1] Suppose that the production function of certain artifacts is determined by:

q = kl - 0.8k2 - 0.2l 2,

where q represents the annual quantity of artifacts produced, k represents the annual quantity

of the capital factor and l represents the annual amount of the labor factor.

a) Suppose that k = 10; draw a graph of the average productivity and total productivity

job. What is the level of the labor factor with which the average productivity reaches

the maximum? How many artifacts are produced at that point?

b) Assuming again that k = 10, draw the curve of the PMgl

. At what level do we have

that the work factor is PMgl = 0?

c) Suppose that the capital factor increased to k = 20. How would its

answers to the previous two sections?

d) Does this artifact production function exhibit constant returns to scale,

increasing or decreasing?

2] A company that produces hockey sticks has a production function

determined by

q = 2 (K L) ?1 / 2

In the short run, the amount of capital equipment in the firm is fixed at K = 100. The rate of

K's rent is r = $ 1 and L's wage rate is w = $ 4.

a) Calculate the curve of the total cost, in the short term, of the company. Calculate the curve of

short-term average cost.

b) What is the short-run marginal cost function of the firm? Which are

the CTcp, the CPcp and the CMg if the company produces 25 canes? Fifty

Canes? One hundred staves? Two hundred sticks?

c) Draw the curves of the CPcp and CMgcp of the company. Indicate the points

calculated in the previous paragraph.

d) Where does the CMgcp curve intersect the CPcp curve? Explain why the

The CMgcp curve always cuts the CPcp curve at its lowest point.

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Diary

Costs

Short term

Long term

The cost of a factor of production is determined by the magnitude of the payment necessary to maintain the resource within its current use (Nicholson; 2008)

Q = f (K, L) = AK ^ ? L ^ ?

Where:

Q is the level of production

K is the capital factor

L is the work factor

?, ? are parameters between 0 and 1

* We will assume a Cobb-Douglas function

There are only 2 factors of production

We are in a perfectly competitive market

Therefore, companies can exchange factors at their prices (r, w)

It is a rational optimizing agent

As seen in the Production Function, the firm seeks to maximize its benefits:

? = R-C

Where:

? are benefits

R is the total income (p * q)

C are the total costs

Fixed Costs: a production expense that does NOT vary with the level of production [CF]

Variable Costs: a production expense that changes with the amount of production. [CV]

Total costs: The result of adding Fixed Costs and Variable Costs

CT = CF + CV

Amount in which the cost varies when the firm decides to change the production level by one unit.

Cmg = ?CT / ?Q

We can also understand marginal cost as the variation of Variable Costs when the level of production changes (see Perloff)

Average Total Cost {Cme}

It can be the CT / Q or the sum of CFme + CVme

Average Fixed Cost {CFme}

CFme = CF / Q

Average Variable Cost {CVme}

CVme = CV / Q

* The nomenclatures vary depending on the book

(a) 400 Cost, $ VC 216 120 B 48 F 0 2 4 10 Cost per unit, $ 3 Quantity, q, Units per day 60 MC 28 AC 27 AVC 20 8 AFC 0 2 4 6 8 10 Quantity, q, Units per day