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Posted: June 14th, 2023
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
Q's = Q'd
2 + p = (25 - 1.5Q)
1.5Q + p = 25 - 2
1.5Q + p = 23
p = 23 - 1.5Q
Q's = 2 + 23 - 1.5Q
2.5Q = 25
Q = 10
p = 23 - 1.5(10)
p = 8
Market supply: Q's = 2 + p
Market demand: p = 25 - 1.5Q
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Market demand intercepts:
p = 25 - 1.5Q = 0 when Q's = 16.67
p = 25 - 1.5Q = 0 when p = 25
Market supply: Q's = -2 + 1p, with a slope of 1
Market demand: p = 16.67 - 0.67Q, with a slope of -0.67
(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:
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.
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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