Question

Suppose these are the following Demand/MV and Supply/MC equations for higher education, where Q is the number of students and P is tuition.
The marginal value equation is: MV=17.80-1.40*Q
The marginal cost equation is: MC=1.00+0.59*Q


13.What is the equilibrium tuition(price)?  

=5.98

Students receive a per-unit $2.00 scholarship if they attend university.

14. What is the new tuition?  

=6.57

15. What is the total amount spent on scholarships?  

Now, in addition to the scholarships received by students, the university receives a $1 per student subsidy.




16. What will the new tuition be?  


17. What is the total revenue (including subsidy) to universities?  

Answer 1

Solution:

13)MV=P=17.80-1.40*Q, MC=1.00+0.59*Q

TR= PQ = (17.8-1.4Q)Q =17.8Q – 1.4Q²

MR = dTC(q)/ dq = 17.8 – 2.8Q

AT equilibrium MC = MR

17.8 – 2.8Q = 1+.59Q

16.8 = 3.39Q

Q= 4.95

P = 17.8 – 1.4*4.95= 17.8 – 6.93 = 10.86

14)When students will receive $2 as scholarship then their marginal value will increase

New MV= 17.8 – 1.4Q+ 2 = 19.8 – 1.4Q

TR= PQ = (19.8-1.4Q)Q =19.8Q – 1.4Q²

MR = dTC(q)/ dq = 19.8 – 2.8Q

AT equilibrium MC = MR

19.8 – 2.8Q = 1+.59Q

18.8 = 3.39Q

Q= 5.54

P = 19.8 – 1.4*5.54= 19.8 – 7.764 = 12.036

15)Total amount spent on scholarship = amount of subsidy * no of students

= 2*5.54 ( number of students will be a whole number) so,

= 2*6 = $12

16) In addition to the scholarships received by students, the university receives a $1 per student subsidy. Then new MC = 1.00+0.59*Q + 1 = 2+ .59Q

AT equilibrium MC = MR

19.8 – 2.8Q = 2+.59Q

17.8 = 3.39Q

Q= 5.25

P = 19.8 – 1.4*5.25= 19.8 – 7.35 = 12.44

17)Total revenue (including subsidy) to universities = price of tuition * number of students + subsidy*no of students= 12.44 *5 + 1*5 (as the no of students will be a whole number)

= 62.2 + 5 = 67.5