1. A firm uses the inputs of fertilizer and labor to produce roses. Suppose that when the quantity of labor is fixed, the relationship between the quantity of fertilizer and the number of roses produced is given by the following table:

Fertilizer: 0 1 2 3 4 5 6 7 8 9 10

Roses: 0 6 25 33 40 45 49 50 41 20 -6

a) What is the average product of fertilizer when 4 tonsare used?

b) What is the marginal product of the 6th ton of fertilizer?

c) Does this total product function exhibit diminishing marginal returns? If so, over what quantities of fertilizer do they occur?

d) Does this total product function exhibit diminishing total returns? If so, over what quantities of fertilizer do they occur?

2. A rm is required to produce 132 units of output using quantities of labor and capital (L;K) = (16; 4). For each of the following production functions, state whether it is possible to produce the required output with the given input combination. If it is possible, state whether producing Q = 132 with input combination is technically ecient or inecient.

(a) Q = 6L + 9K

(b) Q = 2KL + L - 8.

(c) Q = 7KL

(d) Q = min f3L; 17Kg

3. Consider the production function Q = L^2K^5 K^3.

(a) Determine the MRTSL;K for this production function.

(b) Does this production function have an uneconomic region? If so, describe the region algebraically. (Hint: your answer will be an inequality like this: K < 5L)

4. A rm's production function is Q = 6L^(2/5)K^(3/5).

(a) Does this production function have constant, increasing, or decreasing returns to scale?

(b) Determine MRTSL;K for this production function.

(c) What is the elasticity of substitution for this production function? (Hint: what type of production function is this?)

5. A firm experiences technological progress from time 1 to time 2. At one of the times their production function is

QA = L^(1/2)K^(1/3) and at other time it is QB = L^(3/2)K^(7/4).

Assume that L > 1 and K > 1.

(a) What is their production function at time 1 and time 2 if they experienced technological progress?

(b) Is this change labor saving, capital saving, or neutral?