Question

Plastic bags are great 2) The production of plastic bags is given by the production function q K is capital and L is labor. f(LK) s, where Short Run Production a. ) Find the expressions for the Marginal Product of Labor (MP) and Average Product of Labor (APL) in the Short Run, when K is fixed at 400. i) Derive L() in the Short Run, again with K fixed at 400. iii) The Cost Function is given by C K+wl, where is the rental rate for Kand w is the wage paid for L. With K still fixed at 400 and using L(q), derive the Cost Function in terms of the output q, or C(q). iv) Calculate expression Marginal Cost MC(g)]. Average Variable Cost [AVC(4)] and Average Cost [AC(g) v) Show that AVC = w/APL when K is fixed at 400. b. Long Run Production D With Capital no longer fixed, solve the firm's Cost Minimization problem, finding L and K in terms ofr, w and the output level q. i) What is the Firm Long Run Cost Function C(q) in terms of r, w and q? ii) What is the Marginal Cost (MC) and Average Cost (AC) of this firm in the Long Run?

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Answer 1

Q.2.

a)

Production function:

i)

When K is fixed at 400,

0.5

$MP_L = \frac{\partial q }{\partial L} = 40L^{-0.5}$

$AP_L = \frac{ q }{L} = 80L^{-0.5}$

ii)

08

iii)

Cost function:

6400

iv)

$MC(q) = \frac{\mathrm{d} C}{\mathrm{d} q} = \frac{wq}{3200}$

$AVC(q) = \frac{VC}{q} = \frac{wq}{6400}$

$AC(q) = \frac{AC}{q} = \frac{wq}{6400} + \frac{400r}{q}$

v)

L.H.S

$AVC(q) = \frac{VC}{q} = \frac{wq}{6400}$

R.H.S.

$\frac{w}{AP_L} = \frac{w}{80L^{-0.5}} = \frac{wq}{80*80} = \frac{wq}{6400} = R.H.S.$