:solve the following questions.

Problem 1.

Consider the Cobb-Douglas production function f(x,y) = 12x0.4y0.8.

(A) Find the intensities (? and 1 ? ?) of the two factors of production. Does this firm have decreasing, increasing, or constant returns to scale? What percentage of the firm's total production costs will be spent on good x?

(B) Suppose the firm decides to increase its input bundle (x, y) by 10%. That is, it inputs 10% more units of good x and 10% more units of good y. What is the percent increase in output?

(C) Suppose the firm has a production quota of q = 1000 units, and the firm inputs x = 100 units of the first good. How many units of the second good does it need to use to meet the quota?

(D) Assume the firm has a production quota of q = 2000 units, and the input prices are (px,py) = (7,19). Find the minimized cost C(2000) and the conditional factor demands (x?,y?).

Problem 2. Consider the linear (perfect substitutes) production function f (x, y) = 12.7x + 19.4y.

(A) How many units of good y would be a perfect substitute for 1 unit of good x? What is the slope of

the firm's isoquants?

(B) Suppose the input prices are (px,py) = (5,8). What is the slope of the isocost lines? How much output does the firm get when it inputs $1 worth of good x? How much output does the firm get when it inputs $1 worth of good y?

(C) Suppose this firm has a production quota of q = 500 units. Find the minimized cost C(500) and the corresponding conditional factor demands.

(D) Draw the firm's level-500 isoquant, as well as the isocost lines. Indicate the cost minimizer on your diagram.

Problem 3. Consider the Leontiev (perfect complements) production function f (x, y) = M in x , y . 9.6 5.2

(A) How many units of good y would be a perfect complement for 1 unit of good x? What is the equation of the firm's kink line?

(B) Assume the firm has a production quota of q = 400 units. Graph the firm's level-400 isoquant. What are the coordinates of the kink?

(C) Suppose the input prices are (px,py) = (16,9). Find the minimized cost C(400). What is the cost minimizing input bundle (x?, y?)?

(D) Give a complete geometric illustration of this firm's cost minimization. On a single diagram, draw the firm's level-400 isoquant, the isocost lines, and the cost minimizing input bundle.

Problem 4.

Suppose that a firm's production plan is (x, y, z) = (102, 19, 957), and the market prices are (px , py , pz ) = (10, 5, 1.25). How much profit would the firm make if it carried out this plan?

Problem 5.

Suppose that a firm's production function is f(x,y) = 20x0.7y0.3. Starting from the input bundle (x, y) = (40, 60), how much extra output will the firm get if it increases x from 40 to 41? How many units of output will the firm lose if x decreases from 40 to 39?

Problem 6.

Suppose that the production of airframes (for aircraft) uses two inputs: capital (good x) and labor (good y). The production function is f(x,y) = xy. Assume that the price of capital is $1 per unit, and the price of labor is $10 per unit. The manufacturer wants to make 121,000 airframes. Find the cost-minimizing combination of capital and labor inputs.

Use the figure below to answer the following questions 18-20: Two companies, ABC and XYZ, each decide whether to produce a high level of output or a low level of output. In the figure, the dollar amounts are payoffs and they represent annual profits for the two companies. ABC's Decision High output Low output ABCa profit = $3 million ABC's profit = $2 5 million High output XYZ's profit = $3 million XYZ's profit = $4 million XYZ's Decision ABC's profit = $4 million ABC's profit = $3.5 million Low output XYZ's profit = $2:5 million XYZ's profit = $3.5 million 18. The dominant strategy for ABC is to A) produce low output, and the dominant strategy for XYZ is to produce high output. B) produce low output, and the dominant strategy for XYZ is to produce low output. C) produce high output, and the dominant strategy for XYZ is to produce high output. D) produce high output, and the dominant strategy for XYZ is to produce low output. 19. If this game is played only once, then the most likely outcome is that A) both firms produce a low level of output. B) ABC produces a low level of output and XYZ produces a high level of output. C) ABC produces a high level of output and XYZ produces a low level of output. D) both firms produce a high level of output. 20. If this game is played repeatedly and ABC uses a tit-for-tat strategy, it will choose a A) high level of output in the first round and in subsequent rounds it will choose whatever XYZ choose in the previous round. B) low level of output in the first round and in subsequent rounds it will choose whatever XYZ choose in the previous round. C) high level of output in all rounds, regardless of the choice made by XYZ. D) high level of output in all rounds, regardless of the choice made by XYZ.1. A bit of practice with dummy variables and heferoskedasficify: Consider the following model for the logarithm of wage given years of university education and gender of person 1' : log(wage;) = g + qfemale, + lronmi; + lfemale; x tonmi; + u; # where log is the natural logarithm, femlei is a dummy variable that is equal to 1 if person i is female is 0 otherwise, and 10mm",- is the number of years of university education that person 1' has. Based on a random sample of 6763 individuals, we have estimated this model using OLS and obtained the following estimated equation: _--_-__-_ log(wage,z) =3.289 0.360fenmle; +0.050 forum,- +0.0309maie, x forum}, (0011) (0.015) (0.003) (0.005) 1':l,2,...,67l63,1l22 = 0.202. a. Explain how you would test the hypothesis that the conditional expectation of log(wage) conditional on years of university education is exactly the same for men and women. You need to specify the null and the alternative, the test statistic and its distribution under the null, the regression that you should run so that you can compute the test statistic, and the rule for rejection or non-rejection of the null hypothesis. c. Using the estimated equation, nd the value of tomni (total number of years in university) such that the predicted values of log(wage) are the same for men and women. Can women realistically get enough years of university education so that their earnings catch up to those of men? Explain. d. Suppose we suspect that the variation of log(wage) around its conditional mean is larger for women than it is for men. That means that in the Capital Budgeting Argo Airlines is looking to buy some gates at a West Coast airport. The key financial variables are below. Note that the gates revert back to the airport at the end of year 15. Note that any losses trigger tax benefits. Purchase Price $35M Yearly Revenue $15.5M Operating Costs 45% of revenue Discount Rate 9% Gate Renovation (Fit-out Costs) $6M (each in years 5 and 10) Revenue Inflator 2.2% Tax Rate 21% What are the NPV and IRR of the gates? Should Argo invest in them? Why or why not?selected? 8-24 A firm is considering three mutually exclusive alter- First cost $15,000 natives as part of a production improvement program. Maintenance 1,600 and operating The alternatives are as follows: Annual benefit 8,000 Salvage value 3,000 A B C Useful life, in years Installed cost $10,000 $15,000 $20,000 Uniform annual benefit 1.625 1.625 1,890 Useful life, in years No(a) Construct a ch 10 20 20 0% to 100%. For each alternative, the salvage value at the end of (b) MARR = 15 useful life is zero. At the end of 10 years, Alt. A should you b could be replaced by another A with identical cost return analy and benefits. 8-27 The Croc Co. i Noa) Construct a choice table for interest rates from from among 0% to 100%. years: ( b ) The MARR is 6%. If the analysis period is 20 years, which alternative should be selected? 8-25 A new 10,000-square-meter warehouse next door to First cost Annual be