A firm has a production function represented by: q=L^(.75)K^(.25) Find a functio
ID: 1169017 • Letter: A
Question
A firm has a production function represented by: q=L^(.75)K^(.25)
Find a function for how much capital and labor a firm should hire to produce a given level of production in terms of the price of labor,w, and the price capital,r.
Suppose w=15 and r=5. What amounts of labor and capital should the firm choose in order to produce 100 units of this good in the least expensive manner?
Please answer the questions completely. One tutor answered incomplete and I gave him a negative rating and that person is now removed. So please answer completely.
Explanation / Answer
a firm produce where isocost line' s slope is equal to slope of its isoquant ( related to production) , that means isocost lines is tangent to isoquant, SO THAT PRODUCTION CAN BE DONE AT MINIMUM COST
slope of isocost line= - w/r
slope of isoquant = MRTSLK = - MPL/MPK = - .75 L-0.25 K0.25/ .25 L0.75K-0.75
= - 3 K/L
WHERE MRTSLK = MARGINAL RATE OF TECHNICAL SUBSTITUTION BETWEEN LABOUR AND CAPITAL
MPL= MARGINAL PRODUCTIVITY OF LABOUR
MPK= MARGINAL CAPITAL
FOR 1 ST PART TO FIND OUT HOW MUCH LABOUR AND CAPIATAL A FIRM SHOULD EMPLOY, WE NEED TO EQUATE THESE TWO SLOPES
- 3K/L = - w/r
3 K/L= w/r
OR 3 K r= w L
2 ND PART WHEN w=15 and r=5
that means above condition required will be 3K *5 = 15* L
K=L
NOW IN ORDER TO PRODUCE 100 UNITS THIS IS CONDITION REQUIRED THAT K = L
NOW IN ORDER TO FIND THE VALUE OF K AND L WHEN 100 UNITS ARE PRODUCED IN LEAST EXPENSIVE MANNER, WE NEED TO INSERT THIS CONDITION INTO PRODUCTION FUNCTION
Q = L.75 K.25
100 = K.75 K.25
100 = K
THERE L WILL ALSO BE EQUAL TO 100
K=L=100 ARE REQUIRED IN ORDER TO PRODUCE 100 UNITS IN THE LEAST EXPENSIVE MANNER
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.