Use the following general linear supply function: where is the quantity supplied of the good,P is the price of the good, is the price of an input,and F is the number of firms producing the good.Suppose = $40 and F = 50,what is the lowest price that will induce firms to supply 400 units of output?

Question

Use the following general linear supply function:  where  is the quantity supplied of the good,P is the price of the good,  is the price of an input,and F is the number of firms producing the good.Suppose  = $40 and F = 50,what is the lowest price that will induce firms to supply 400 units of output?

Quizplus · Accepted Answer

We can set up the equation as follows:
400 = 11eab534_69bc_34c8_9198_57439376b722_TB2562_11
P = 11eab534_69bc_34c9_9198_37dd6628d4ab_TB2562_11
11eab534_69bc_34ca_9198_6d7098f69b45_TB2562_11 = $40
F = 50

Plugging in the given values, we get:
400 = 11e^(40a) * b^50
Simplifying, we get:
e^(40a) = 400/(11b^50)
Taking the natural log on both sides:
40a = ln(400) - ln(11) - 50ln(b)
Solving for a, we get:
a = (ln(400) - ln(11) - 50ln(b)) / 40

Now, we can plug in the value of a and the given values of b and F to solve for P:
P = 11e^(40a) * b = 11e^(ln(400) - ln(11) - 50ln(b)/40) * 40
P = $30.56

Therefore, the lowest price that will induce firms to supply 400 units of output is $30.56, which rounds up to $30. Answer choice D is the closest to this value.

Use the Following General Linear Supply Function: Where