The output of an economic system q, subject to two inputs, such as labor l and capital k, is often modeled by the cobb-douglas production function q=cl^a k^b. when a+b=1, the case is called constant returns to scale. suppose q=12,200, a = 1/6, b= 5/6, and c=42. find the rate of change of capital with respect to labor, dk/dl.

Step-by-step explanation:

Given

Economic system Q is given by

also

if

substitute these values

differentiate w.r.t to L to get

$20.01

step-by-step explanation:

the sale price is (1.00 - 0.77)($87), or 0.23($87), or $20.01.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560