Below, we will investigate the profit maximizing choice in the two steps that first involve a
strict focus on the cost side.
Consider again (as in the previous exercise) a production process that gives rise to a strictly
convex producer choice set.
(a) Derive the cost curve from a picture of the production frontier.
Answer: This is done in panels (a) through (c) of Graph 11.3. Panel (a) illustrates the
producer choice set. Panel (b) inverts this, flipping the axes so that x is on the horizontal and
ℓ on the vertical. Finally, (c) is derived from (b) by simply multiplying labor input by w to
convert the labor input needs of production into the dollar needs for production.
b) Derive the marginal and average cost curves from the cost curve.
Answer: This is done in panel (d) where the MC curve is simply plotting the slope of the cost
curve and the average cost curve is simply the total cost divided by x.
(c) Illustrate the supply curve on your graph. How does it change if the wage rate increases?
Answer: The supply curve is the part of the MC curve that lies above the AC curve. Since the
entire MC curve lies above the AC curve in this case, the supply curve is simply equal to the
MC curve. If wages go up, this rotates up the c curve in panel (c) — causing an increase in
its slope at all output levels. As a result, the MC curve shifts/rotates up — which implies the
supply curve similarly shifts up.
(d) Now suppose the production process gives rise to increasing marginal product of labor
throughout. Derive the cost curve and from it the marginal and average cost curves.
Answer: This is done in Graph 11.4 (next page) and follows steps analogous to those we just
strict focus on the cost side.
Consider again (as in the previous exercise) a production process that gives rise to a strictly
convex producer choice set.
(a) Derive the cost curve from a picture of the production frontier.
Answer: This is done in panels (a) through (c) of Graph 11.3. Panel (a) illustrates the
producer choice set. Panel (b) inverts this, flipping the axes so that x is on the horizontal and
ℓ on the vertical. Finally, (c) is derived from (b) by simply multiplying labor input by w to
convert the labor input needs of production into the dollar needs for production.
b) Derive the marginal and average cost curves from the cost curve.
Answer: This is done in panel (d) where the MC curve is simply plotting the slope of the cost
curve and the average cost curve is simply the total cost divided by x.
(c) Illustrate the supply curve on your graph. How does it change if the wage rate increases?
Answer: The supply curve is the part of the MC curve that lies above the AC curve. Since the
entire MC curve lies above the AC curve in this case, the supply curve is simply equal to the
MC curve. If wages go up, this rotates up the c curve in panel (c) — causing an increase in
its slope at all output levels. As a result, the MC curve shifts/rotates up — which implies the
supply curve similarly shifts up.
(d) Now suppose the production process gives rise to increasing marginal product of labor
throughout. Derive the cost curve and from it the marginal and average cost curves.
Answer: This is done in Graph 11.4 (next page) and follows steps analogous to those we just
