Question

A shipping company moves cars from Texas to Maryland with the demand curve Q=5000-100P, and ships motorcycles back from Maryland to Texas with the demand curve Q=1000-100P. The cost of round trip is $20. Find the equilibrium price and quantity graphically. I am having trouble with how to incorporate the roundtrip cost of $20. I graphed the two demand curves and then got stuck.

Answer 1

Here $20 is the marginal cost (MC)

As it is the cost of round rip it means it is the cost of both from Texas to Maryland and from Maryland to Texas. so we will add the both demand curve and find MR = MC to find equilibrium.

Here you dono have to make two separate graph.

Demand 1: Q1 = 5000-100P or, P = 50-0.01Q

Demand 2: Q2 = 1000-100P or, P = 10-0.01Q

Compute total demand curve by adding individual demand curves as follows:

2P = 60-0.02Q or,

P = 30-0.01Q  

MR = 30 -0.02Q  

MC = $20

Set MR = MC

That is, 30-0.02Q = 20

Or, Q* = 500

P = 30 - 0.01*500 = $25

On the graph:

Demand :

when P= 0, Q = 3000

When Q = 0, P = 30

MR curve :

when P = 0, Q = 1500

when Q = 0,P = 30

MC= $20

Thus equilibrium price is $25 and quantity is 500

Price and cost 30 $20 МC Demand MR 500 1500 3000 25