5 Steps to a 5 AP Microeconomics, 2014-2015 Edition

2. You can only spend $TC. Now find the highest level of output (Q*).

There is only one combination of two resources (we’ll use labor and capital) that satisfies

either of these two constraints, and it is found by using thisleast-cost rule. The price of

labor is PLand the price of capital (K) is PK.

MPL/PL=MPK/PK, or equivalently, MPL/MPK=PL/PK

Example:

If each of the inputs is hired at $1 per unit and at the current amount of labor

and capital you have employed, the MPL= 100 and the MPK= 10. Clearly, the

least-cost rule is not satisfied:

100 units/$l >10 units/$1

If you could spend $1 more on labor, you would see output increase by 100 units. That

extra $1 would come from spending $1 less on capital, which would decrease output by

10 units. So you spend the same amount of money but get 90 more units of output.

Great deal! In situations like this, where MPL/PL>MPK/PK, the firm is going to find

it in its best interest to increase spending on Land decrease spending on K. The law of

diminishing marginal returns predicts that as you increase L, MPLfalls. And as you decrease

K, MPKrises. The substitution of labor for capital ceases to be a great deal at the combina-

tion of Land Kwhere the ratios of marginal product per dollar are equal again.

WHICH

SITUATION FIRM WILL... CAUSES... AND... UNTIL

MPL/PL>MPK/PK ≠L and ØK ØMPL ≠MPK MPL/PL=MPK/PK

MPL/PL<MPK/PK ≠K and ØL ØMPK ≠MPL MPL/PL=MPK/PK

Example:

A producer of gadgets pays $5 for each hour of labor and $10 for each hour of

capital employed. Table 10.4 describes the marginal products of each at various

levels of employment. Told that you must produce Q=360 gadgets, find the

least-cost combination of labor and capital.

Table 10.4

# OF L EMPLOYED MPL # OF K EMPLOYED MPK

1 50 1 100

24 0 29 0

33 0 38 0

42 0 46 0

51 0 54 5

65630

Find all of the combinations of L and K where our rule is satisfied:

MPL/PL=MPK/PK

or MPL/MPK=$5/$10 =1/2.

146 á Step 4. Review the Knowledge You Need to Score High

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