ECO303 – Spring 2017

Assignment 6

Please, note the following: In your answers you must always explain what you are doing and make your calculations explicit.

Otherwise you will not obtain any points, EVEN THOUGH your answer might be correct.

In your explanations, use whole sentences and a clear syntax, similarly to the textbook.

Whenever it is not explicitly required, it is up to you to use equations and/or graphs in your answers.

If you use equations, remember to define each variable and what the equation stands for.

If you use graphs, remember to label clearly the a. axes; b. curves; c. initial equilibrium point(s); d.

terminal or final equilibrium point(s); and e. the direction the curves shift. ………………………………………………………………………………………………………………

1. A widget manufacturer has an infinitely substitutable production function of the form = 2 + .

a) Graph the isoquant map (in blue) for q=20, q=40, and q=60. What is the RTS(of L for K) along

each isoquant?

b) If the wage rate (w) is $1 and the rental rate of capital (v) is $1, write the algebraic expression for

the isocost line. Give an expression for the y-intercept, x-intercept and slope. Use your graph in

(a) to graph also the isocost map (in red).

c) What cost-minimizing combination of K and L will the manufacturer employ for the three

different production levels in (a)? What is the manufacturer’s expansion path?

d) How would your answer in (b) change if v rose to $3 with w remaining at $1? Explain your

result briefly.

e) How would your answer in (b) change if w rose to $3 with v remaining at $1? Explain your

result briefly.

2. Suppose the Round Balloon Company has a fixed proportions production function that requires it to

use two machines and one worker to produce 1000 balloons per hour.

a) Explain why the cost per hour of producing 1000 balloons is 2w+v, where w is the hourly

wage rate and v is the machine rental rate per hour.

b) Assume Round Balloon can produce any number of balloons it wants using this technology.

Explain why the total cost function in this case would be

= (2 + ), where q is

output of balloons per hour, measured in thousands of balloons.

c) What is the average and marginal cost of balloon production? Remember to measure output

in thousands of balloons.

d) Graph the average and marginal costs curves for balloons assuming v=3 and w=5.

e) Now, graph the average and marginal cost curves for v=6 and w=5. How have the cost

curves changed? Why? 3. The long-run total cost function for a firm producing bicycles is

=

? 40 + 430 , where q

is the number of bicycles per week.

a) Plot the total cost function for q=0, q=10, q=20, q=30 and q=40. What is the general shape of

this total cost function?

b) Calculate the average cost function for bicycles. Graph the average cost function for for q=0,

q=10, q=20, q=30 and q=40. What shape does the graph of this function have? At what level

of bicycle output does average cost reach a minimum? What is the average cost at this level

of output?

c) What is the marginal cost function for bicycles? Graph the marginal cost function for q=0,

q=10, q=20, q=30 and q=40. Does this function intersect the average cost function? At what

level of output? Why would that be?

4. A firm producing golf sticks has a production function given by = 2? . In the short run, the

firm’s amount of capital equipment is fixed at K=100. The rental rate for K is $1 and the wage rate is

$4.

a) Calculate the firm’s short-run total cost function (STC). Calculate the short-run average cost

function (SAC).

b) Calculate the firm’s short-run marginal cost function (SMC). What are the STC, SAC, and

SMC for the firm if it produces 25, 50, 100, and 200 golf sticks?

c) Graph the SAC and the SMC curves for the firm. Indicate the points found in (b).

d) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will

always intersect the SAC curve at its lowest point.

5. Returning to the balloon producer in Problem 2,

a) What type of returns to scale in production does the TC function indicate? Explain briefly.

b) Now, suppose instead that the balloon cost function is given by

= (2 + ) . What

type of returns to scale in production does this function illustrate? Explain briefly.

c) How does the graph of the TC function in (b) look like? What do the implied average and

marginal cost curves look like?

d) Suppose now that the balloon cost function is

= (2 + ) . What type of returns to

scale does this function illustrate? Graph the total, average, and marginal cost curves for this

function.