• Any point below the PS characterizes inefficiency.Theory of Production...QUESTIONS(1) Given CD PF of• If A = 25, and a = /,Q = AK" L'-aDetermine:AP = TP/LMP,= dTP/ƏLMPK = dTP/ƏK(2) Given a PF of the type1-aDetermine:Q = AK" + L"• AP = TP/L• MP,= dTP/ƏLMPK = dTP/ƏK%3D(3) If in (1) above, A = 100, a = 0.6, K = 25, and L= 100,determine MPL, MPK, AP, APK and TP.%3DTheory of Production..(4) Suppose a production function is represented byQ = F(K,L) = 600K²L² - K3L3• To construct MP, and AP, assume that K = 10• The production function becomesq = 60,000l2 - 10ool3Q = 60,000L? - 1000L3The marginal productivity function isMPL = dTP/dL = 120,000L - 30ooL? which diminishes as L increases• This implies that Q has a maximum value:• 120,000L - 30ooL? = 0; 40L = L2; L = 40• Labour input beyond L= 4o reduces output.• To find average productivity, we hold K=10 and solve AP, = Q/L = 60,000L1000L?• AP, reaches its maximum where ô APL/L = 60,000 - 2000L = 0; L = 30• In fact, when L = 30, both APL and MPL are equal to 900,000%3D• Thus, when AP_ is at its maximum, AP, and MP are equalTheory of Production...Long Run production function• The long run is a period sufficiently long that all inputs ofproduction including capital can be adjusted or are all variables.Long-run production function therefore shows the maximumquantity of output that a firm can be produced using a set ofinputs with the assumption of varying all inputs.• With this the firm can choose any combination of inputs forproduction.• One approach to choosing the optimal (least costly) mix of inputsis to compare the (marginal) cost of producing one extra unit ofoutput across different inputs.

Marginal product of labour means a unit change in labour how much TP will change . Whereas MPK…

Theory QUESTIONS (1) Given CD PF of - If A = 25, and a = Q = AK“L-a || /2 %3D - Determine: - AP = TP/L - MPL= dTP/ƏL - MPK = dTP/ƏK %3D %3D - (2) Given a PF of the type - Determine: - AP = TP/L - MPL= dTP/ƏL - MPK = dTP/dK Q = AK" + L'a %3D %3D (3) If in (1) above, A = 100, a = 0.6, K = 25, and L= 100, determine MPL, MPK, APL, APK and TP. %3D %3D

Theory QUESTIONS (1) Given CD PF of - If A = 25, and a = Q = AK“L-a || /2 %3D - Determine: - AP = TP/L - MPL= dTP/ƏL - MPK = dTP/ƏK %3D %3D - (2) Given a PF of the type - Determine: - AP = TP/L - MPL= dTP/ƏL - MPK = dTP/dK Q = AK" + L'a %3D %3D (3) If in (1) above, A = 100, a = 0.6, K = 25, and L= 100, determine MPL, MPK, APL, APK and TP. %3D %3D

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter3: Scarcity, Trade-offs, And Production Possibilities

Section: Chapter Questions

Problem 13P

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