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demand and supply

Problems: For each of the following problems, provide a mathematical solution, well-labeled diagrams, and written explanations

1) Suppose the demand and supply curves for broccoli in the U.S. market are given by:
Qd = 1000 - 5P Qs = 4P - 80
Quantities are in hundreds of bushels per year and price is in dollars per hundred bushels.

a) Find the equilibrium market price and quantity for broccoli, and plot the demand and supply curves on a graph.

b) Calculate the elasticities of demand for and supply of broccoli at the market equilibrium, and interpret the meaning of these numbers.

c) Suppose you calculate the cross price elasticity of demand for broccoli with respect to green beans and find it is equal to 2.3. Interpret the impact on broccoli demand of a 10% increase in the price of green beans.

d) If a price floor (minimum allowable price) set at $150/hundred bushels is imposed on broccoli, how will this affect the market? Sketch a diagram showing the impact on consumer and producer surplus. (No calculations required; demonstrate graphically.) Assume the government only imposes the price floor, and doesn't intervene in other ways in this market.

Solution Preview

Problems: For each of the following problems, provide a mathematical solution, well-labeled diagrams, and written explanations
1) Suppose the demand and supply curves for broccoli in the U.S. market are given by:
(1) Qd = 1000 - 5P
(2) Qs = 4P - 80
Quantities are in hundreds of bushels per year and price is in dollars per hundred bushels.
a) Find the equilibrium market price and quantity for broccoli, and plot the demand and supply curves on a graph.

At the market equilibrium, the quantities for demand and supply are the same.
Since Qd =Qs, then
1000 - 5P = 4P - 80
1080 = 9P
Then P = $120
Thus, Q = 1000 - 5P = 1000 - 5*120 = 400 (hundreds of bushels)
...

Solution Summary

Demand and supply are emphasized.

$2.19