26. The demand and supply functions for a good in the market are linear. Initially, equilibrium in the market was established at a price of $14 per unit of the good and a quantity of 42 units. The government decided to support producers: for this purpose, it buys any quantity of the good that producers are willing to sell at a price of $20 per unit. The good purchased by the government never reappears on the market. It is known that as a result of these purchases, the quantity of the good sold on the market increased by 12 units compared to the initial equilibrium, at

Social Studies (Economic Sphere), 10th Grade

this price, no unit of the good will be sold for more than $29. How much of the good did the government purchase?
Solution: demand has increased, it is necessary to find a new demand function from two points: $p 1=20$, $q 1=42+12=54 ; \quad p 2=29, \quad q 2=0 . \quad p=a-b q, \quad b=(29-20) / 54=1 / 6 ; \quad a=29$. The new demand function is $p=29-1 / 6 q: p=14, q=90$. The state will purchase 90-42=48 units