Question

Production function is Q = x [K + 1/2L]
x > 1 is the productivity factor
r = 10 and w = 5 and s=8
Derive the cost function for any value of x. Also, note that the market is perfectly competitive following a merge. Determine the values of x for which the DOJ will approve this merger

Answer 1

The demand function will have the following general form:

$$Q_D=a-pb+s$$

If s=8, then demand function will have next form:

$$Q_D=(8+a)-bp$$

Given the given conditions, the production function will be:

$$Q=x[10+\frac{5}{2}]$$

$$x=\frac {Q}{12.5}$$

$$x=\frac{(a+8)-bp}{12.5}$$