Suppose that the market supply for frozen yogurt in small ville is given by Q’s=2+p. The market demand for frozen yogurt is given by p=25-1.5Q

(a) find the equilibrium price and quantity

(b) graph the curves and label correct intercepts, slope and equilibrium values

(C) given a price of $12 is being regulated by the government, what Was will occur in the market? Calculate the values and show on a graph

solution

(a) To find the equilibrium price and quantity, we need to set the market supply equal to the market demand:

2 + p = 25 – 1.5Q

Simplifying the equation, we get:

p = 23 – 1.5Q

2 + p = Q’s

Substituting p from the second equation into the first equation, we get:

2 + 23 – 1.5Q = Q’s

25 – 1.5Q = Q’s

Setting Q’s equal to Q’d, we get:

25 – 1.5Q = 25 – 1.5Q

Simplifying, we get:

Q = 8

Substituting Q back into either the market supply or market demand equation, we get:

p = 23 – 1.5(8) = 11

Therefore, the equilibrium price is $11 and the equilibrium quantity is 8 units of frozen yogurt.

(b) To graph the curves, we plot the market supply and market demand curves on the same graph. The vertical axis represents price and the horizontal axis represents quantity. The intercepts and slopes of each curve are labeled below:

Market Supply Curve: Q’s = 2 + p

Intercept on the vertical axis: 2

Intercept on the horizontal axis: 0

Slope: 1

Market Demand Curve: p = 25 – 1.5Q

Intercept on the vertical axis: 25

Intercept on the horizontal axis: 0

Slope: -1.5

The equilibrium price and quantity are labeled on the graph as well.

(c) If the government regulates the price of frozen yogurt to be $12, there will be a shortage in the market because the price is below the equilibrium price. To calculate the quantity demanded and quantity supplied at a price of $12, we substitute p = 12 into the market demand and market supply equations:

Market Demand: Q’d = (25 – 1.5p)/1.5 = (25 – 1.5(12))/1.5 = 5.33

Market Supply: Q’s = 2 + p = 2 + 12 = 14

Therefore, at a price of $12, the quantity demanded is 5.33 units and the quantity supplied is 14 units, resulting in a shortage of 8.67 units. On the graph, the price of $12 is shown as a horizontal line, and the quantity demanded and quantity supplied are labeled as well.