Question

A certain kingdom features a competitive market for rye bread. The inverse demand for rye bread is
p = 10–(q/10) and the supply function is q = 10 + 5p, where p is the price in dollars and q is loaves of
bread. The king made it illegal to sell rye bread for a price above 5 dollars per loaf. To avoid shortages, he
agreed to pay bakers enough of a subsidy for each loaf of bread so as to make supply equal demand.
How much would the subsidy per loaf have to be?
(a) 8 dollars
(b) 4 dollars
(c) 10 dollars
(d) 5 dollars
(e) 3 dollars

Answer: e

Could you please show the working steps? Thanks

Answer 1

Price fixed for rye bread = $5 per loaf

Calculate the quantity demanded at $5 per loaf -

p = 10 - (q/10)

5 = 10 - (q/10)

5 - 10 = - (q/10)

-5 = - (q/10)

q/10 = 5

q = 50

The quantity demanded at $5 per loaf is 50 loaves.

Calculate the quantity supplied at $5 per loaf -

q = 10 + 5p

q = 10 + (5*5) = 10 + 25 = 35

q = 35

The quantity supplied at $5 per loaf is 35 loaves.

It can be seen that the supply is less than the demand.

The sellers have to raise the supply to the 50 loaves in order to make the supply equal to the demand.

Calculate the price at which sellers will supply 50 loaves -

q = 10 + 5p

50 = 10 + 5p

50 - 10 = 5p

5p = 40

p = 40/5 = 8

So, sellers will supply 50 loaves when the price is $8 per loaf.

This means that the King have to pay a subsidy of ($8 - $5) $3 per loaf of bread to sellers to make supply equal demand.

Hence, the correct answer is the option (e).