ECO 303 Exam 2 Review
Slope of isocost line formula
-w/r
draw a separate graph showing a price taking firm earning... 1. a profit 2. a loss 3. breaking even
1) A firm facing a market price above its average total cost curve at Q* will earn a positive economic profit, π > 0. 2)A firm with average total cost above the market price, at Q*, will earn negative economic profit (loss), π < 0. 3)A firm facing a market price equal to its average total cost at Q* earns zero economic profit.
When you see the question: Find expressions for the firm's fixed cost, variable cost, average total cost, average variable cost, and marginal cost.
FC = the constant VC= everything but the constant ATC = the whole TC equation divided by Q AVC= the whole TC equation NOT INCLUDING THE CONSTANT divided by Q MC = the derivative of the TC
AFC Formula
FC/Q (if its from the TC formula, take only the fixed costs (constant) and divide it by Q)
Whenever you see "Find the cost-minimizing combination of labor and capital"
Find MRTS and solve for K, L and then C if it asks for the total cost.
Profit maximizing/loss minimizing rule
(MR = (P) = MC)
why is the firm's short run total cost greater than its long run total cost?why does a perfectly competitive firm face a horizontal demand curve?
In long run, firm has sufficient time to plan its input to produce output in the least costly way. Long run costs have no fixed factors of production whereas in short run, due to availability of less time, firm has no control over fixed costs. Whether it increases or decreases production, it will have to bear fixed costs which they once incurred so that's why SR TC is > LR TC. The demand curve facing a firm in a perfectly competitive market is perfectly elastic (horizontal) at the market equilibrium price because a perfectly competitive firm is a price taker.
If P = minAVC, stay open or shut down?
Indifferent (can stay open and produce where MR=MC or it can shut down, loss equal to TFC)
When it asks to find increasing, diminishing or constant marginal returns
It means what happens to MPL as L increases while holding K constant and vice versa.
minAVC and minATC equation
MC=AVC and MC=ATC
Marginal rate of technical substitution of labor for capital (MRTS) formula
MPL/MPK
Long run costs minimization condition formula
MPL/MPK = w/r
Break-even price and quantity
MR = (P) = minATC
Shut down price and quantity
MR = (P) = minAVC
What is MR in a perfectly competitive firm?
MR = P
the slope of the isoquant is the marginal rate of technical substitution (MRTS). what does it measure?
MRTSxy- the rate at which the firm can trade input X for input Y, holding output constant the negative slope of the isoquant that looks at the tradeoff between labor (X) and capital (Y)
When you see the question: How much capital does the firm need to hire in order to produce at its target of 8,000 units per day?
Plug everything into the production function and solve for K
If P < ATC, profit is?
Profit < 0
If P = minATC, profit is?
Profit = 0
If P > ATC, profit is?
Profit > 0
Average product formula
Q/L
When you see the question: What is the lowest possible average cost at which Peter can produce piping?
Set ATC = MC and solve for Q. Plug that Q into LAC and solve.
When you see the question: Find the output level that minimizes average total cost
Set MC = ATC and solve for Q
When you see the question: Find the output level that minimizes average variable cost
Set MC = AVC and solve for Q
If P < minAVC, stay open or shut down?
Shut down
When you see the question: Compare the marginal product per dollar spent on K and on L when the firm operates at the input choice in part (a). What does this suggest about the way the firm might change its choice of K and L if it wants to reduce the total cost in meeting its target?
Solve for MPL and MPK, find MPL/w and MPK/r and figure out if its >, <, or =. Then state if the firm should increase or decrease K and L. If MPK/r > MPL/w, increase K and reduce L; vice versa.
When you see the question: What ratio of capital to labor minimizes the total costs?
Solve for MRTS, and set it equal to w/r.
If P > minAVC, stay open or shut down?
Stay open
Equation of isocost line
TC = wL + rK
ATC Formula
TC/Q
When you see the question: Over what range of output does Peter's Pipers experience economies of scale? Over what range of output does Peter's Pipers experience diseconomies of scale?
The Q where ATC = MC is the QMES so anything less than that there is economies of scale and anything greater there is diseconomies of scale
why do economies of scope rise? give a specific example of economies of scope
exist when a firm can use the same input(s) to produce two or more different goods An example can be a dairy farm that produces cheese, milk, yogurt so it is cheaper for this one dairy farm to produce the goods rather than have each farm producing only one good
what does the curvature of an isoquant imply about the two inputs, capital and labor?
implies that you can substitute one of the inputs (ie labor or capital) for the other (ie labor or capital)
why does a firm experience diminishing marginal returns to labor in the short run?
in the short run you have fixed inputs which tend to take the form of capital. when capital is fixed, labor will become less productive after you reach the peak of marginal product
A firm with decreasing returns to scale would see
increasing long-run marginal costs.
In the short run, the marginal product of labor:
will eventually fall
Why are the slopes of isocost lines constant
because firms can hire as much of an input as they desire without changing wages or rental rates
Marginal product formula
change in Q / change in L
Marginal Revenue equation
change in TR/change in Q
what does diminishing marginal product of labor tell us about the relationship between labor inputs and marginal product? what does it tell us about the relationship between labor inputs and total output?
diminishing marginal product- a feature of the production function; as a firm hires additional units of a given input, the marginal product of that input falls so, it's the reduction in the extra output obtained from adding more and more labor and is why the production curve flattens at higher quantities of labor with a fixed amount of capital, every time you add a worker, each worker has less capital to use a mix of labor and capital is more productive than labor alone or capital alone
define economies of scope using cost functions TC(Q1, Q2), TC(Q1, 0), and TC(0, Q2).
economies of scope- the simultaneous production of multiple products at a lower cost than if a firm made each product separately they're defined for a particular level of output of each good and economies of scope don't have to be related to economies of scale TC (Q1, Q2) < TC(Q1, 0) + TC(0, Q2) => economies of scope (essentially means that TC(Q1, Q2) < TC(Q1) + TC(Q2) .: your'e reducing costs by producing two or more goods diseconomies of scope- the simultaneous production of multiple products at a higher cost than if a firm made each product separately TC (Q1, Q2) > TC(Q1, 0) + TC(0, Q2) => diseconomies of scope
how can returns to scale be constant or increasing if inputs have diminishing returns?
Diminishing marginal returns refers to short-run changes, while returns to scale is a long-run phenomenon because we are changing all inputs simultaneously
Suppose that a firm faces the production function y = K*L and is currently minimizing costs in the long run with marginal product of labor and marginal product of capital given by K and L, respectively. If the price of capital falls by 50%, the capital-to-labor ratio will
Double
a firm operating at a loss will decide whether to shut down based on the relationship between the market price and the firm's average variable cost. when will a firm choose to operate? when will a firm shut down? why does a firm ignore its fixed cost when making this decision?
A firm should operate as long as its revenue is greater than or equal to its variable cost, not its total cost (TR ≥ VC). That's because fixed cost needs to be paid whether the plant operates or not, so it doesn't enter into the operate/shut-down decision. Making enough revenue to cover the firm's variable cost is sufficient to justify operating in the short run, even if the firm can't cover all of its fixed cost, because it would lose more money if it shut down. However, if the firm has total revenue that is lower than its variable cost (TR < VC), the firm should shut down. It can't cover its variable cost at this point and loses money on every unit it sells.
what is the relationship between sunk and fixed costs? are all sunk costs fixed? are all fixed costs sunk? give specific examples
A fixed cost that you cannot avoid is called a sunk cost. Once a firm pays a sunk cost, it can never be recovered. Not all fixed costs are sunk costs but all sunk costs are fixed. For a restaurant, for example, money spent on advertising is a sunk cost. You spent the money, and there's no getting it back. If you've signed a long-term rental agreement and cannot sublet the building, the rent is a sunk cost, too. You cannot recover it even by shutting down.
what is the relationship between the marginal revenue and the price for a perfectly competitive firm?
A perfectly competitive firm's marginal revenue is the market price for the good. To see why, remember that these firms can only sell their goods at the market price P. Therefore, the extra revenue they obtain from selling each additional unit of output is P. In a perfectly competitive market, marginal revenue equals the market price; that is, MR = P:
When MC < AVC (or MC < ATC), what does that mean for AVC and ATC?
AVC and ATC are decreasing
When MC > AVC (or MC > ATC), what does that mean for AVC and ATC?
AVC and ATC are increasing
what is the difference between a firm's account and economic costs? How do these relate to a firm's accounting and economic profits?
Accounting costs are the direct costs of operating a business, including costs for raw materials, wages paid to workers, rent paid for office or retail space, and the like. Economic costs—the costs that economists pay attention to—include accounting cost and the producer's opportunity costs. Economic profit (total revenue minus economic costs) should be considered when making decisions rather accounting profit (total revenue minus accounting costs).
for the firm producing in the short run, draw a graph and describe the relationship between marginal and average product
Average product is the total quantity of output divided by the number of units of input used to produce it - APL = Q/L. Marginal product is the incremental output that a firm can produce by using an additional unit of an input (holding use of the other input constant) - MPL = change in Q/change in L.
When you see the question: Suppose you want to find the cost of producing a more general Q units of output.
Basically solve for the whole MRTS and then when you get to the K=L part, plug the production function in and basically solve for K and L but in terms of Q. Then plug that K and L into the TC function.
what is the perfectly competitive firm's short run supply curve?
Because a firm will only operate in the short run when the market price is above its average variable cost curve AVC, the perfectly competitive firm's short-run supply curve is the portion of the marginal cost curve MC above AVC. Because of this relationship between marginal cost and the firm's short-run supply curve, anything that changes marginal cost will shift supply.
what is the reason why LAC is "U" shaped?
Because of economies of scale and diseconomies of scale. DMR does not apply because all inputs are variable.
MC Formula
Change in TC/change in Q OR the derivative of TC
When you see the question: Darken the long-run average total cost curve your specialty bicycle company faces.
Darken the whole outer part of all three curves to make one big curve
what is the sunk cost fallacy? why a firm should not consider sunk costs when making a decision? what are some explanations why people make decisions based on sunk costs?
The fallacy is that they act like sunk costs matter (when they should be ignoring them). In making economic, finance, and life decisions, you want to avoid falling victim to this fallacy, but it's not hard to imagine scenarios where you might be tempted to do so. They should not affect current and future production decisions because they are lost no matter what action is chosen next, they cannot affect the relative costs and benefits of current and future production decisions. People usually make decisions based on sunk costs b/c an investment in money, effort or time has been made.
AVC Formula
VC/Q (if its from the TC formula, take the whole formula, not include the fixed costs (constant) and divide it by Q)
what is the reason why short run average costs (all but AFC) and the marginal cost are "U" shaped?
When the marginal cost of the additional unit is above average cost, then producing it increases the average cost. Therefore, if the marginal cost curve is above an average cost curve at a quantity level, average cost is rising, and the average cost curve slopes up at that quantity. Again, this is true for both average total cost and average variable cost. This property explains why average variable cost curves and average total cost curves often have a U-shape. If marginal cost continues to increase as quantity increases, it eventually rises above average cost and begins pulling up the average variable and average total cost curves.
define returns to scale
a change in the amount of input response to a proportional increase in all of the inputs (is a long run concept)
what does an isoquant curve show?
a curve representing all the combinations of inputs that allow a firm to make a particular quantity of output the inputs are usually labor and capital in this class
what does an isocost curve show?
a curve that shows all of the input combinations that yield the same cost the inputs are usually labor and capital in this class C = RK + WL
differentiate between increasing, decreasing, and constant returns to scale and explain why each may occur
increasing rts- 2x all inputs => output more than doubles very large firms experience increasing rts occurs when production becomes more specialized and learning by doing (as Q increases the firm becomes more efficient), so they can become more efficient ex- Boeing decreasing rts- 2x all inputs => output less than doubles not desirable, but possible could happen to companies that's very large or engaged in the exploration of natural resources ex- Duke Energy could potentially see this constant rts- 2x all inputs => output doubles usually small businesses experience constant rts esp when it's easy to replicate the exact same production ex- car wash or travel agent company
what do the slopes of an isoquant and isocost curve measure?
isocost curve slope= -w/r measures isoquant slope= MRTS = MPl/MPk = -ΔK/ΔL
What is the short run supply for a price taking firm?
portion of MC curve above shutdown point
Under free entry and exit, to find the quantity where ATC is minimized, the firm can:
set marginal cost equal to average total cost and solve for Q or take the first-order condition of average total cost with respect to Q and solve for Q
