Suppose that demand and supply in the market for Brazil nuts is linear, with a historic market price of $.50 per pound and 10 million pounds sold. In 2004, a news item raised health fears about the nuts. That year, the market price fell to $.45 per pound and only 8 million pounds traded. An estimate for the equation of the supply of Brazil nuts (where QS is in millions of pounds and P is in dollars)would be:

Question

Quizplus · Accepted Answer

We know that when the market price was $.50 per pound, 10 million pounds were sold, and when the market price fell to $.45 per pound, only 8 million pounds were sold. Using these two data points, we can find the slope of the supply curve:

Slope = (Quantity2 - Quantity1) / (Price2 - Price1) = (8 - 10) / (.45 - .50) = 40

Now we can use one of the data points and the slope to find the intercept of the supply curve:

Quantity = Slope * Price + Intercept
10 = 40*.50 + Intercept
Intercept = -10

Therefore, the equation for the supply curve is:
Qs = -10 + 40P
which corresponds to choice D. To estimate the supply equation, we need to use the information given about the change in the quantity supplied and the change in price. We have:
Historic price = $0.50 per pound, Quantity sold = 10 million pounds
New price = $0.45 per pound, Quantity sold = 8 million pounds

Using the midpoint method to calculate the price elasticity of supply, we have:

Price change = (0.45 - 0.5)/((0.45 + 0.5)/2) = -0.1
Quantity change = (8 - 10)/((8 + 10)/2) = -0.2

Price elasticity of supply = -0.2/-0.1 = 2

Therefore, the supply equation would have a coefficient of 2 for P:
Qs = a + bP
8 = a + b(0.45)
10 = a + b(0.5)
Subtracting the first equation from the second, we get:
2 = 0.05b
b = 40
Substituting b into either equation, we get:
a = 30
So the supply equation is:
Qs = 30 + 40P, or in millions of pounds:
Qs = 0.03 + 40P

Suppose That Demand and Supply in the Market for Brazil Qs=30+40PQ s = 30 + 40 PQs=30+40P

Suppose That Demand and Supply in the Market for Brazil $Q s = 30 + 40 P$