period a. lasting about six months. b. lasting about two years. c. in which all inputs are fixed. d. in which at least one input is fixed.
Answer: D. By definition, the short-run is a period of time in which at least one input (either K or L) is fixed.
At any given point on the curve, the slope of the total product curve always equals a. the ratio of the marginal product and the average product. b. the change in input divided by the change in output. c. the average product of the input. d. the marginal product of the input.
Answer: D. By definition, the slope of the total product (or production function) is the 𝑀𝑃l (if the function depends only on Labor) or the 𝑀𝑃𝑘 (if the function depends on Capital). In fact, 𝑀𝑃l is the derivative of production function with respect to L. the derivative is nothing else but the slope of the function.
The idea of improving cash flow by exploiting the cyclical nature of different product lines is represented in: a. vertical integration. b. horizontal integration. c. cointegration. d. conglomerate integration.
Answer: D. Conglomerate integration can happen when when imperfections in capital markets prevent a firm from using financial market to obtain working capital.
A firm is currently employing 10 workers. The marginal product of an additional worker is 4 units of output per hour. The wage rate for additional workers is $20/hour. The price of the product is $5. The firm would increase profits by: a. hiring more workers b. hiring less workers c. closing down d. it should keep the number of workers unchanged.
Answer: D. Cost Minimization in Short-Run:𝑃 ∗ 𝑀𝑃𝐿 = 𝑤 is satisfied. This means we have the optimal amount of workers and should keep the number of workers as is.
If your budget as a manager decreases, what will happen to the isocost line? a. It will shift outward. b. It will become steeper. c. It will become flatter. d. It will shift inward.
Answer: D. If the budget decreases, the isocost shifts inwards parallel to itself (the slope of the isocost which is ALWAYS determined by wr does not change, since only C changed and not the ratio of the prices of inputs).
A student in a managerial economics class calculated the four-firm concentration ratio and HHI for industries A and B. What is the proper conclusion she can draw from the following findings? Industry A: four-firm C =.09 and HHI=3200 Industry B: four-firm C =1 and HHI=2500 a. Industry B is a monopoly. b. The market power of firms in industry A is greater than that in industry B. c. C4 is higher for industry A while the HHI is higher for industry B. This inconsistency must be due to a calculation error. d. Neither industry is perfectly competitive.
Answer: D. Industry B's HHI is 2,500, which is smaller than 10,000. This suggeusts that Industry B is not Monopoly. It is possible that C4 and HHI are not consistent due to two reasons: 1. C4 only based on four firm HHI: all firms. So C4 does not take into account the fifth largest firm. 2. HHI is based on squared market share, so it places greater weights on firms with large market shares than the four-firm concentration ratio. If an industry is perfectly competitive, we expect to see HHI =0. Thus, neither industry is perfectly competitive.
The marginal rate of technical substitution shows a. how many machines can be replaced by computers, keeping output constant. b. how many computers are needed to replace workers so that output can increase. c. the rate at which technology advances change marginal productivity. d. how many workers can do the job of one computer, keeping output constant.
Answer: D. It shows how many workers can do the job of one machine (computer) while staying on the same isoquant (keeping output constant). If MRTS=2, this means 1 worker substitutes 2 machines (or 1 worker does the job of 2 computers).
L-shaped isoquants imply that production requires that the inputs a. are perfect substitutes. b. are imperfect substitutes. c. cannot be used together. d. must be used together in a certain proportion.
Answer: D. L-shaped isoquants (or min functions) capture the fact that inputs are used in exact proportion. In these cases, L and K are not substitutable at all: they just need to be used in exact proportions.
As we move downwards along the isoquant: a. MRTS increases b. The substitutability of machines by labor increases c. Capital becomes less productive d. None of the above
Answer: D. We know that as we move downward along the isoquant: 1) MRTS diminishes since the slope of the isoquant gets flatter, 2) it takes more labor to substitute each machine, and 3) labor (and not capital) becomes less productive because as we add more labor the law of diminishing product says that labor becomes less productive and capital is more productive. So none of these statements are correct.
Given that the budget is $200 and the price of capital is $40, what is the vertical intercept of the isocost?
Answer: The vertical intercept of the isocost, corresponds to the maximum amount of capital we can purchase if we spend all our budget in capital. The vertical intercept is given by: C/r =200/40=5
For a cost function 𝑇𝐶 = 100 + 10𝑄 + 𝑄2 ,the average fixed cost of producing 10 unit of output is a. 10 b. 5 c. 1 d. None of above
Answer:A. AFC=FC/Q=100/Q. Evaluate at Q=10 . AFC=100/10=10
Suppose the marginal product of labor is 8 and the marginal product of capital is 2. If the wage rate is $4 and the price of capital is $2, then in order to minimize costs the firm should a. use more capital and less labor. b. use more labor and less capital. c. use three times more capital than labor. d. none of the above.
Answer:B. First we check 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 8/2 = 4 > 4/2 = 𝑤/𝑟, so we are not the cost minimization point. You need to moive from 𝑀𝑃𝐿 /𝑀𝑃𝑘 > 𝑤/𝑟 towards 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 𝑤/𝑟. Currently we have 𝑀𝑃𝐿 /𝑤 > 𝑀𝑃𝑘 /𝑟, which means the productivity of labor relative to its cost is more than the productivity of Capital relative to its cost. we should higher more workers. As we increase L, 𝑀𝑃𝐿 increases, and as you decrease K ,𝑀𝑃𝑘 inncreases, so the ratio 𝑀𝑃𝐿 /𝑤 decreases while 𝑀𝑃𝑘 /𝑟 increases. You keep subtracting L and adding K until the two ratios are equal to each other.
For the cost function 𝑇𝐶 = 100 + 2𝑄 + 3𝑄2, the marginal cost of producing 2 units of output is a. MC=$2 b. MC=$14 c. MC=$12 d. MC=$3
Answer:B. 𝑀𝐶 = 2 + 6𝑄. Evaluate at Q=2; MC=2+6*2=14
A Herfindahl index of 10,000 suggests: a. perfect competition. b. monopolistic competition. c. monopoly. d. oligopoly.
Answer:C. 𝐻𝐻𝐼 = 10,000 ∗ ∑Si/sr. If HHI=10,000, we can get 𝐻𝐻𝐼 = 10,000 ∗ ∑si/sr =10,000. which means that 10,000 -> ∑si/sr=1 There a single firm with market share of 1 in the industry, thus it is a monopoly.
If, by increasing the quantity of labor by 1 unit the firm can give up 2 units of capital and still produce the same output, then the MRTS is: a. 0.5 b. 2 c. 1 d. 4
B. The MRTS is the negative of the slope of the isoquant (or the absolute value of the slope of the isoquant) MRTS= -2/1=2
Isocost formula
C = (W x L) + (r x K) Solve for K.
LINEAR PRODUCTION FUNCTIONS
Inputs are perfect substitutes Q=aK+bL
The leontief production function implies
L-shaped isoquants. The designation of min refers to the smallest numbers for K and L. Capital and labor are fixed proportions. They are perfect complements and cannot be substituted for one another. Q= min(aL,bK)
HHI Index
On a scale of 0-10,000. 10,000 represents a monopoly.
Vertical Integration
Practice where a single entity controls the entire process of a product, from the raw materials to distribution
Conglomerate integration
The coming together of firms operating in unrelated markets.
Suppose the production function is given by: 𝐹(𝐿, 𝐾) = 𝐿0.5𝐾0.5 . Suppose that you have employed L=4 and K=9 units of inputs. What is the marginal product of the fourth worker? What is the average product of labor?
We can find 𝑀𝑃𝐿 = 0.5𝐿−0.5𝐾0.5. Substutting K=9 and L =4, we can get 𝑀𝑃 = 0.5𝐿−0.5𝐾^0.5 = 0.5 ∗ 4−0.5 ∗ 9^0.5 = 3.To find 𝐴𝑃L we need to find the total output Q produced with L=4 and K=9 and then divide that number by the total amount worker L =4.
Short Answer question 2 Suppose that w=$2 , r=$4 and your budget as the manager of a firm is C=$20 a. Draw the isocost. Clearly specify the x-intercept, the y-intercept and the slope for this isocost. For all cases below, draw first the original isocost and then indicate (in the graph) what happens to the isocost in each case. In each diagram, clearly specify the x-intercept, the y- intercept and the slope for the new isocost and the old isocost. b. Suppose the price of labor rises to $4, the price of capital declines to $2 and your budget (C) rises to $40. c. Suppose there is a "buy-one-get-one-free" promotion on capital AND you your budget increases by $6.
a. Isocost: 2L+4K=20 → 𝐾 = 5 - 0.5𝐿 Y-intercept=5 X-intercept=10 Slope= -0.5 b. New Isocost: 4L+2K=40 → 𝐾 = 20 - 2𝐿 Y-intercept=20 X-intercept= 10 Slope= -2 c.The "buy-one-get-one-free" promotion on capital effectively cuts the price of capital in half. So now r=2. Your budget increases to C=6. As such,we have: w=$2; r=$2; C=$26. The new isocost is: 2L+2K=26 → 𝐾 = 13 - 𝐿 Y-intercept: 13 X-Intercept= 13 Slope= -1
Short Answer 3 Suppose that the production function for your firm is given as: 𝐹(𝐾, 𝐿) = 𝐾^0.75*𝐿^0.25 a. Suppose that in the short-run, capital is fixed at 1 unit. If the firm can sell its output at a price of $216 per unit, w=2 and r =6 , how many units of labor should this firm hire in order to maximize profits? b. How many units of output does the firm produce in the short-run? c. What are the profits in the short-run? d. Assuming that in the long-run both capital (K) and labor (L) are variable inputs, what is the optimal combination (profit-maximizing/cost-minimizing L and K ) to produce the amount of output you found in part (b)? e. What are the profits in the long-run?
a. Profit-Maximization/Cost-Minimization in the short-run: 𝑉𝑀𝑃𝐿 = 𝑤 → 𝑃 ∗ 𝑀𝑃𝐿 = 𝑤 Since 𝑀𝑃𝐿 = 0.25 ∗ 𝐾^0.75*𝐿^−0.75 and K =1 in the short run, we have 𝑀𝑃𝐿 = 0.25 ∗ 1^(0.75)*𝐿^(−0.75) = 0.25𝐿^(−0.75) We can plug this into VMPL=W and we get and get 2=216∗0.25𝐿^(−0.75) 2=54L^(-.75) 2/(L^(.75)=54 Thus, 𝐿^0.75 = 27 → 𝐿 = 81 b. since K =1 and L =81, we have 𝐹(𝐾, 𝐿) = 𝐾^0.75*𝐿^0.25 = 1^(0.75)*81^(0.25) = 3 c. To find the profit in the short-run, we need to find total revenue and total cost. 𝑇𝑅 = 𝑃 ∗ 𝑄 = 216 ∗ 3 = 648 𝑇𝐶 = 𝑤𝐿 + 𝑟𝐾 = 2 ∗ 81 + 6 ∗ 1 = 168 Thus, profit= TR- TC= 480 c. In the long-run, we can freely choose the combination of K and L that maximize the profit. At the profit maximization point, the following condition is satisfied: 𝑀𝑅𝑇𝑆 = 𝑀𝑃𝐿/MPK = 𝑤/r =[0.25𝐿^(-0.25)𝐾^(0.75)]/[0.75𝐿^(0.25)*𝐾^(-0.25) =[𝐾^(0.25)*𝐾^(0.75)]/[3𝐿^0.25)*𝐿^(0.75)] =k/3L = w/r =k/3L = 2/6 = K=L Now we can plug this relationship into the production function. Based on part (b) we know that we want to produce Q=3: 𝐾^0.75*𝐿^0.25 = 3 → 𝐾^0.75*𝐾^0.25 = 3 → 𝐾 = 3 Thus, L=K=3 e. The profit in the long-run: Profit=TR-TC= P*Q -(wL+rK)=216*3-(2*3+6*3)=624
Cobb-Douglas production function
capital and labor inputs are not perfect substitutes for each other. There can be input substitution, but it is not linear. Q=AK^a*L^b
