4a. Short-run Costs and Production Flashcards
What is the TC equation?
TC = VC(q) + FC
What is “total cost”?
the sum of a firm’s variable cost and fixed cost
What is specific about “variable cost” in the short run?
remember, in the SHORT RUN, only variable cost changes, hence MC must be marginal variable cost
What is “marginal cost”?
Marginal cost (MC) – the amount by which a firm’s cost changes if the firm produces one more unit of output.
What is the equation of “marginal cost”?
How are Marginal Cost and Marginal Product related in the short-run?
If a firm in the SR cannot vary capital, the only way to increase output is by using more labor.
The extra labor required to produce one more unit of output is (delta L / delta Q). The EXTRA labor costs the firm w per unit, so the firm’s cost RISES
by w(delta L / delta Q)…
HOWEVER, we can flip (delta L / delta Q) to (delta Q / delta L) which IS MPL (the additional output per extra unit of labor),
however, as we flipped we now have to divide w by MPL, hence forming that equation
What does an MPL of 3 say about Q and L?
1 unit of L = 3 units of output
What is the equation to calculate MC using MPL (in the SR)?
MC = w / MPL
What is the equation to calculate AVC using MPL (in the SR)?
AVC = w / MPL
What do we assume about fixed costs in the long run?
Fixed costs are avoidable in the long run.
Hence why.. we assume that all inputs can be varied in the long run so that the firm has no long-run fixed costs (F = 0).
-> As a result, the long-run total cost equals: C=VC
What is the long run total cost equal to?
C = VC
Variable cost!!
-> Because we assume that all inputs can be varied in the long run so that the firm has no long-run fixed costs (F = 0).
What is the long run cost equation of the firm?
w = wage
r = rental rate
What is challenging about cost minimization in the long run?
Short Run problem: choose L to produce q and maximize profit
But in the long run…
choose how to combine L and K to produce q and maximize profit
–> Different combinations of L and K to produce a given q (isoquant) have different costs!
–> To maximize profit, the firm must choose the cheapest combination of L and K that allow to produce q.
-> Along an isocost line, cost is fixed at a particular level, C, so by setting cost at C (BASICALLY LIKE AN ISOQUANT)
What is the mathematical expression of cost minimization in the long run?
mathematical expression:
-> row 1: choose the value of L and K that make the equation (wL + rK) the minimum
-> row 2: provided that L and K PRODUCES the quantity of output Q i desire
What two curves are required for cost minimization?
You need two ingredients, isocosts and isoquants
What is an “isocost” line?
Isocost Line:
Expenditure when firm buys L and K
-> Expenditure = wL + rK
-> Fix the expenditure and find all combination of L and K that firm can buy in the market spending the same.
-> In terms of K? Re-write
What is the equation of the isocost line?
What is important to remember about the slopes of isocost lines?
Always the SAME slope
-> The slope shows the rate at which the firm can substitute capital for labor holding total cost constant
What are the 3 justifications for cost minimizations?
Lowest-isocost rule
Tangency rule
Last-dollar rule
What is the “lowest-isocost rule”?
Pick the bundle of inputs where the lowest isocost line touches the isoquant.
What is the “tangency rule”?
Pick the bundle of inputs where the isoquant is tangent to the isocost line.
What is the “last-dollar rule”?
Pick the bundle of inputs where the last dollar spent on one input gives as much extra output as the last dollar spent on any other input.
Using all the rules, justify which point minimizes cost?
Point x is the answer
Lowest-Isocost rule:
the $2k isocost is the lowest isocost that TOUCHES the isoquant
Tangency rule:
at point x, the slope of the isocost is the same as MRTS, slope of the isoquant
Last-dollar rule:
at point x, the last dollar spent on labor adds as much extra output as the last dollar spent on capital
Using the “last dollar rule”, explain point y does not minimize costs
-> spending 1 extra dollar on capital would result in “only” an additional 0.017 units of output
-> on the other hand… spending 1 extra dollar on labour would result in an additional 0.1 units of output
-> hence why y is cost-inefficient