The demand and supply of corn are as follows:Qd = 2,200 - 125P
Qs = 700 + 175P,
where quantities are in millions of bushels and prices are in dollars per bushel.
(a) Calculate the equilibrium price and the equilibrium quantity.
(b) Calculate the consumer surplus at the equilibrium price and quantity.
(c) Calculate the price elasticity of demand (at the equilibrium values).
(d) Calculate the price elasticity of supply (at the equilibrium values).
(e) Calculate the arc elasticity of demand if the price of corn increases by 20% above the current equilibrium price.
(f) Calculate the arc elasticity of supply if the price of corn increases by 20% above the current equilibrium price.
(g) Assume that the government has introduced a price floor of $7 per bushel (i.e., the market price cannot go below $7 per bushel).
(i) What quantity of corn will consumers be willing to buy?
(ii) What quantity of corn will consumers be able to buy?
(iii) What quantity of corn will producers be willing to sell?
(iv) What quantity of corn will producers be able to sell?
(v) Will the market clear (i.e., will the quantity demanded equal the quantity supplied)? If not, will there be excess demand (shortage) or excess supply (surplus) of corn? How many bushels?

(a) We must set Qd equal to Qs in order to determine the equilibrium price and quantity:

2,200 - 125P = 700 + 175P

If we solve for P, we obtain:

300P = 1,500

$5 per bushel is P.

By adding P = $5 to either Qd or Qs, we may determine the equilibrium quantity as follows:

Q = 2,200 - 125(5) = 1,575 million bushels

The discrepancy between the highest price consumers are prepared to pay and the market price is known as consumer surplus (b). The quantity demanded at the equilibrium price of $5 per bushel is 1,575 million bushels, hence the highest price consumers would be prepared to pay is:

2,200 - 125(5) = $1,875 million

The consumer surplus is as a result:

$1,847.5 million is equal to (1/2) * (1,875 - 5) * 1,575.

(c) The following formula can be used to determine the price elasticity of demand at the equilibrium:

E is calculated as (% change in amount demanded) / (% change in price).

Qd = 1,575 million bushels and P = $5 per bushel are the values at equilibrium. The quantity requested will vary if the price increases by 1% in the following ways:

(125 / 2,200) * 100 = 5.68%

As a result, the equilibrium price elasticity of demand is:

E = 5.68 / 1 = 5.68

(d) The same formula can be used to get the price elasticity of supply at equilibrium.

E is equal to (% change in provided quantity) / (% change in price).

Qs = 1,575 million bushels and P = $5 per bushel are the values at equilibrium. The amount delivered will alter if the price changes by 1% in the following ways:

(175 / 2,200) * 100 = 7.95%

As a result, the equilibrium price elasticity of supply is:

E = 7.95 / 1 = 7.95

(e) We employ the following formula to get the arc elasticity of demand:

E = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

The new price is: If the price rises by 20% above the $5 equilibrium price, the new price is:

Each bushel, $5 + 0.20 ($5) equals $6.

The newly desired quantity is:

1,450 million bushels - 2,200 - 125(6)

Applying the old and new equilibrium values, we get at:

E = ((1,450 - 1,575) / ((1,450 + 1,575) / 2)) / ((6 - 5) / ((6 + 5) / 2)) = -1.71

Demand is elastic, as indicated by the negative sign.

(f) We apply the same formula to determine the arc elasticity of supply:

E = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

The new price is: If the price rises by 20% above the $5 equilibrium price, the new price is:

Each bushel, $5 + 0.20 ($5) equals $6.

The updated quantity given is:

700 plus 175 (6) equals 1,550 million bushels.

Applying the old and new equilibrium values, we get at:

E = ((1,550 - 1,575) / ((1,550 + 1,575) / 2)) / ((6 - 5) / ((6 + 5) / 2)) = -0.19

The negative sign denotes an inelastic supply.

(g) The new market circumstances when the government sets a price floor of $7 per bushel are:

Qd = 2,200 - 125P

Max Qs = (700 + 175P, 875)

where the maximum function assures that suppliers will only produce and sell at the $7 per bushel price floor level, making 875 million bushels the minimum amount that must be delivered.

I Because their demand function hasn't altered, consumers will be willing to make the same number of purchases as previously. As a result, they are prepared to purchase 1,575 million bushels.

(ii) At the price floor level of $7 per bushel, consumers will only be able to purchase the quantity offered, which is the minimum of the demand and supply functions:

1,525 million bushels are equal to Qd = 2,200 - 125(7).

875 million bushels equals Q.

Hence, only 875 million bushels will be available for purchase by consumers.

Given that their supply function hasn't changed, producers will be willing to sell the same volume as previously. As a result, they are prepared to sell 1,575 million bushels.

(iv) At the price floor level of $7 per bushel, producers will only be able to sell the quantity demanded, which is the minimum of the demand and supply functions:

Qd equals 1,525 million bushels.

Qs equals 700 plus 175 plus 7 to 1,225 million bushels.

Hence, the total number of bushels that farmers can sell is 1,225 million.

(v) There will be an excess of demand (a shortage) of the following since the quantity demanded (1,525 million bushels) exceeds the supply curve (875 million bushels):

875 minus 1,525 equals 650 million bushels.

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