ECON 110 Lecture 14: Producers in the Long Run

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10 Nov 2015

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Econ 110 - lecture 14 - chapter 8 producers in the long run. The relationship between lrac and sratc curves. All factors are variable in the long run, including capital. Cost minimization is producing its output at the lowest possible cost. Cost minimization can be found with the following formula, where k represents capital, l represents labour, mp represents marginal product, and p represents price: Equation: mpk / pk = mpl / pl. Whenever the ratio of the marginal product of each factor to its price is not equal for all factors, there are possibilities for factor substitutions that will reduce costs (for a given level of output) In the equation above we would use the side that is the largest one. If mpk / pk is 4 while mpl / pl is 10, then we can reduce costs and produce more with the last dollar spent on labour, as it adds 10 units to output.

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3. A firm has a long-run production function:

(a) In the short run, K = 81 is fixed. Find the short-run production function. What is the marginal product of labor in the short-run?

(b) If w = 10 and r = 15.24, find the short-run cost function. To do this, first, figure out how many workers are needed to produce Q units of output, and then add up the (fixed) SR cost of capital and the cost of labor as a function of Q. How many workers are needed to produce Q = 10?

(c) Write down equations for an average total cost (ATC) and average variable cost (AVC) as a function of Q. What is ATC when Q = 10? What as AVC when Q = 10?

(d) Write down the equation for the marginal cost (MC) as a function of Q. What is the marginal cost of producing Q = 10 in the short run?

(e) Verify that MC = w*MPL, evaluating the marginal product of labor from part (3a) at the number of workers needed to produce 10 units of output.

(f) In the long run, both capital and labor are variable. Find the marginal product of labor and the marginal product of capital. Find the marginal rate of technical substitution. On a properly-labeled graph, draw an isoquant for Q = 10.

(g) Does the production function exhibit increasing, decreasing, or constant returns to scale?

(h) Find the lowest cost method of producing Q = 10 (two unknowns: K and L). To do this, equate the MRTS with the input price ratio w r (one equation) and use the isoquant for Q = 10 as the second equation.

(i) Use the fact that the cost, in the long run, is wL + rK to find the LR cost of producing Q = 10. What is the long-run average cost (LRAC) at Q = 10?

(j) (Hard) More generally, use the MRTS and the production function to find the cost of producing any quantity Q. To do this, repeat the above exercise but keep Q as an (unknown) variable, and solve for K and L as functions of Q.

(k) On a properly labeled graph, depict ATC from part (3b) and LRAC from part (3j). Why is LRAC everywhere below ATC?

(l) What is the production level at which SRAC is minimized?

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20) When price is less than average variable cost at the profit-maximizing level of output, a firm should: A) continue to produce the level of output at which marginal revenue equals marginal cost if it is operating in the long run. B) shutdown, because it cannot even cover all of its variable costs let alone its fixed costs if it stays in business. C) shutdown, because it will lose nothing in that case. D) continue to produce the level of output at which marginal revenue equals marginal cost if it is operating in the short run. 21) When price is greater than average variable cost but less than average total cost at the profit-maximizing level of output, a firm should: A) continue to produce the level of output at which marginal revenue equals marginal cost. B) shutdown to minimize its losses. C) reduce output to the level at which price equals average variable cost to minimize its losses. D) increase output to minimize its losses. 22) Assume that at the current market price, a perfectly competitive firm's profit-maximizing level of output yields total revenues that are just equal to total costs. Which of the following statements applies to this firm? A) The firm should increase its explicit costs to reduce its tax burden. B) The firm should shut down right now. C) The firm should continue to operate in the short run to minimize losses, but shut down if things don't improve over the long run. D) The firm is earning zero economic profit and should continue to operate. 23) The perfectly competitive firm's supply curve: A) coincides with its perfectly elastic demand curve. B) is the firm's average total cost curve above the shutdown point. C) is perfectly inelastic at the market price. D) is the firm's marginal cost curve above the minimum point on the AVC curve. 24) Assume there is a decrease in the market demand for a good sold by price-taking firms that are initially producing the profit-maximizing level of output. How will the market adjust over time? A) Firms will exit the market, causing price to rise until losses are eliminated. B) Firms will exit the market, causing price to fall until positive profits are eliminated. C) Firms will enter the market, causing price to fall until positive profits are eliminated. D) Firms will enter the market, causing price to rise until losses are eliminated. 25) What is the "most efficient capacity" for the perfectly competitive firm? A) The plant size for which Price = AR. B) The plant size at which LRAC is at its minimum. C) The plant size at which MR = MC. D) The plant size at which any of the SRATC curves are tangent to the LRAC curve.

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4. A firm's short-run production function describes how the

A. Maximum possible output varies as the quantity of labor hired varies in a given factory.

B. Minimum possible output varies as the quanity of labor hired varies in given factory.

C. Maximum possible output varies as a firm enlarges the size of its factory.

D. Minimum possible output varies as a firm enlarges the size of its factory.

5. For U.S. Steel, the total product curve represents the

A. maximum amount of steel attinable for each quanity of variable input hired.

B. Minimum amount of Steel attinable for each quanity of variable input hired.

C. Lowest cost of producing various amounts of steel.

D. Maximum profit when producing and selling various amounts of steel.

6. Kaiser Aluminums total product Curve will shift upward if the firm

A. Hires additonal quanities of labor and materials.

B. Pays lower wages to accuire additonal workers.

C. employs more efficient technologies in aluminum production

D. Initiates work rules leading to falling productivity of labor.

7. Margianl cost is defined as

A. total fixed costs plus total variable cost.

B. Total cost divided bt the level of output.

C. The increase in total cost as a frim produces an additonal unit of output.

D. Total cost minus total fixed cost.

8. The range over which marginal cost is decreasing is the same range over which

A. Total product is Increasing.

B. Marginal product is Increasing.

C. Total cost is increasing at an increasing rate.

D.total cost is decreasing.

9. General motors will realize diseconomics of scale if an increase in plant size causes.

A. A decrease in a long-run average total cost.

B. An increase in long-run average cost.

C. The short -run total product curve to shift upward.

D. The short-run total product curve to remain constant.

10. For Boeing, thechnological advances in the production of jetliners will tend to shift the total product and marginal product curves

A. Downward, and total cost and marginal cost curves upward.

B. Upward, and total cost and marginal cost curves downward.

C. Upward, and no change in total cost and marginal cost curves.

D. Downward, and no change in total cost and margial cost curves.

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ECON 110 Lecture 14: Producers in the Long Run

ECON 110 Full Course Notes

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