Production (6 points) The firm Avanti produces custom-made sports cars that appe

Question

Production (6 points) The firm Avanti produces custom-made sports cars that appeal to a certain clientele because of their high price and thus exclusivity. Avanti has the following production function: q = f(k, l) = k2/311/3 where k and I are the capital and labor input respectively (a) What additional output does one additional s unit of capital produce when the capital- (b) If you employed three workers less (again, small units), how many additional units of capital labor ratio is (k/l)-8? (2) would you need to produce the same output? Assume that the capital-labor ratio is (k/t) 8 Do not assume this any further.] (2) (c) How many units of labor does the firm need to produce 10 units of output in the short run when the capital stock is fixed at a level of k 5? (2)

Explanation / Answer

a) q=k2/3l1/3

dq/dk when l is assumed to be constant=2/3k-1/3l1/3=2/3(l/k)1/3 at k/l=8 dq/dk=2/3*1/2=1/3 additional Output

b)dq/dl= 1/3(k/l)2/3+2/3(l/k)1/3dk/dl for dq=0; 1/3(k/l)2/3*dl+2/3(l/k)1/3dk=0

givenk/l=8 and dl=-3;1/3(8)2/3*(-3)+2/3(1/8)1/3dk=0

this gives dk=12 hence we need to increase capital by 12 units fo same output

c)for q=k2/3l1/3

q=10,k=5 putting into equation 10=52/3l1/3

this gives l=40

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.