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 APL (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 the equation of the isocost line?
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
What happens to an isocost if a factor (r or w) changes in price?D
In this example the wage falls from $24 to $8 but the rental rate of capital stays constant at $8.
Because of the wage decrease, the new isocost lines have a flatter slope, -w/r = -8/8 = -1, than the original isocost lines, -w/r = -24/8 = -3.
The new, flatter isocost line is tangent to the isoquant at Bundle v
Thus, the firm uses more labor and less capital as labor becomes relatively less expensive. Moreover, the firm’s cost of producing 100 units falls from $2,000 to $1,032 because of the decrease in the wage.
What is the “long run expansion path”?
As a firm increases output, the expansion path traces out the cost-minimizing combinations of inputs employed to produce each possible level of output q.
Why is the LRAC curve U shaped?
Shape is due to economies and diseconomies of scale.
Why must SRACs always be greater than the LRAC?
eg. want to produce quantity 2.. if you are using the wrong quantity of capital in the short run (which you thus cant vary) in SRAC1, you will have a much higher average cost of price d. Whereas in the long run you can choose the optimal quantity of capital which allows you to produce q2 at a price of point e.
In the long run, the firm chooses the plant size that minimizes its cost of production, so it picks the plant size that has the lowest average cost for each possible output level. At q1, it opts for the small plant size, whereas at q2, it uses the medium plant size. Thus, the long-run average cost curve is the blue-green, scalloped section of the three short-run cost curves.
What is the difference between short-run and long-run expansion paths?
In the short run, the firm cannot vary its capital, so its short-run expansion path is horizontal at the fixed level of capital
In the long run, the manufacturer increases its output by using more of BOTH inputs, so its long-run expansion path is upward sloping
This also confirms the LRAC “envelope”, as the long-run expansion path is hence always lower or equal to the short-run
What price control do firms have in “perfect competition”?
NONE.
They take the price of the market
