Isoquants

1. In this chapter we want to explore ideas about production of output from using inputs and then look at how much that production will cost. Isoquants An isoquant is a curve or line that has various combinations of inputs that yield the same amount of output.

2. Production function Here we will assume output is made with the inputs capital and labor. K = amount of capital used and L = amount of labor. The production function is written in general as Q = F(K, L), where Q = output,and F and the parentheses are general symbols that mean output is a function of capital and labor. The output, Q, from the production function is the maximum output that can be obtained form the inputs. Two screens from now we will see some isoquants. Note: on a given curve L and K change while Q is fixed.

3. Time Frame In production, we have said that firms have the ability to use both capital and labor. When you consider the fact that capital is basically the production facility – the building, equipment, machines and the like – you can get the feeling that it is probably less easy to change the capital than it is to change the amount of labor used. When you look at how long it takes to change the amount of capital in production, during that time when capital can not be changed in amount the time period of production is said to be the SHORT RUN. When all inputs can be changed we are in the LONG RUN.

4. Long run Capital On a curve we have different combinations of L and K that give the same amount of output. Curves farther out in the northeast direction have more output. Later we will say more about what the firm uses as a guide to choice of position in the graph. The position chosen will have implications for the amount of labor demanded. Labor

5. Short Run Capital In the short run the firm would have a given amount of capital, say K* here. Production would occur along the dotted line. K* Labor

6. Marginal Rate of Technical Substitution - MRTS Capital Change in K Change in L On the next slide I will refer to a change with the use of a triangle. slope = Labor

7. MRTS The slope of the curve at a point is K/ L Now, if the marginal product of an input is defined as the change in output divided by the change in the input, the slope can be manipulated to be: K Q and since K = 1 L Q Q MPK So the slope is MPL/MPK and is called the MRTS (in absolute value) and it is a measure of the rate at which inputs can be substituted and output remains the same.

8. A few slides back I showed an isoquant. I also put a tangent line at a point on the curve. The slope of a curved line is really the slope of a tangent line. You will notice that as you move along the curved line from left to right that the slope of a tangent line gets smaller (in absolute value).

9. Production and Costs in the Short Run

10. Overview In this section we want to 1) Think about how production might occur and change as different amounts of inputs are used in the production process, and 2) Translate the production data into cost data. In other words, we will want to understand how the cost of producing various units of output might change as different amounts of inputs are used.

11. Fixed/variable inputs Inputs can be classified as either fixed or variable. A variable input is one that can be changed as the level of output is changed . A fixed input is one that can not be changed as the level of output is changed. We often think of labor as a variable input and capital or land as a fixed input.

12. Short run/long run The notion of a fixed or variable input is related to the time frame of production. The short run is that period of time when at least one input is fixed in amount. The long run is that period of time in which all inputs are variable. As an example of this consider fast food in Wayne. About any store in town could remodel and increase floor space in about 3 months. So after 3 months we have the long run, all inputs can vary - even floor space. But less than three months is the short run because there is only so much floor space to use.

13. Note here that as K = 2, if L = 1, Q = 76 and if L = 2, Q = 248, and if L = 3, Q = 492, and so. On the next slide I show this information and more. Note: the numbers are made up Short run Capital K=2 and not based on any specific mathematical function. Q = 492 Q = 248 Q = 76 Labor 1 2 3 and so on

15. example continued In the example, the relationship between the labor used and the total product (TP), or output, is called the short run production function. Behind the scenes we assume there is a given amount of capital. The marginal product of labor is the additional output forthcoming from the additional unit of labor. Note the first unit of labor has a marginal product of 76. Note that as the units of labor increases the marginal product first increases, but then begins to diminish after the third unit of labor is employed.

16. example continued The marginal product curve has the pattern it does because of the way the fixed input is used. Remember that the variable input is used in conjunction with only so much of the fixed input. In the beginning, as more labor is added, specialization of labor can occur and increasing returns to labor can result, but eventually as more labor is added there will be less of the fixed input to work with and thus additions to output have to diminish. The way output changes as the variable input is changed, with a given amount of a fixed input, is summarized with the phrase diminishing marginal product.

17. The average product of labor is for each amount of labor the output produced divided by the labor amount. The average product mimics, or follows, the marginal product. It is just a math thing. Next let’s look at some graphs.

18. TP and MPL, APL

19. Notes about MPL and APL • Note • When the MPL is above the APL the APL rises. • When the MPL is below the APL the APL falls. • The APL continues to rise while the MPL is falling only when the MPL is above the APL.

20. short run costs In the short run we will consider the fixed and variable costs of production and how they change as more of the variable input is used. Definitions: Total cost (TC) = Total variable cost(TVC) + Total fixed cost (TFC). Marginal cost(MC) = (change in TC)/(change in output). where change in output = 1 when possible. Average cost (AC) = TC/Q. Average variable cost(AVC) = TVC/Q. Average fixed cost(AFC) = TFC/Q. Note that in the short run fixed costs must be paid whether output is zero or 100,000 units.

21. example Let’s take the production example we had before and translate the production data into cost data. Say the fixed costs is $1000 per unit of capital and we had two units before in our example, and the cost of labor is $400 per unit. The next screen shows the continuation of our example.

24. COST Curves

25. Idealized graph of per unit costs in the short run $/unit AC AVC MC Q Note AVC and AC equal MC when AVC and AC are at their minimum values.

26. When you look back at the marginal product and average product curves note that the horizontal axis is measuring labor units used and the curves are inverted u-shaped curves. When you look back at the marginal cost and various average cost curves note that the horizontal axis is measuring output units and the curves are u-shaped curves. There is a relationship between these two graphs. When you move to the right by adding labor in the one graph you are moving to the right in the other by having output increased.

27. How much output should the firm make? How much of the variable labor should be hired? At this stage of our study we can say in general that additional units of output should be made if the additional revenue on those units is at least as great as the cost on those units. Even if the additional revenue is equal to the additional cost nothing has been lost, so we say produce units until the marginal revenue equals the marginal cost. Now, if we assume all the units are sold at the same price, then the additional revenue per unit sold is the price of the output. In this case MR = P.

28. The marginal cost of production is the change in total cost divided by the change in output. The marginal product of labor is the change in output divided by the change in labor. MC = ▲TC/▲Q, and MPL = ▲Q/▲L, so MC = ▲TC/(MPL ▲L) = price labor/MPL. So MR = MC implies P of output = price labor/MPL on the last unit of output made or on the last unit of labor hired. This can also be seen as P of output times MPL = price labor. So a rule of thumb is make output until MR = MC, or from a different point of view, hire labor up to the point where the value of the marginal product, VMP (this is P of output times MPL) = the wage (the price of labor).

30. On the previous slide assume price of output is $3 per unit, and the wage is $400. Note 9 units of labor is desired because VMP is at least as great as the wage, but not on 10 units. Also, 2124 units of output should be made, but not more because P of output is at least as great as the MC, but not on more units.