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
(a) To find the equilibrium price and quantity, we need to set the market supply and demand equations equal to each other and solve for Q and p:
Q’s = Q’d
2 + p = (25 – 1.5Q)
1.5Q + p = 25 – 2
1.5Q + p = 23
p = 23 – 1.5Q
Substituting this expression for p into the supply equation:
Q’s = 2 + 23 – 1.5Q
2.5Q = 25
Q = 10
Substituting this value for Q into either the supply or demand equation:
p = 23 – 1.5(10)
p = 8
Therefore, the equilibrium price is $8 and the equilibrium quantity is 10 units of frozen yogurt.
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Start My Order(b) To graph the supply and demand curves, we can use the equations we found in part (a):
Market supply: Q’s = 2 + p
Market demand: p = 25 – 1.5Q
To find the intercepts, we set Q or p equal to zero:
Market supply intercepts:
Q’s = 2 + p = 0 when p = -2
Q’s = 2 + p = 0 when Q’s = -2
Market demand intercepts:
p = 25 – 1.5Q = 0 when Q’s = 16.67
p = 25 – 1.5Q = 0 when p = 25
To find the slopes, we can rearrange the equations into slope-intercept form:
Market supply: Q’s = -2 + 1p, with a slope of 1
Market demand: p = 16.67 – 0.67Q, with a slope of -0.67
We can now plot the supply and demand curves on a graph, labeling the intercepts and slopes, and showing the equilibrium price and quantity:
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Frozen Yogurt Graph
(c) If the government sets a price ceiling of $12, this means that the price cannot exceed $12 in the market. To determine the new equilibrium quantity, we can set the demand equation equal to $12 and solve for Q:
p = 25 – 1.5Q
12 = 25 – 1.5Q
1.5Q = 13
Q = 8.67
This means that at a price of $12, the market demand is for 8.67 units of frozen yogurt. However, the market supply at a price of $12 is:
Q’s = 2 + p = 2 + 12 = 14
This means that at a price of $12, the market supply is for 14 units of frozen yogurt. Since demand is less than supply, there will be a surplus of frozen yogurt in the market.
We can show this on a graph by drawing a horizontal line at a price of $12, and then finding the points where this line intersects with the supply and demand curves:
Frozen Yogurt Graph with Price Ceiling
As we can see from the graph, the quantity demanded at a price of $12 is less than the quantity supplied, so there is a surplus of 5.33 units of frozen yogurt in the market.
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