Question

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?

a. 21 zlotys
b. 14 zlotys
c. 8 zlotys
d. 20 zlotys
e. none of the above

Answer 1

The subsidy per loaf required to make supply equal demand at a price ceiling of 32 zlotys is 8 zlotys.

Step-by-step explanation:

To find the necessary subsidy per loaf to make supply equal demand at the maximum legal price of 32 zlotys, we need to substitute p = 32 into both the demand function and the supply function to calculate the quantities. The demand at this price is calculated by q = 381 − 3(32), and the supply is calculated by q = 5 + 7(32). After performing these calculations, we get the quantities demanded and supplied at 32 zlotys are 285 loaves and 229 loaves, respectively.

To avoid shortages, the king must ensure the supply is equal to the demand. Therefore, the king needs to subsidize the difference between the demand quantity and the supply quantity to bakers for each loaf of bread. The required subsidy is then: 285 loaves − 229 loaves = 56 loaves. To get the subsidy per loaf, divide by the price impact on the supply: 56 loaves / 7 (price impact on supply per loaf) = 8 zlotys.