Answer to Question #298979 in Macroeconomics for MULE

Question

1. A tour operating firm plans to take tourists between Addis Ababa and Jimma. its estimated cost function given by C =100 +50 N+4N2 (Where N denotes the number of passengers per day)

A. State the average cost function.

B. State the marginal cost of the average cost function.

C. Find the number of passengers per day that minimize average cost.

D. What is the minimum average cost at the optimal level of passenger?

E. What will be the total cost at the optimal level?

Answer 1

a) $Average Cost function=\frac {C}{N}$

=$\frac{100+50N+4N^2}{N}$

=$\frac{100}{N}+50+4N$

b) Marginal cost is obtained by differentiating cost function;

$C'=MC=50+8N$

c) Number of passengers per day that minimizes average cost;

Marginal cost=Average cost

$50+8N=\frac{100}{N}+50+4N$

$8N^2=100+4N^2$

$4N^2=100$

$N^2=25$

$N=25^\frac{1}{2}$

$N=5 Passengers$

d)Minimum Average Cost at the optimal level of passengers;

$=\frac{100}{5}+50+4*5$

=$20+50+20$

$= 90 dollars$

e)Total Cost At Optimal Level;

$TC= 100+50*5+4*5^2$

$TC=100+250+100$

$TC= 450 dollars$