If mplw < mpkr, the firm should use capital and labor to minimize costs.

You are an executive for a firm like VCA​ Antech, which operates over 600 animal hospitals in the United States. Each hospital is treating the desired number of cases per day.

At each​ hospital, you estimate that hiring another veterinarian enables the location to treat 50 additional cases per day and firing one decreases the number of cases treated by 50 per day. Hiring another veterinary assistant enables the location to treat 12 more cases per​ day, and firing one decreases the number of cases treated by 12 per day.​ Finally, hiring another veterinary technician enables the location to treat 14 more cases per​ day, and firing one decreases the number of cases treated by 14 per day.

A veterinarian is paid ​$400 per​ day, a veterinary assistant is paid ​$144 per​ day, and a veterinary technician is paid ​$168 per day.

When will the hospitals be able to minimize​ costs?

A. The hospitals will be able to minimize costs when the ratio of marginal product to price is equal for any two inputs.
B. The hospitals will be able to minimize costs when the input with the lowest price is employed the​ most; assistants in our example.
C. The hospitals will be able to minimize costs when an equal number of​ veterinarians, assistants, and technicians are employed.
D. The hospitals will be able to minimize costs when the ratio of marginal product to price is equal for​ veterinarians, assistants, and technicians.

The animal hospitals are not minimizing their cost of treatment.

As an​ executive, your advice to the animal hospitals should be to hire fewer ​assistants, fewer ​technicians, and more veterinarians.

$\begingroup$

Question:

A firm produces chairs using labor and capital. The price of labor is \$50 dollar per unit, and the price of capital is $100 per unit. At current output, the marginal product of labor is 10 chairs, and the marginal product of capital is 15 chairs. To reduce the total cost of producing the current quantity of chairs, how should the firm change its spending on labor and capital?

Answer:

Increase labor; Decrease capital. In order to reduce the total cost of producing the current quantity of chairs, one of the inputs to production must increase and the other must decrease. If neither changed, the cost would not be reduced. If one increased or decreased and the other did not change, the firm wouldn’t be producing the current quantity of chairs – it would be producing more or less, respectively. While the marginal product of labor (MPL = 10) is less than the marginal product of capital (MPK = 15), the RATIO of the MPL to the price of labor (10 / 50 = 0.2) is greater than the RATIO of the MPK to the price of capital (15 / 100 = 0.15). To reduce the total cost, the firm should increase spending on labor, which increases output by 0.2 chairs for every dollar spent, and decrease spending on capital, which only increases output by 0.15 chairs for every dollar spent.

luchonacho

8,4874 gold badges24 silver badges54 bronze badges

asked Sep 3, 2017 at 4:04

$\endgroup$

$\begingroup$

You can do both. Effectively you say "let me move one dollar from labor to capital expenditure and see what happens". By doing so you have reduced labor by 0.01 and thus reduced production by 0.15 chairs, but increased capital by 0.02 and thus production by 0.2 chairs. Net effect is 0.05 chairs more at the same cost.

Equivalently, MPL/MPK = 1.5< w/r =2, or MPL/w= 0.15 < MPK/ r = 2. Second is just rearrangement of the first, but with both you answer where the dollar of you cost is more efficient.

answered Sep 3, 2017 at 7:25

$\endgroup$

Economics 3307

Main Points of Chapter 3

1.� A production process converts inputs into outputs.� This chapter introduces the aggregate production function Y = F(K,L), which says that total output in the economy, or Real GDP (Y) is a function of the total amount of capital (K) and labor (L) used by firms in the production process.�

2.� K and L have positive but decreasing marginal products.� That is, Y increases with increases in K or L (positive marginal product), but as K or L gets larger and larger the marginal increase in Y caused by using still more K or L gets smaller and smaller.

3.� Firms maximize profits, which means they will hire additional capital and/or labor as long as the marginal revenue of doing so exceeds the marginal cost.� Firms are maximizing profits when the marginal revenue of each input equals the marginal cost.� These conditions are (i) P�MPL = W for labor, and (ii) P�MPK = R for capital, where P is the price of output, MPL is the marginal product of labor, W is the wage rate, MPK is the marginal product of capital, and R is the rental price of capital.

4.� We can rearrange these conditions to imply MPL = (W/P) and MPK = (R/P).� These conditions give us the demand curve for labor and the demand curve for capital.

5.� We assume in Chapter 3 that the supplies of capital and labor are exogenous.� This means that the labor supply curve and capital supply curve are vertical lines.

6.� In equilibrium, (W/P) has adjusted so that the aggregate demand for labor equals the supply of labor, and (R/P) has adjusted so that the aggregate demand for capital equals the supply of capital.�

7.� The total real income earned by labor is (W/P)�L, which in equilibrium is equal to MPL�L.� The total real income earned by owners of capital is (R/P)�K, which in equilibrium is equal to MPK�K.

8.� The total income earned in the economy is equal to (MPL�L + MPK�K), which under certain conditions -- that seem to be satisfied in practice -- is equal to real output Y.� (The "certain conditions" are that the aggregate production function exhibits constant returns to scale.)

9.� Thus the relative income earned by labor and capital is� � =�� � .� This is the neoclassical theory of income distribution, which says that factors of production each earn their marginal products.

10.���� If L rises, the equilibrium W/P falls.� If L falls, the equilibrium W/P rises.� If K rises, the equilibrium (R/P) falls.� If K falls, the equilibrium (R/P) rises.

11.���� If something happens (such as a technological innovation) to increase MPL at any given L, the labor demand curve shifts right and the equilibrium (W/P) rises.� If something happens to decrease MPL at any given L, the labor demand curve shifts left and the equilibrium (W/P) falls.

12.���� If something happens to increase MPK at any given K, the capital demand curve shifts right and the equilibrium (R/P) rises.� If something happens to decrease MPK at any given K, the capital demand curve shifts left and the equilibrium (R/P) falls.

13.���� In practice, it is possible that a change in the supply of one factor will change the marginal product of the other factor.� For example, an increase in K might increase MPL, or an increase in L might also increase MPK.

14.���� In general, the total demand for GDP goods and services is C + I + G + NX, where C = personal consumption expenditures, I = gross private domestic investment, G = government purchases, and NX = net exports.� In Chapters 3-6 we assume the economy is closed -- that is, the economy has no international trade -- so that NX = 0.� This implies that total demand� =� C + I + G.

15.���� The supply of goods and services is given by Y = F(K,L).� Y is completely determined by the exogenous values of K and L.

16.���� C depends positively on after-tax income (= disposable income) Y-T, so we write C = C(Y-T).� The marginal propensity to consume (MPC) is the fraction of any change in disposable income that is spent on consumption.�� If Y-T increases by $100 and the MPC is 0.8, then C will rise by $80 and consumer saving will therefore rise by $20.

17.���� The real interest rate (r) is the cost of borrowing (and the return to lending) after adjustment for inflation.� If the nominal interest rate on a loan is 10% and the inflation rate is 7%, the real interest rate is 3%.�

18.���� I depends negatively on the real interest rate, so we write I = I(r).

19.���� We assume in Chapter 3 that G and T are exogenous.

20.���� Thus supply = demand in the goods market implies that� Y = C(Y-T) + I(r) + G.� Y is completely determined by the exogenous values of K and L.� T is exogenous, so Y-T completely determines C.� G is exogenous.� Thus the only variable that can adjust to maintain the above equality is I, which depends on r.� This means that the real interest rate adjusts so that the aggregate market� for goods and services moves to equilibrium.

21.���� If Y > C+I+G, then r needs to decrease.� This increases I, and should occur until C+I+G has risen enough to equal Y.�

22.���� If Y < C+I+G, then r needs to increase.� This decreases I, and should occur until C+I+G has fallen� enough to equal Y.�

23.���� For an intuitive understanding of why the real interest rate (r) adjusts, note that Y� =� C + I + G implies (Y - C - T) + (T - G) = I.� (Y - C - T) is private saving, and (T - G) is government saving.� The sum of private and government saving is total saving, which we denote S.� Thus the goods market is in equilibrium with Y = C+I+G if and only if S = I.� In the market for loans, we can think of S as the supply of loans and I as the demand for loans.� If Y > C+I+G, then S > I and the excess supply of loans makes the real interest rate decrease as in #21 above.� If Y < C+I+G, then S < I and the excess demand for loans makes the real interest rate increase as in #22 above.

24.���� If C depends only on Y-T, then private saving is determined entirely by K and L (which determine Y) and T.� Government saving equals T-G, both of which are exogenous.� Thus total saving S depends only on Y (which depends only on K and L), T, and G.� This means that the "supply curve" in the loan market graph is vertical.� The demand curve, which depends on investment spending I, is downward sloping.

25.���� If we allow C to depend negatively on the real interest rate (r), then S will depend positively on the real interest rate and the supply curve in the loan market will be upward-sloping.

What is the cost minimizing combination of labor and capital?

How do you calculate cost minimization?

What does MPL W mean?

How does capital affect marginal product of labor?