8-3 ### Question 3 (1 Point)**Minimizing costs implies that which of the following conditions are true? (check all that apply)**- [ ] MPL/w = MPK/r- [ ] Q = wL + rK- [ ] MPL = w- [ ] MPK = r- [ ] MRTS = w/r**Key:**- **MPL:** Marginal Product of Labor- **MPK:** Marginal Product of Capital- **w:** Wage rate- **r:** Rental rate of capital- **MRTS:** Marginal Rate of Technical Substitution- **Q:** Total output- **L:** Quantity of labor- **K:** Quantity of capitalParticipants are instructed to select all conditions that are true for cost minimization. There are no graphs or diagrams accompanying this text.

Answered: Minimizing costs implies that which of…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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8-3

Expert Solution

Step 1

Answer:

Correct options:

(1). MP_L/w = MP_K/r

(2) MRTS = w/r

Explanation:

Cost minimizing condition: a firm minimizes its cost where the marginal product of labor divided by the wage (w) is equal to the marginal product of capital divided by the rental price of capital (r).

$\frac{M P_{L}}{w} = \frac{M P_{K}}{r} w h e r e, M P_{L} = m a r g i n a l p r o d u c t o f l a b o r w = w a g e r a t e M P_{K} = m a r g i n a l p r o d u c t o f c a p i t a l r = r e n t a l p r i c e o f c a p i t a l$

After restructuring the above equation:

$\frac{M P_{L}}{M P_{K}} = \frac{w}{r} a n d \frac{M P_{L}}{M P_{K}} (t h e r a t i o o f m a r g i n a l p r o d u c t o f l a b o r a n d m a r g i n a l p r o d u c t o f c a p i t a l) i s c a l l e d m a r g i n a l r a t e o f t e c h n i c a l s u b s t i t u t i o n (M R T S) . S o, M R T S = \frac{w}{r}$

So, option 1 and option 5 are correct.

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