In a certain kingdom, the demand function for rye bread was q = 381 - 3p and the supply function was q = 5 + 7p, where p is the price in zlotys and q is loaves of bread. The king made it illegal to sell rye bread for a price above 32 zlotys 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?

Question

Quizplus · Accepted Answer

First, we need to find the equilibrium price and quantity of rye bread by setting the demand equal to the supply:

381 - 3p = 5 + 7p

Solving for p, we get:

p = 32

Substituting this back into either the demand or supply function, we can find the equilibrium quantity:

q = 381 - 3(32) = 285

Now, we know that the king is willing to pay a subsidy per loaf of bread to ensure that the price does not exceed 32 zlotys. Let's call this subsidy s. Then the effective supply function becomes:

q = (5 + 7p + s)

Setting this equal to the demand function:

381 - 3p = 5 + 7p + s

Solving for s, we get:

s = 8 zlotys

Therefore, the subsidy per loaf would have to be 8 zlotys in order for supply to equal demand and for the price to remain at or below 32 zlotys.

In a Certain Kingdom, the Demand Function for Rye Bread