Question

Labour Demand with Perfect Competition in the Labour Market and Perfect Competition in the Output Market in the Long Run. You are the manager of a business that operates in perfectly competitive markets {both the Labour Market and Output Market}. The production function of the business is given by:Q =2L^1/4K^1/4 .The price of the product is “10”. The wage rate is “1”. The price of capital is “2”.

1. Find the use of labour and capital in the long run.

2. Explain the difference between the Short Run and Long Run

3. Sketch a diagram illustrating the relationship between Short Run and Long Run Labour Demand Curves.

Answer 1

1.

Q = 9 (44 kW4 W=1, r= 2 l. Let Cost (c) = wLark C= L+ 2K Setting-up Lagoongean - A = 2114 kellu +9 (C-L-2x) - -0 = &Rx+xytry - 150 = 0 on 22" x 7 x tapeta 22 -0 » t = 1 — using eqs. O bO, 42 > RK = 1 → 2X=2 Put QK = L in poroduction function. Q = 2 Qk)'4 14 Q = 3514 k'2 *= 2K -

2.

In short run, at least one resource is fixed. However in the long run all factors and resources are variable. In short run, scale of output doesn't change whereas it can change in the long run. Short run is studied under return to factor. Long run is studied under return to scale.

3.

A short run labor demand curve shows the changes in the wage rate on the employment keeping capital constant. However, the long-run labor demand curve shows the change in the wage rate on the employment and capital as both factors are considered as a variable in the long run.

Both the curves are downward sloping.

Long run demand curve is more elastic (flat) than the short run demand curve.

* SR Demand Curve & LR Labor Demand Labor