Finding Equilibrium Price and Quantity for Education at Harvard

[Trizz]

Homework Statement

Assume Harvard has the following marginal cost equation and acts like a competitive firm:
MC = 10X + 100

The aggregate demand for education at the College is:
X^D("D" simply stands for demand)= 200 - .5p

The demand function above does not account for an additional benet to society from education.
Specically, society benets $6 per unit of education consumed.

What is the equilibrium price and quantity of education units (X) if there is no government
intervention.

Homework Equations

Equilibrium occurs when supply equals deman

The Attempt at a Solution

I have MC, which I know also equals the supply. But the thing that throws me off with this problem is the presence of different variables. I cannot solve for X by setting the two equations together because of the existence of the P variable.

Any ideas on how to approach this?

Thanks!

 

[Mark44]

Homework Statement

Assume Harvard has the following marginal cost equation and acts like a competitive firm:
MC = 10X + 100

What does X represent in this equation?

The aggregate demand for education at the College is:
X^D("D" simply stands for demand)= 200 - .5p

Is this really X^D or did you mean X_D? As you wrote it, it means X to the power D.

What is p in the demand equation? Price? If so, in what units?

The demand function above does not account for an additional benet to society from education.
Specically, society benets $6 per unit of education consumed.

What is the equilibrium price and quantity of education units (X) if there is no government
intervention.

Homework Equations

Equilibrium occurs when supply equals deman

The Attempt at a Solution

I have MC, which I know also equals the supply. But the thing that throws me off with this problem is the presence of different variables. I cannot solve for X by setting the two equations together because of the existence of the P variable.

Any ideas on how to approach this?

Thanks!