Production functions and the shape of cost curves The production function determines the shape of a firm’s cost curves. Diminishing marginal return to.

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Production functions and the shape of cost curves The production function determines the shape of a firm’s cost curves. Diminishing marginal return to labor: If a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increase in output will become smaller eventually.

Shape of the marginal cost curve Shape of the marginal cost curve: –Marginal cost is the change in variable cost as output increase by one unit: –In the short run, capital is fixed, so the only way the firm can produce more output is to use extra labor. –The extra labor required to produce one more output is. –The extra labor costs the firm per unit. –As a result, the firm’s marginal cost is

Shape of the average cost curve Diminishing marginal returns to labor, by determining shape of the variable cost curve, also determine the shape of the average variable cost curve. The average variable cost is. Only variable input is labor, variable cost is, so the average variable cost is Because the average product of labor is q/L, average variable cost is wage divided by the average product of labor

Long-Run Costs In the long run, the fixed costs are avoidable: All inputs can be varied in the long run, no long-run fixed cost. Input choice –A firm wants to choose particular bundle with the lowest cost of production, which is economically efficient. Isocost line: All the combinations of inputs that require the same total expenditure. The cost of producing a given level of output depends on the price of labor and capital. C=wL+rK –The firm hires L hours of labor at a wage of w per hour, so its labor cost is wL. –The firm rents K hours of machinery at a rental rate of r per hour, so its capital cost is rK.

Bundles of Labor and Capital That Cost the Firm $100

A Family of Isocost Lines

Isocost line By substituting, w=$5, and r=$10, we find that the $100 isocost line is K=10-1/2L 1. Intersects capital axis at K==10 units and labor axis at L= Isocosts further from the origin have higher costs 3. The slope of each isocost line is the same.

Combining cost and production By combining the information about costs constraint in the isocost line and production summarized by isoquant, we examine how a firm chooses lowest cost way to produce a given level of output. –Lowest-isocost rule: Pick the bundle of inputs where the lowest isocost line touches isoquant. –Tangency rule: Pick the bundle of inputs where the isoquant is tangent to the isocost.

Cost Minimization

Interpretation of tangency or cost minimization conditions At the point of tangency, the slope of the isoquant (MRTS) equals slope of the isocost –MRTS =change K/change L =-w/r

Change in Factor Price

Expansion Path and Long-Run Cost Curve

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