a.). The geometric relationship that holds among these three curves is the total cost function. When marginal cost is less than average variable cost, average variable cost is decreasing. When marginal cost is greater than average variable cost, average variable cost is increasing. Marginal cost equals average variable cost when the average variable cost is neither rising nor falling at a minimum or maximum.
b.). An increase in the wage rate paid to labor is a variable cost increase. As more of a variable factor such as labor is added to a fixed factor such as capital, a firm will reach a point where it has a disproportionate quantity of labor to capital and so the marginal product of labor will fall increasing marginal cost and average variable cost. Therefore, the short-run average, marginal cost curve, and average variable cost curves will increase due to the law of diminishing returns. The three curves will move up together retaining their shape and relative orientation.
c.). An increase in the rental rate paid is an increase in the fixed cost that does not vary with production. If the price of a fixed input increases, only the average total cost is affected. The average variable and marginal cost are not affected. The curves retain their shape and characteristics. The marginal cost curve intersects the new average total curve and the old average variable curve at their minimums and the difference between average total cost and average variable cost is still the average fixed cost.