Find the average cost function. What is the efficient scale of production? Illustrate it on your graph for the previous part by drawing an appropriate secant line. What is the average cost at this scale?

1 Convex-concave costs

Consider the 1-input, 1-output technology defined by the cost function
f (z) = {(z+1)2— 1, z<1
8-V.Z — 5, z> 1

1.  Fix the price of the input good at w = 1. 1. Find the total cost function. Plot it for quantities up to 10.

2. Find the average cost function. What is the efficient scale of production? Illustrate it on your graph for the previous part by drawing an appropriate secant line. What is the average cost at this scale?

3. Find the marginal cost function. On a new graph, plot it and the average cost function for quantities up to 10, and mark the efficient scale and corresponding average cost.

4. Derive the firm’s supply correspondence for the output good as a function of the output price p. Illustrate it on the same graph you used for the previous part.