University of Calgary Department of Economics Econ 301 Assignment 2 Dr. Vojtassak Fall 2016 Instructions: You are encouraged to work with your...

Question 1. To produce an airline flight, capital and labor are used in fixed proportions. It takes two pilots and one plane to produce a one safe trip. Daily rent of airplane is $50,000 and daily price of a pilot is $1,000

. a) Describe the isoquant map for the production of air trips.

b) Write down a production function of an airline company that produces safe air trips.

c) Suppose an airline company would like to provide 2 trips a thus rented 2 planes and hired 6 pilots. Explain both graphically and in words why this would be a foolish thing to do.

d) On the graph you drew for part (a), show how many planes and pilots airline company hires that minimize the cost of producing 2 trips, and draw the isocost line through the optimal input combination.

e) Repeat the part d) if the daily rent of an airplane is $60,000, while the price of a pilot stays at $1,000. Suppose technical progress in avionic equipment made it possible for a single pilot to handle a plane safely.

f) How would this shift the isoquant map described in part a)?

) How would this affect the average productivity of labor in this industry?

h) How would this affect the average productivity of capital (planes) in this industry?

i) Show graphically how the labor productivity increases when I. firm experiences “technical progress”; II. firm primarily substitutes of capital for labor.

Question 2: Suppose that the monthly output of bicycles is characterized by ???? = 20√????????, where K is the capital used in production and L is the number of worker hours employed. ???????????? = 10√????/???? and ???????????? = 10√????/????. a) Graph the isoquant with 2,000 bicycles.

b) How many units of capital firm has to employ to produce 2,000 bicycles, if firm employs 100 units of labour? How many units of capital firm has to employ to produce 2,000 bicycles, if firm employs 101 units of labour? What is the approximate value for the MRTS at L= 100?

c) Compare the result from past b) with MRTS calculated using a formula.

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Assume price of labour is w and price of capital is r.

d) Derive conditional demand for labour and capital. Derive minimized total cost.

e) Derive the equation of firm’s expansion path. Draw the expansion path. f) Suppose both wages and rental rate double. How would this affect the firm’s expansion path? How would long-run average and marginal cost be affected? What can you conclude about the effect of uniform inflation of input costs on the costs of bicycle production?

g) Suppose wages rise doubles but rental rate stay fixed. How would this affect the firm’s expansion path? How would this affect the long-run average and marginal cost of bicycle production? Why does a doubling of the wage result in a much smaller increase in average costs? Assume that technical progress shifted the production function to ???? = 40√????????, that is all of the input combinations identified earlier can now produce 4,000 bicycles per year. h) Would the value calculated for the MRTS in parts b) and c) be changed as a result of this technical progress, assuming now that the MRTS is measured along the q = 4,000 isoquant? i) Assuming this shift does not change the cost- minimizing expansion path, how are long-run total, average, and marginal costs affected?

Question 3. A manufacturing firm’s production function is Q = KL + K +L. For this production function, MPL = K + 1 and MPK = L + 1. Suppose that the price r of capital services is equal to 1, and let w denote price of the labour services. If the firm is required to produce 10 units of output, for what values of w would a cost-minimizing firm use a) only labour? b) only capital? c) both labour and capital?

Question 4: Research suggests that successful performance on exams requires preparation (that is, studying - L) and rest (that is, sleep - S). Neither by itself produces good exam grades, but in the right combination they maximize your exam performance. We can then model your exam grades as emerging from a production process that takes hours of studying and hours of sleep as inputs. Suppose this production process has increasing returns to scale.

a) On a graph with hours of sleep on the horizontal axis and hours of studying on the vertical, illustrate an isoquant that represents a particular exam performance level qA.

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b) Suppose you are always willing to pay $20 to get back an hour of sleep and $5 to get back an hour of studying. Illustrate on your graph the least cost way to get to the exam grade qA.

c) Suppose a new caffeine/ginseng drink comes on the market, and you find it makes you twice as productive when you study. What in your graph will change? Suppose that the production technology described above can be captured by the production function q = 40LS, where q is your exam grade, L is the number of hours spent studying, and S is the number of hours spent sleeping. MPL = 40S and MPK =40L.

d) Prove that this production process indeed have increasing returns to scale. e) What is the equation of isoquant?

f) What is the equation for a slope of an isoquant? What is this called? What does it indicate? g) Set up the cost minimization problem and solve for the conditional studying and sleeping demands as functions of pL(what you are willing to pay to get back an hour of studying) ,pS (what you are willing to pay to get back an hour of sleep), and q (your exam performance).

h) Discuss the demand functions you derived in g). Is sleep and studying normal inputs? What happens to optimal amount sleep and pS increases? What happens to optimal amount of studying as pL increases?

i) Now, assume that you are always willing to pay $20 to get back an hour of sleep and $5 to get back an hour of studying. What is your “optimal production plan”? j) Derive the cost function and simplify the function as much as you can. k) Continue with total cost function derived in part jand derive the average cost. Are marginal and average cost curves for this problem upward or downward sloping? Explain. What is the relationship between MC and AC? Draw the MC and AC. l) What is your “optimal production plan” if you wish to reach the exam performance of 160? m) What is the cost of this 160- score performance? Now suppose your instructor Lucia clearly tells you that you have to study for 5 hours to get 160-score performance. Reconsider the “short-run” problem where studying is fixed at L. n) What is your “optimal production plan”? What is your “optimal production plan” if you wish to reach the exam performance of 160? Draw this short run solution along with long run solution in one graph. o) What is the short-run cost function? What is the short-run marginal cost function? Average cost function? p) Compare cost functions from part o) with cost functions from part k).