Q1.A production process uses only one input, labor, and is described by the following production function:

Q = 12L²- 1/3 L³

(a)At what level of input L does diminishing returns start?

(b)Calculate the range of values for labor over which stage II occurs.

Q2.A firm uses only one variable input and faces the following Average Cost function:

AC = Q²- 12Q + 408 + 20/Q

Calculate the output level (Q) at which diminishing returns set in.

Q3.A production process uses only one input, labor, and is described by the following

production function:

Q = 24L²- 1/3 L³

(Note: This function is applicable only for labor input rates between 0 and 72.)

Calculate the range of values for labor over which stage II occurs.

Q4.Suppose the production function for widgets is given by:

Q = KL - 0.8K²- 0.2L²

where Q represents the quantity of widgets produced, K represents the annual capital input and L represents annual labor input.

(a)For K = 10, what is the average productivity of labor equal to?

(b)At what level of labor input does this average productivity reach a maximum? How many widgets are produced at this point?

(c)Again assuming that K = 10, what is the marginal product of labor equal to?

(d)Graph the AP_Land MP_Lcurves.

Q5.Given the following short-run production function (x = variable input, Q = output):

Q = 3x²- 0.1x³

(a)Determine the marginal product function (MP_x) and the average productfunction (AP_x).

(b)Find the value of x that maximizes Q.

(c)Find the value of x for which MP_xis maximum.

(d)Find the value of x for which AP_xis maximum.

(e)Determine the boundaries of the three stages of production.

Q6.A firm faces the following production function:

Q = - 0.1 L³+ 12 L²+ 360L

At what level of employment (L) does diminishing returns set in?

Q7.Consider the following short-run information regarding the production of widgets:

Labor

Total Product

8

40

9

54

10

64

To which stage of production do these quantities of labor correspond? How do you

know?

Q8.The Average Product of labour at the firm Widgets, Woozles, and Whatits located in the Western Wheatbelt of Westonia (www.www.www on the web) is given by:

AP_L= -L²+ 18L + 350

At what level of input L does diminishing returns start?

Q9. A perfectly competitive firm operates in the short-run with labor as its only variable factor. Its production function is:

Q = -L³+ 10L²+ 88L

where Q is output per week measured in tons and L is the number of workers employed. The weekly wage is $324 and the product sells for $3.24 per ton.

(a) At what weekly output is marginal cost equal to average variable cost?

(b) What is the minimum product price at which the firm will operate in the short-run?

(c) How many workers should the firm employ to maximize profits?

(d) Calculate the firm's point elasticity of demand for labor at the equilibrium in (c) above.

Q10.For each of the following production functions, determine whether returns to scale are decreasing, increasing or constant:

(a) Q = 2K + 3L + KL

(b) Q = 30L^0.6K^0.5

(c) Q = 10 + 3K + 2L

(d) Q = K/L