Question

7. Suppose the marginal costs (and therefore the market supply) for ketchup is given by P = 0.5 Qs + 1; and the market demand is given by Qd= 20-4P. If this is a competitive market, the price and the quantity produced is:

a.) P = 4, Q = 4

b.) P = 3, Q = 4

c.) P = 11/3, Q = 4

d.) P = 11/3; Q = 16/3

Answer 1

Ans: d.P=11/3; Q=16/3

In the above question, MC is given by P=0.5Qs+1

which can be used to derive the supply equation as

P-1=0.5Qs or P-1/0.5= Qs

Demand equation is given as

Qd= 20-4P

Now, in a competitive market, the equilibrium output and price can be determined by equating the supply and demand equation as

Qd=Qs

here, P-1/0.5 = 20 -4P

or P-1= (20- 4P)0.5

or P-1= 10-2P

or P+2P=10+1

or 3P=11 or P=11/3

For quantity, substitute the value of p in the demand equation

as, Qd= 20- 4 (11/3)

Qd=20-44/3

Qd= (60-44)/3

Qd=16/3