Say whether the following is true or false. Explain it briefly (For a true state
ID: 1191995 • Letter: S
Question
Say whether the following is true or false. Explain it briefly (For a true statement, an explanation is not necessary. For a false statement, no explanation, no credits!) If the production function is y - f(x1, x2) = X1 + min{x1,x2}, then there are constant returns to scale If the production function is y - f(x1, x2) - x^1/2 1 x^1/2 1 and the price of factor 1 (x1) is $12 and the price of factor 2 (x2) is $24, the proportions of factor I and factor 2 to maximize profits is x1 - 0. 5x2 If a firm's technology is represented by y - 2x1 + x2, and the price of factor I (x1) is $2 and the price of factor 2 fo) is $1, the long run cost function is C(y) =y/2Explanation / Answer
a) False.CONSTANT RETURNS TO SCALE means homegeneous of degree 1 i.e. an increase in inputs by a same factor leads to same amount of increase in output.However overhere when we increase x2 by a cetain factor x1 rises 2 times the factor.
For example we use a factor t:
t *f(x1,x2) = t*x1 + min(t*x1,t*x2)
Thus x1 increases 2 times as much as x2 rises.
b) FALSE
According to given production function its clearly a cobb douglas function.Accordingly we find out the equilibrium values of x1 = 1/2 * m/12
x2 = 1/2 * m/24. Thus calculating the equilibrium ratios of x1/x2 = (m/12)/(m/24).
Thus we get x2 = 0.5x1.Clearly price of factor 2 is higher hence factor 1 must be used more.Thus its not x1 = 0.5x2 but x2 = 0.5x1.
c)FALSE. Given the technology y = 2x1 + x2 and the facror prices p(x1) = $2 and p(x2) = $1 our LONG RUN cost function would be = 2x1 + x2 which is just equal to our production function.Hence C = y and not C = y/2.