Answers
q = K1/3L1/3
(a) Cost is minimized when (MPL/MPK) = w/r
MPL = 
q/L = [(1/3) x K1/3] / (L2/3)
MPK = q/K = [(1/3) x L1/3] / (K2/3)
MPL/MPK = K/L = w/r
K = L x (w/r)
Substituting in production function,
q = (wL/r)1/3L1/3
q = (w/r)1/3L1/3L1/3
q = (w/r)1/3L2/3
L2/3 = q x (r/w)1/3
L = [q x (r/w)1/3]3/2
L = q3/2 x (r/w)1/2 [Conditional factor demand for labor]
K = [q3/2 x (r/w)1/2] x (w/r) = q3/2 x (w/r)1/2 [Conditional factor demand for capital]
(b) Total cost: C = wL + rK
C = w x [q3/2 x (r/w)1/2] + r x [q3/2 x (w/r)1/2]
C = [q3/2 x (wr)1/2] + [q3/2 x (wr)1/2]
C = q3/2 x [(wr)1/2 + (wr)1/2]
C = q3/2 x (2wr)1/2 [Cost function]
(c) Firm's supply function is its Marginal cost (MC) function.
P = MC = dC/dq = (3/2) x q1/2 x (2wr)1/2 [Supply function]
(d) Substituting K = L x (w/r) into the cost function,
C = wL + r x [L x (w/r)]
C = L x [w + (w/r)]
C = L x [(wr + w)/r]
C = L x [w x (r + 1)/r]
L = (rC) / [w x (r + 1)] [Input demand for labor]
K = [(rC) / [w x (r + 1)/r] x (w/r) = (wC) / [w x (r + 1)/r] [Input demand for capital]
.Similar Solved Questions
1 answer
W20 oubam Part 2/4/lusershutch2&key ASH2NAPVIEM1OtqwdE9OGPRwNdueffectiveUsershutch (5 points) Solve the following system using augmented matrix methods -121,...
W20 oubam Part 2/4/lusershutch2&key ASH2NAPVIEM1OtqwdE9OGPRwNdueffectiveUsershutch (5 points) Solve the following system using augmented matrix methods -121, +63+ 121, --18 -21, +lx, +213 = -3 -121, +6x, + 121, --18 (a) The initial matrex is (b) First, perform the Row Operation R, R, The resulti...
1 answer
Please answer all fill in the blanks, thanks! In the United States, tire tread depth is...
Please answer all fill in the blanks, thanks! In the United States, tire tread depth is measured in 32nds of an inch. Car tires typically start out with 10/32 to 11/32 of an inch of tread depth. In most states, a tire is legally worn out when its tread depth reaches 2/32 of an inch. A random sample ...
1 answer
1. Suggest the method and approximate conditions that you feel would be appropriate to prepare 1-ethyl-1-chlorocyclohexane.
1. Suggest the method and approximate conditions that you feel would be appropriate to prepare 1-ethyl-1-chlorocyclohexane....
1 answer
A certain radio station broadcasts at a frequency of 30 MHz. (Hint: see the back cover...
A certain radio station broadcasts at a frequency of 30 MHz. (Hint: see the back cover of your book for the matrix prefixes.) = a. the speed of light is 300,000 km/s. who’s is the speed in m/s? b. what is the wavelength of this radio wave in meters?...
1 answer
A cncrie dam retaining 45 ft of water is shown in Pis 3-36 The specific (or...
A cncrie dam retaining 45 ft of water is shown in Pis 3-36 The specific (or unit) weight of the e S Assume there is hydrostatic uplift that varies uniformly from full hydrostatic ecand at tlee lhod of the dam to zero at the toc. Determine: (a) the factor of safety against sliding, if the . IKYO'...
1 answer
Answer check before I submit my final answer Problem 23 Intro You're about to buy a...
answer check before I submit my final answer Problem 23 Intro You're about to buy a new car for $10,000. The dealer offers you a one-year loan where you pay $871.73 every month for the next 12 months. Since you pay $871.73 12 $10,461 in total, the dealer claims that the loan's annual interes...
1 answer
10. (10 points) What current is required in the windings of a long solenoid that has...
10. (10 points) What current is required in the windings of a long solenoid that has N=1000 turns, over a length of 1=0.4 m to produce a magnetic field of 1.00x10-4 T?...
1 answer
4. Suppose you approximate the area under f(x) = sin(x)+2 on the domain sxs with n=4...
4. Suppose you approximate the area under f(x) = sin(x)+2 on the domain sxs with n=4 rectangles, using right endpoints. Hint- Be sure your calculator is in radian mode. a. Find the width of each rectangle. b. What are the x-values of the right endpoints that you will need? c. Draw a sketch of this f...
1 answer
Joe Dean, a 38-year-old male client, is admitted to the medical–surgical unit with newly diagnosed acquired...
Joe Dean, a 38-year-old male client, is admitted to the medical–surgical unit with newly diagnosed acquired immunodeficiency syndrome (AIDS) and pneumocystic pneumonia (PCP). He states that he shares needles with other IV drug users. He has had unprotected sexual intercourse with several partn...
1 answer
Those are JAVA Programs. Please write them in recursions , it requires the methods have to be...
Those are JAVA Programs. Please write them in recursions , it requires the methods have to be recursive(I understood how to write them by using for loop). Please don't use any syntax beyond chapter of Recursion. I only covered the materials to recursions and the materials before recur...
1 answer
Solve the logarithmic equation. Be sure to reject any value that is not in the domain...
Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 12) log 3 (x+6) + log 3 (x - 6) - log 3x = 2 A) (-3) B) (12, -3) C) (12) D) 12) — Solve the problem. 13) Find out how long it takes a $3100 inve...
1 answer
McOww.eConnect Math Deline Where the correlation Cell Che Question 16 of 44 (point) Atempt 1 of...
McOww.eConnect Math Deline Where the correlation Cell Che Question 16 of 44 (point) Atempt 1 of 1 View question in ou Oh 47m Remaining 42 Section Ele 3 Visit your local library: On a recent Saturday, a total of 1469 people visited a local library. Of these people, 240 were under age 10, 463 were age...
1 answer
If the charge on q1 is tripled, what will happen to the force between the two charges?
If the charge on q1 is tripled, what will happen to the force between the two charges?...
1 answer
Kindly write your answers to the following question according to the drwg. 1Lütfen göre yaniıt veriniz 2.1 Pls. Kin...
Kindly write your answers to the following question according to the drwg. 1Lütfen göre yaniıt veriniz 2.1 Pls. Kindly Indicate points of a,b.c.d,e on the drawing Lütfen çizimdeki ab.c a,b,c,d,e noktalarinin hangi 2.2 Pls. Kindly evaluate "PV diagrahm below" and wr...
1 answer
Review | Constants | Periodic Table The label on a can of ”Healthy Request” chicken noodle...
Review | Constants | Periodic Table The label on a can of ”Healthy Request” chicken noodle soup indicates that each 1-cup portion supplies 149 kcal and has 11 g of protein, 15 g of carbohydrate, and 5 g of fat. Calculate the percentage of calories that come from protein. Calculate the pe...
1 answer
CH3 A 60.0 mL solution of 0.183 M potassium alaninate (H2NC,H,CO,K) is titrated with 0.183 M...
CH3 A 60.0 mL solution of 0.183 M potassium alaninate (H2NC,H,CO,K) is titrated with 0.183 M HCl. The pKa values for the amino acid alanine are 2.344 (pKal) and 9.868 (pKa2), which correspond to the carboxylic acid and amino groups, respectively. H2NCH——0 Calculate the pH at the first eq...
1 answer
Describe two or more defining characteristics of the U.S. system that you believe are particularly important...
Describe two or more defining characteristics of the U.S. system that you believe are particularly important to bear in mind when considering the delivery of healthcare. Explain why. Describe potential implications of these characteristics for healthcare administrators, including opportun...