ef2452_B07_PS10

# ef2452_B07_PS10 - MP L and capital MP K and fnd the rate oF...

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(EF 2452) Problem Set#10 Due: Week 12 Tutorial Class Please write your name, student ID and tutorial number on top of your answer sheet. Q1. A competitive frm sells its output ‘Q’ at the market price ‘P.’ Its production Function is given by Q = aL b ; where, a > 0 , 0 < b < 1 and L is the labor input. Suppose the frm can hire labor at a constant wage oF w . (a) Set up the frm’s proft Function and fnd it’s optimal (proft maximizing) demand For labor. (b) Conduct comparative statics exercises with respect to output price and the wage and interpret your answers. Q2. Consider the Following Cobb-Douglas production Function Q = F [ L,K ] = 12 L 0 . 7 K 0 . 4 . (a) Derive the slope oF the isoquants For the production Function. Are the isoquants negatively sloped? ±ind the marginal rate oF technical substitution (MRTS), which is the negative oF the slope oF the isoquant. (b) Derive the expressions For the marginal products oF labor (

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Unformatted text preview: MP L ) and capital ( MP K ) and fnd the rate oF change oF MP L due to a change in labor and MP K due to a change in capital respectively. Does the law oF diminishing marginal productivity oF labor and capital, hold For this production Function? (c) VeriFy that the rate oF change oF MP L with respect to (w.r.t.) K is the same as the rate oF change oF MP K w.r.t. L . [ This is an application of Young’s Theorem ] Q3. IF a frm spends \$ a per unit oF output on advertising then it can sell q units oF output at a price given by p = 100-2 q + 8 a 1 2 . ±urther, in order to produce q units oF output it costs the frm 4 q + q 2 . (a) Find the proft ±unction ( π ) ±or the frm. (b) I± the frm maximizes profts, how much will it spend on advertising and how much output will it produce? Remember to check the SOC’s....
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ef2452_B07_PS10 - MP L and capital MP K and fnd the rate oF...

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