Question

A firm (The Flying Elvis Copter Rides) is making a long-run planning decision. It
wants to decide on the optimal size of plant and labor force. It is considering
building a medium-sized plant and hiring 100 workers. Engineering estimates
suggest that at those levels, the marginal product of capital will be 100 and the
marginal product of labor will be 75.

If the wage rate is $5 and the rental rate on capital is $10, is the firm making
the right decision? (2 points). Support your answer (3 points).

Suppose The Flying Elvis Copter Rides has the following cost schedules in Table 1.
Table 1-The Flying Elvis Copter Rides

Quantity	Total cost	Fixed Cost	Variable Cost	Marginal Cost	Average fixed cost	average variable cost	Average total cost
0	$50	$50	$0	---	---	---	---
1	$150	A	B	C	D	E	F
2	G	H	I	$120	J	K	L
3	M	N	O	P	Q	$120	R

1. Refer to Table 1. What is the value of C?

2. Refer to Table 1. What is the value of R?

Answer 1

FOR THE FIRM TO DECIDE ABOUT ITS DECISION , WE NEED TO MARGINAL PRODUCT OF LABOUR , MARGINAL PRODUCT OF CAPITAL , WAGE RATE AND RENTAL RATE.....ALL THESE ARE GIVEN....

AT THE OPTIMAL/EQUILIBRIUM LEVEL , A FIRM EQUATES ITS MARGINAL RATE OF TECHNICAL SUBSTITUTION (THAT IS RATIO OF MARGINAL PRODUCT OF LABOUR TO THE MARGINAL PRODUCT OF CAPITAL) TO THE RATIO OF PRICES OF INPUT FACTORS ( THAT IS THE RATIO OF WAGE RATE TO RENTAL RATE ) ....

IN THE ABOVE CASE , MARGINAL RATE OF TECHNICAL SUBSTITUTION :- 75/100 WHICH EQUALS .75

RATIO OF FACTOR INPUT PRICES :- 5/10 WHICH EQUALS .50

AS MARGINAL RATE OF TECHNICAL SUBSTITUTION IS NOT EQUAL TO THE FACTOR INPUT PRICES , THE FIRM IS NOT MAKING THE OPTIMAL DECISION.....FIRM NEEDS TO INCREASE THE USE OF LABOUR TO LOWER DOWN THE MARGINAL RATE OF TECHNICAL SUBSTITUTION TILL IT GETS EQUAL TO FACTOR INPUT PRICE RATIO.....

TO GET THE VALUE OF C :-

FIXED COST REMAINS CONSTANT FOR ALL VALUES OF OUTPUT...THEREFORE , IT IS $50 ( POINT A) ....HENCE , VARIBALE COST (POINT B) IS $150 - $50 = $100 ....MARGINAL COST IS THE CHANGE IN THE COST DUE TO CHANGE IN QUANTITY.....AT 0 QUANTITY MARGINAL COST IS 0 AND AT QUANTITY 1 , POINT C , MARGINAL COST IS CHANGE IN THE COST THAT IS $150 - $50 = $100

HENCE , POINT C IS $100.....

FOR POINT R :-

WE NEED FIRST POINT G WHICH IS $150 + $120 ( AT QUANTITY OF 2)

THIS SHOWS THE TOTAL COST AT QUANTITY 2

POINT G IS $150 + $120 = $270

POINT N IS $50 (ALWAYS FIXED)

POINT O IS AVERAGE VARIABLE COST TIMES QUANTITY THAT IS $120*3 = $360

THEREFORE POINT M = N + O

= $50 + $360

= &410

HENCE , POINT R IS POINT M DIVIDED BY QUANTITY

THAT IS ,

R = $410/3

R = $136.66