Chapter 14 - Market for factor inputs Flashcards
What type of factor markets do we consider?
1) Perfectly competitive factor markets
2) Monopsony
3) Monopoly
Consider the function w(L). What does it do?
It is a supply function that associate a number of labor-units L with a wage level w.
Consider the function r(K). What does it do?
It is a supply function that associate the relationship between the amount of kapital K and the interest level r.
Draw up the profit maximization problem for a firm in regards to factor inputs
MAX[Q,L,K] pi = p(Q)Q - w(L)L -r(K)*K
S.T. Q = f(K,L)
Since the restriction is an equation of equality type, we can use Lagrange’s.
Note that the profit function is basically just the same as Revenue - Costs.
Using lagrange
ø = p(Q)Q-w(L)L-r(K)K - lamda(Q-f(K,L))
We are interested in Q, L and K.
∂ø/∂Q = Q∂p(Q)/∂Q + p(Q) - λ = 0
∂p/∂Q * Q + p = λ
FOR L:
∂ø/∂L = -L*∂w(L)/∂L-w(L) + ∂(λf(K,L)/∂L = 0
We simplify a little and get:
L∂w/∂L + w = λ∂f/∂L
We can use the fact that we derived an expression for lamda from the previous first order condition.
L∂w/∂L + w = (Q∂p/∂Q + p)∂f/∂L
WE recognize some terms here.
L∂w/∂L + w is actially marginal expenditure for labor. The second term, w, indicate the wage rate we have to pay to add another unit of labor. the first term reflect the overall change this added unit will have on the previous units.
(Q∂p/∂Q + p) this is actually marginal revenue. Same argument as right above.
∂f/∂L is the marginal product(ivity) of labor.
So, in other words, we get the following relation:
ME_L = MR*MP_L
it is common to use the term MRP_L (Marginal revenue product of labor) to fuse the two together.
The interpretation is like this: The cost of adding another unit of labor (ME_L) is equal to the additional revenue we get by producing an extra unit of output multiplied with the actual increase in the number of outputs we get from adding another unit of labor.
NB: This is for the profit maximization point.
it is essentially the same as MC = MR.
We apply exactly the same process to capital.
What slope is present at the demand curve for factors of production?
The slope downward, just like regular demand curves.
What is the difference between demand curve of factors of production and demand curve in general?
We say that the demand curve of factors of production is “derived demand”. Derived demand means that the demand curve is a result of the price of the factor and the firm’s level of output.
Consider the case where capital is fixed, and labor is variable. A firm has plant and equipment in place. It wants to know if it is profitable to add another unit of labor. What should it do?
We have to consider whether the additional revenue we get from the increase of labor is larger than the increased costs.
The additional revenue is given as marginal revenue, MR. Recall that MR is the additional revenue by producing another unit of output.
Regarding costs: We need to know how much our output will increase by adding another unit of labor, AND we need to know how adding the unit will impact expenditure. Recall that expenditure is associated with costs on input factors.
By following the same rule as before, we get this:
ME_L = MR*MP_L
Right side says: the number of output increase we can produce by adding an additional unit of labor, multiplied with the additional revenue we get from producing another unit. So, unitsUP*incomePerUP.
Left side says: Costs of buying the unit.
Therefore, we use the rule of finding the point where these two are balanced.
if we consider a perfectly competitive output market: What will MR be?
If we consider short run situaiton, what does the profit optimization rule look like?
Equal to the price.
We get:
ME_L = MP_L * P
Consider the short run scenario. Say we are in a perfectly competitive output market. How does the MRP_x curve look like?
What about non-perfect competitive, say monopoly?
MRP = (MR)(MP_x)
If perfectly competitive, MRP_L = PMP_L
So, the price remains constant. But, since we have the law of diminishing marginal returns to labor, the marginal product of labor will decrease as the number of labor increase. Therefore, the MRP-curve will slope down.
In a monopoly, we have to consider MRP_L = (MR)*(MP_L)
WE KNOW that in a monopoly, we have a downward facing demand curve. Therefore, if the firm wants to sell more, it will have to reduce the price. If they reduce the price, the marginal revenue will decrease as well. This means that the MRP_L curve will slope down even harder in monopoly than in perfectly competitive markets.
If we consider the short run, and wage rate is constant, what is the profit maximizing condition?
What market is this likely the case?
MRP_L = w
(MR)*MP_L = w
this essentially means that as long as the additional revenue from the additional unit of labor is larger than the cost of thus unit, then we add more labor.
Perfectly competitive factor market holds w constant
Elaborate on how to determine industry demand for labor
As the price of inputs change, we will see a change in output price and output produced by a firm.
If there is only a single producer in the industry, the marginal revenue product curve (MRP_L) will be the demand curve.
If the wage rate for all firms in an industry fall, then the industry as a whole will hire more labor. This will drive the price of output DOWN, and lead to a higher level of output.
Another word/term for “average expenditure curve”?
Supply curve
Elaborate on how the supply curve for labor can be backwards bending
Backwards bending supply curve of labor indicates that as the wage rate becomes higher, at some point, the result COULD BE declining supply.
To see why the supply of labor could be backwards bending, one has to understand the effect that happens. There is both a substitution effect AND an income effect.
The wage rate measures the price that the worker places on leisure time. This is because the wage is the amount of money he gives up to enjoy leisure. As the wage rate increase, the price of leisure also increases. The price change brings both a substitution effect and an income effect:
Substitution effect: Sub-effect is the relative change in prices with utility held constant. The higher price of leisure encourages workers to substitute work for leisure.
Income effect: in-effect is a change in utility with relative prices held unchanged. Higher wage rate increases the worker’s purchasing power. With higher income, the worker can buy more goods, one of which is leisure. If leisure was chosen, it is because the income effect has encouraged the worker to work FEWER hours.
When the income effect outweighs the substitution effect, we get this backwards bending effect.
Define economic rent for factor inputs for labor
Economic rent is the area above the labor supply curve and beneath the wage level up to the point where we have the intersect point between supply curve and demand curve.
What is derived demand?
Derived demand is demand that comes NOT from utility of a consumer, but exists as an intermediate step where a firm use the goods or input factors as means of their own production.
You dont really want to mix up regualr demand with derived demand. Espeicially in the context of market analysis. Understanding demand from raw materials in complicated, as it follows the rules of many other industries and firms.
