The demand and supply equations for the peach market are:
Demand: P = 24 - 0.5Q
Supply: P = -6 + 2.5Q
where P = price per bushel, and Q = quantity (in thousands).
a. Calculate the equilibrium price and quantity.
b. Suppose the government guaranteed producers a price of $24 per bushel. What would be the effect on quantity supplied? Provide a numerical value.
c. By how much would the $24 price change the quantity of peaches demanded? Provide a numerical value.
d. Would there be a shortage or surplus of peaches?
e. What is the size of this shortage or surplus? Provide a numerical value.
a. Quantity = 10 thousand bushels: {24 - 0.5Q = -6 + 2.5Q; 30 = 3Q; Q = 10}
Price = $19: {P = 24 - 0.5(10); P = 24 - 5; P = $19}
b. Quantity supplied would increase to 12 thousand bushels: {24 = -6 + 2.5Q; 30 = 2.5Q; Q = 12}
c. Quantity demanded would fall to zero bushels: {24 = 24 - 0.5Q; 0 = -0.5Q; Q = 0}
d. There would be a surplus.
e. Surplus = 12,000 - 0 = 12 thousand bushels.
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