Question

Afirm has production function q=10"(L^0.5)*(K^0.5), where "L"0.5" means "L raised to the 0.5 power," and the same applies to the K term. (The reason for this is that canvas doesn't understand the usual way of writing a power function.) In the short term, capital K is fixed at 9. 2(a) What is the multiplicative constant term in the firm's short run inverse demand for labor? Question 6 1 pts 2(b) What is the multiplicative constant term in the firm's short run direct demand for labor? Question 7 1 pts 2(c) What is the multiplicative constant term in the firm's long run inverse demand for labor?

Answer 1

Answer:

(A) 15 × p

(B) $225\times p{^2}$

(C)  $P\times 5\times k^{0.5}$

Explanation:

(B) direct= demand function of labor will be,

Q: f(w),

where Q is labor demand quantity and is function of wage

K=9 constant, then production function changes to,

$=30L^{0.5}$

Marginal product of labor:

$= 15L^{-0.5}$

Marginal revenue product or value of marginal product:

$=15p\times L^{- 0.5}$

This is showing what revenue a firm will generate due to hiring one additional unit of labor.

So firm will keep hiring until the revenue the additional labor is generating is equal to its hiring cost or wage.

So, putting MRP or VMP to wage:

$P\times15\times L^{-0.5}=W$

By solving,

$\frac{(225\times p^{2})}{W^{2}}=L$

And the multiplicative term is $225\times p{^2}$

(A) Inverse demand function of labor will be,

W: f(Q)  

where W is wage rate and demand function of labor demanded quantity.

As previously solved,

$P\times15 \times L^{0.5}=W$

and the multiplicative constant term is 15 × p.

(c) In long run capital will also variate, so production function will be,

$=10L^{0.5}\times k{^0.5}$

$MP=\frac{(5\times k^{0.5})}{L^{0.5}}$

$VMP=\frac{P(5\times k^{0.5})}{L^{0.5}}$

( p is market price of good that firm is producing using labor)

putting it equal to Wage)

$W=\frac{(5\times k^{0.5})}{L^{0.5}}$

and the constant term is  $P\times 5\times k^{0.5}$.

Note:

I did a) second place and b) on first . I already put the serial alphabet on the start of the answer.