10. construction of cost function Ralph must select the best combination of four factors of production, denoted z1 ≥ 0, z2 ≥ 0, z3 ≥ 0 and z4 ≥ 0, to produce q units of output.

Technical requirements are defined by the following constraints

(where you should notice the first two are perfect substitutes and the last two are also perfect substitutes):

z1 + z2 ≥ q z3 + z4 ≥ q z1 ≤ 5 z3 ≤ 6 The respective factor prices are 1, 2, 3, and 4 per unit.

(a) Determine Ralph’s cost curve, for 0 ≤ q ≤ 10. Plot the cost curve. How do you interpret the shadow prices?

(b) Repeat for a particular short-run setting of
z1 = 3.