question
To maximize profits, a firm must produce as efficiently as possible. A firm engages in efficient production if:
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It cannot produce its current level of output with fewer inputs, it is maximizing profit, given the quantity inputs, cannot produce more output. This level of production is also known as technological efficiency
question
Consider Boeing (a producer of jet aircraft), General Mills (a producer of breakfast cereals), and Wacky Jack's (which claims to be the largest U.S. provider of singing telegrams). For which of these firms is the short-run the longest period of time? For which is the long-run the shortest? Explain
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Boeing has the longest short-run because aircraft production requires large, specialized machines. The long-run is the shortest for Wacky Jack's because providing singing telegrams requires primarily labor.
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Longer short runs result from...
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Needing more specialized resources and thus capital
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Shorter long runs result from...
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Needing mainly labor
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If q= Z, L = X, K = Y is a point on the production function ,where Z,X,Y are all quantities; can q= Z, L= X, K= P and Y < P also be a point on the production function?
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No, since we assume production functions are efficient, if I produce Z units with K=Y and L=X, I should produce more with K=P since K<P
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Given a cobb-douglas function Q=K^(.5)L^(.5) and a set L and Q, how do you find the production for the isoquant when Q= 1000
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Replace Q with 1000 so set 1000=K^(.5)L^(.5), solve for K
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Finding when the Marginal Product of Labor is positive
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Find the MPL and set it equal to zero, solve for L to find where it shifts, then plug in that number to see where its positive
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Finding when there are diminishing marginal returns
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take the derivative of the MPL with respect to L and set it equal to zero, then solve for L, then plug in that number to see where its negative and thats when it will decrease
question
What is the difference b/w an isoquant and an indifference curve?
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An indifference curve shows all combinations of goods that result in the same level of utility; an isoquant shows all the combinations of inputs that result in a given level of output. The numbers attached to each isoquant are cardinal. However, in the case of the indifference curves they are ordinal
question
Which of the following statements best summarizes the law of diminishing marginal returns?
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In the short run, as more labor is hired, output increases at a diminishing rate
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Perfect Substitutes Graph
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Straight, linear line
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Imperfect Substitute Graph
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See Graph
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For MRTS, MPx (whatevers on the x-axis) goes ____
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In the numerator
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If the MRTS of hours studying marginal analysis problems (A) for hours studying supply-and-demand problems (R) is -3 A/R, this means
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3 hours of studying marginal analysis problems per hour studying supply-and-demand problems
question
Is it possible to have different marginal productivity functions but the same MRTS functions?
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Yes, A^(.72) times R^(1.28) and A^(.36) times R^(.64) are different marginal productivity functions but give the same MRTS function
question
Michelle's business produces ceramic cups using labor, clay, and a kiln. She can manufacture 25 cups a day with one worker and 35 with two workers. Does her production process necessarily illustrate decreasing returns to scale or diminishing marginal product of labor? What is the likely explanation for why output doesn't increase proportionately with the number of workers?
answer
The first worker increases output by 25 and the second by 10. That is, the marginal productivity of the first worker is 25, and the marginal productivity of the second worker is 10. This is an illustration of diminishing marginal product of labor. This diminishing return to extra labor may be due to too many workers sharing too few machines or to crowding.
question
Firm 1 and Firm 2 use the same type of production function, but Firm 1 is only 90% as productive as Firm 2. That is, the production function of Firm 2 is q2 = f(L, K) and the production function of Firm 1 is q1 = 0.9f(L, K). At a particular level of inputs, how does the marginal product of labor differ between the firms?
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The marginal product of labor of Firm 1 is only 90% of the marginal product of labor of Firm 2 for a particular level of inputs.
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If the average product of labor is higher for Firm 1 than for Firm 2, must Firm 1 be more productive in the sense that it can produce more output from a given amount of inputs? Why?
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We do not have enough information to determine which company is more productive, as Firm 1 may use more capital input than Firm 2. If that is the case, it is possible that with the same capital/labor mix as Firm 2, Firm 1 would produce less than Firm 2
question
Which graph corresponds to each case?
a) ) 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 Capital per day is on the vertical axis and Labor per day is on the horizontal axis?
b) The production function for hamburgers can be written as q = 0.1X + 0.1Y, where X is Canadian ground beef and Y is U.S. beef, both measured in pounds. Which graph in the figure best represents the isoquants for the hamburger production when U.S. ground beef is on the vertical axis and Canadian ground beef is on the horizontal axis?
a) ) 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 Capital per day is on the vertical axis and Labor per day is on the horizontal axis?
b) The production function for hamburgers can be written as q = 0.1X + 0.1Y, where X is Canadian ground beef and Y is U.S. beef, both measured in pounds. Which graph in the figure best represents the isoquants for the hamburger production when U.S. ground beef is on the vertical axis and Canadian ground beef is on the horizontal axis?
answer
a) A
b) C
b) C
question
See Image
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see image
question
A company has purchased a large parcel of land for $1 million. The company recently discovered that the land is contaminated and is worthless to all possible buyers. The opportunity cost of the land is
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$0
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Sarah earns $40,000 per year working for a large corporation. She is thinking of quitting this job to work full time in her own business. She will invest her savings of $50,000 (which currently has an annual 10% rate of return) into the business. Her annual opportunity cost of this new business is
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$45,000
question
Finding the short-run production function given q=L^(x) times K^(y)
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Plug in whichever is fixed, whether thats capital or labor, and find q=..., then solve for L to find what L(q) =
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Finding the short run variable cost function
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VC(q)= wage times L(q)
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Finding the short-run marginal cost function
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Take the derivative w/ respect to q of the total cost function
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Price of capital in the short run is usually used to find ___
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the fixed cost, by mutiplying the price of capital by the level of capital
question
You have a ticket to go to a concert by one of your favorite groups, the Hives, which you cannot resell. However, you can buy a ticket for $35 to attend a talk by Steven Colbert, at the same time as the concert. You are willing to pay up to $130 to hear Colbert. Given that there are no other costs involved in attending either event, what is your opportunity cost of attending the Hives concert?
answer
130-35 = $95
question
A firm purchased copper pipes a few years ago at $8 per pipe and stored them, using them only as the need arises. The firm could sell its remaining pipes in the market at the current price of $4. What is the opportunity cost of each pipe and what is the sunk cost? The opportunity cost is $____ and the sunk cost is $_____ .
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The opportunity cost is $4 and the sunk cost is $4. A sunk cost is a cost that cannot be recovered. We can recover $4 of the total $8 cost, and so the sunk cost is $8 - $4 = $4.
question
What is the principle distinction between explicit costs and implicit costs?
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Explicit costs are direct, out-of-pocket payments, while implicit costs are all foregone opportunity costs
question
The only variable input a janitorial service firm uses to clean offices is workers who are paid a wage, w, of $6 an hour. Each worker can clean four offices in an hour. Use math to determine the production function, the variable cost, the average variable cost, and the marginal cost. Plot the VC, the AVC and the MC
answer
Production Function: q=4L
C=VC = 6 times q/4 (q/4=L) = 1.5q
AC=AVC = 1.5
MC= 1.5
C=VC = 6 times q/4 (q/4=L) = 1.5q
AC=AVC = 1.5
MC= 1.5
question
If a firm buys a building so as to have office space for its workers, what is the monthly opportunity cost of the building?
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The rent the firm could earn if it rented the building to another firm
question
Isocost Equation
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C = wL + rK, then pick a C to be held constant, along with a wage (w), and price of capital (r)
question
Finding the conditional labor demand
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Find the tangency condition (MRTS = -w/r) to find one of K, then plug that into the production function to find L, then use L to find K.
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Finding the long run cost function
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Using the conditional labor and conditional capital demands, plug those into C(q)=wL + rK, then use w and R to find C(q) = Xq, where X is a number
question
Finding how much labor should be used to minimize costs given K
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Find tangency condition, -w/r = -MPL/MPk, then solve for L by plugging in K
question
Finding the ratio of prices
answer
w/r
question
Finding Labor and Capital to produce Q units
answer
find tangency condition, then plug that into the initial production function, solve for L and K (even if it requires going back to the tangency condition for one of them)
question
If MPk/r < MPL/w then...
answer
The cost of production is not being minimized and the firm should use more labor (L), and less capital (K)
question
What is the effect of a lump-sum franchise tax T on the firm's short run AC curve? What is the effect on the short run MC curve? Consider that the SR AC curve before tax is U-shaped
answer
A lump-sum franchise tax will increase the FC and therefore it will affect the AC and AFC. I won't affect neither the MC nor the VC. The graph below shows the AC before and after the tax and the MC. The MC does not vary.
question
What is the long run cosr function of things that are perfect complements/fixed proportions
answer
q=min(L,K), at the corner L=K=q, so the LR cost function is C=wq + rq = (w+r) times q
question
Finding which functions will change from a tax per unit of production
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Add the tax to the AVC(q), AC(q), and MC, those are the functions that will change
question
Finding the best technology for a firm
answer
Find the conditional labor and capital demands, since you need to find optimal tech and minimized costs
question
If both the price of labor and capital rise in the same proportion, which of the following will occur (holding production costs constant)?
answer
The isocost line makes a parallel shift inward
question
The long run average cost curve may initially slope downward due to
answer
Economies of scale
question
The production of cigarettes is highly automated; the production function shows increasing returns to scale. Then the average cost function shows:
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Economies of scale
question
What does the long-run expansion path show?
answer
It shows combinations of capital and labor that minimize the cost of producing any level of production while input prices are kept constant.
question
Explain the following statement: the long run average cost curve envelops the short run average cost curves.
answer
The long run cost is always lower or equal to the short run cost. The long run average cost is always lower or equal to the short run average cost. Therefore, long run average cost curve envelopes the short run average cost curves
question
In the short-run, the expansion path is
answer
Horizontal
question
Fixed proportions production function if it takes 4 units of labor and 2 units of capital to produce one unit of output. What is the cost function C(q)? What type of economies of scale does the function show?
answer
q=min(1/2K, 1/4L)
C(q) = (4w + 2r) times q
It shows no economies of scale
C(q) = (4w + 2r) times q
It shows no economies of scale
question
If a firm manufactures in its home country, it faces input prices for labor and capital of w and r and produces q units of output using L units of labor and K units of capital. Abroad, the wage and the cost of capital are half as much as at home. If the firm manufactures abroad, will it change the amount of labor and capital it uses to produce q? Determine whether the change in factor prices affects the isoquant or the isocost lines. The change in factor prices will....
The change in factor prices will...
The change in factor prices will...
answer
Not affect the isoquants b/c the production function hasn't changed. ; not affect the slope of the isocost lines because relative prices are unchanged
question
According to Haskel and Sadun (2009), the United Kingdom started regulating the size of grocery stores in the early 1990s, and today, the average size of a typical UK grocery store is roughly half the size of a typical U.S. store and two-thirds the size of a typical French store. What implications would such a restriction on size have on a store's average costs.
answer
Since grocery stores in the UK are smaller, their long-run average cost of production is lower if there are diseconomics of scale.
question
...
answer
...
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