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Satsume Satsume
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5 years ago
The U.S. Department of Agriculture is interested in analyzing the domestic market for corn.  The USDA's staff economists estimate the following equations for the demand and supply curves:
   Qd = 1,600 - 125P
   Qs = 440 + 165P

Quantities are measured in millions of bushels; prices are measured in dollars per bushel.

a.   Calculate the equilibrium price and quantity that will prevail under a completely free market.
b.   Calculate the price elasticities of supply and demand at the equilibrium values.
c.   The government currently has a $4.50 bushel support price in place.  What impact will this support price have on the market?  Will the government be forced to purchase corn under a program that requires them to buy up any surpluses?  If so, how much?
Textbook 

Microeconomics


Edition: 8th
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boransalboransal
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5 years ago
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a.   
Set Qd = Qs to determine price.
   1600 - 125P = 440 + 165P
   1160 = 290P
   P = 4

Obtain Q by substituting into either expression.
   Qd = 1600 - 125(4)
   Qd = 1600 - 500
   Q = 1100
   P* = $4, Q* = 1100

b.    
For the Own Price Elasticity of Demand E = -125 ×   = -0.45 (approximately)
For the Own Price Elasticity of Supply E = -165 ×   = 0.60

c.   
Calculate Qd and Qs at the $4.50 price.
   Qd = 1600 - 125(4.5)
   Qd = 1037.5
   Qs = 440 + 165(4.5)
   Qs = 1182.5
   surplus = Qs - Qd = 1182.5 - 1037.5 = 145
The support price would create an excess supply of 145 million bushels that the government would be forced to buy.
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