An economist models the market for corn by the following equations. Here, p is t

Question

An economist models the market for corn by the following equations.

Here, p is the price per bushel (in dollars), and y is the number of bushels produced and sold (in billions).

(a) Use the model for supply to determine at what point the price is so low that no corn is produced. (Round your answer to the nearest cent.)
$  per bushel

(b) Use the model for demand to determine at what point the price is so high that no corn is sold. (Round your answer to the nearest cent.)
$  per bushel

(c) Find the equilibrium price. (Round your answer to the nearest cent.)
$  per bushel

Find the quantities that are produced and sold at equilibrium. (Round your answer to one decimal place.)
billion bushels

Explanation / Answer

supply equation is

y = 4.14 p - 11.6

a) if no corn is produced y = 0

4.14 p - 11.6 = 0

adding 11.6 on both sides

4.14 p = 11.6

p = 2.80

therefore , at $ 2.8 no corn is produced

b) demand equation

y = -1.03p + 19.5

setting y = 0

-1.03p + 19.5 = 0

-1.03 p = - 19.5

p = 19.5 / 1.03

p = 18.9

therefore, at $ 18.9 no corn is sold

c) for equilibrium price set demand and supply equation equal to each other

4.14 p - 11.6 = -1.03p + 19.5

adding 1.03 p on both sides and 11.6 on both sides

5.17p = 31.1

p = 6.01

equillibrium price is $ 6

quantity that is produced and sold at equillibrium are

4.14 (6.01) - 11.6 = 13.3

quantities produced and sold are 13.3 billion bushels

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