Question

A rm has the following production function:y = L^1/3K^1/2

(a) Does this production function exhibit increasing, decreasing, or constant returns to scale? Prove.

(b) Suppose in the short run, capital is xed at K = 100. Assuming that the output and factor prices are p, w; and r respectively, find firm's factor demand for labor. What will the effects be when w, r and p increase? Explain your results intuitively.

(c) Now, suppose the government decides to impose a payroll tax of $t per worker employed. What will the effect be on L*? Why?

(d) Alternatively, if the government decides to impose a lum-sum tax of $T, what will the e¤ect be on L*? Why?

Answer 1

A rm has the following production function:

y = L1/3K1/2

(a) Does this production function exhibit increasing, decreasing, or constant returns to scale? Prove.

: - The sun of expinents is

=1/3 + 1/2

= 2+3/ 6

= 5/6

= 0.833

0.833 < 1

Therefore , the production function has decreasing returns to scale.

(b) Suppose in the short run, capital is xed at K = 100. Assuming that the output and factor prices are p, w; and r respectively, find firm's factor demand for labor. What will the effects be when w, r and p increase? Explain your results intuitively.

:- k =100

The demand of labor for the firm × value of MPL  = wages rate

P × MPL = w

P × (1/3 × (L)-2/3 × (K)1/2 ) = w

1/3 × p × 1/ (L)2/3 × (K)1/2 = w

1/3 × p × (K)1/2/ w = (L)2/3

(1/3 × p × 10/w)3/2 = Ld

This is demand for Labour , As in increase demand for labour will decrease . As P increases demand for labour also increases and vice versa r has no impact on demand for labour because it is cobb-denglas where input are demanded in fixed ratio.

(c) Now, suppose the government decides to impose a payroll tax of $t per worker employed. What will the effect be on L*? Why?

:- The government decide to impose a payroll tax then This will increase wage rate to $(w+t). Therefore the wage rate increases labour demanded will fall as beth are directly related to each other.

(d) Alternatively, if the government decides to impose a lum-sum tax of $T, what will the e¤ect be on L*? Why?

:- Imposition of lumpurum tax that will reduce overall level of prediction in the economy and the Y is decreased labour demanded that will also decrease and therefore the effect be on L* is decreases .