Exam 13: Production Decisions in the Short and Long Run

If the cross-price demand curve for capital (relative to the wage)is vertical,the short run response by a firm to an increase in the wage is the same as its long run response.

Conditional input demand curves always slope down,but unconditional input demand curves can slope up.

When output price rises,the long run increase in labor input will be larger than the short run increase in labor input.

The parameter A re-scales the production function $f ( k , \ell ) = A \left( \alpha \ell ^ { - \rho } + ( 1 - \alpha ) k ^ { - \rho } \right) ^ { - \beta / \rho }$ -- allowing us to transform a decreasing returns to scale production function to an increasing returns to scale production function.

Short run economic costs must be lower than long run economic costs because long run economic costs include the cost of inputs that are fixed in the short run (and thus are not part of short run cost).

If labor and capital are perfect complements in production,short run supply curves are vertical.

Long run marginal cost curves are increasing for decreasing returns to scale production technologies.

The cross-price demand for capital (relative to the wage)may slope up or down.

Short run average expenditure curves are tangent at their lowest point to the long run average cost curve.

The production function $f ( k , \ell ) = A \left( \alpha \ell ^ { - \rho } + ( 1 - \alpha ) k ^ { - \rho } \right) ^ { - \beta / \rho }$ can have increasing returns to scale or decreasing returns to scale -- but it cannot have initially increasing and eventually decreasing returns to scale.

Suppose GE produces 1 million light bulbs per month While labor is variable both in the short run and the long run,capital is fixed in the short run.Labor is sold at a rate w and capital is rented at a rate r. a.On a graph with labor on the horizontal axis,illustrate the current isocost and isoquant for GE.Carefully label the slope of the isocost. b.For the rest of the problem,suppose a new tax on capital is implemented but GE intends to continue to produce 1 million light bulbs per year.What will GE do differently in the short run and the long run? Explain using your graph from part (a). c.Using your answer to part (b),explain what happens to the short run cost curve in the short run.What happens to this short run curve in the long run? Do costs rise more or less in the long run than they do in the short run? d.Do total costs rise more or less in the long run than total expenditures do in the short run? Explain.

If the wage falls,we know for sure that the firm will produce more in the long run but we cannot be sure whether it will use more or less capital.

The more substitutable capital and labor are in production,the more likely it is that the cross-price demand curve for capital (relative to the wage)is upward sloping.

If the rental rate increases,we know for sure that the firm will produce less and will (in the long run)use less capital.

The fixed expense on a fixed level of capital in the short run becomes a fixed cost for the firm in the long run.

Suppose the AC curve is U-shaped.Then an increase in a recurring fixed cost will cause the AC curve to shift up,with its lowest point shifting to the right.

(Long run)average cost curves are U-shaped when the production technology has decreasing returns to scale and the firm faces recurring fixed costs.

Long run average cost curves are downward sloping for increasing returns to scale production technologies.

Except for the output level for which short-run fixed capital is long run cost-minimizing,short-run average expenses incurred by the firm are higher than long run average costs.

If the rental rate increases,we know that output and labor input will fall in the long run.