# Question

American Airlines produces round- trip transportation between Dallas and San Jose using three inputs: capital (planes), labor (pilots, flight attendants, and so on), and fuel.

Suppose that American’s production function has the following Cobb– Douglas form:

T = aKbLcFd = 0.02 K0.25 L0.2 F0.55,

where T is the number of seat- miles produced annually, K is capital, L is labor, and F is fuel.

a. If American currently employs K = 100, L = 500, and F = 20,000, calculate the marginal products associated with K, L, and F.

b. What is American’s marginal rate of technical substitution (MRTS) between K and L? How about the MRTS between K and F? Should American try to ensure that all its MRTSs are equal? Explain.

c. Does the law of diminishing returns apply to K in the production of seat- miles between Dallas and San Jose by American? to L or F? Explain. Would the law of diminishing returns apply to L if c = - 0.2 instead of 0.2? If c = 1.2?

d. Given that the exponent associated with F is larger than the exponent associated with L, would it be wise for American to spend all its money on either fuel or capital and none on labor? Explain.

e. Does American’s production function exhibit constant, increasing or decreasing returns to scale? Explain. How would your answer change if c = - 0.2 instead of 0.2? If c = 1.2?

f. Does the law of diminishing returns imply decreasing returns to scale? Explain. Would decreasing returns to scale imply the law of diminishing returns?

g. In the real world, do you think that the production of seat-miles between Dallas and San Jose is characterized by a multiplicative, Cobb–Douglas technology? If not, explain the nature of the production function that might characterize a typical firm producing seat- miles in this city- pair market.

Suppose that American’s production function has the following Cobb– Douglas form:

T = aKbLcFd = 0.02 K0.25 L0.2 F0.55,

where T is the number of seat- miles produced annually, K is capital, L is labor, and F is fuel.

a. If American currently employs K = 100, L = 500, and F = 20,000, calculate the marginal products associated with K, L, and F.

b. What is American’s marginal rate of technical substitution (MRTS) between K and L? How about the MRTS between K and F? Should American try to ensure that all its MRTSs are equal? Explain.

c. Does the law of diminishing returns apply to K in the production of seat- miles between Dallas and San Jose by American? to L or F? Explain. Would the law of diminishing returns apply to L if c = - 0.2 instead of 0.2? If c = 1.2?

d. Given that the exponent associated with F is larger than the exponent associated with L, would it be wise for American to spend all its money on either fuel or capital and none on labor? Explain.

e. Does American’s production function exhibit constant, increasing or decreasing returns to scale? Explain. How would your answer change if c = - 0.2 instead of 0.2? If c = 1.2?

f. Does the law of diminishing returns imply decreasing returns to scale? Explain. Would decreasing returns to scale imply the law of diminishing returns?

g. In the real world, do you think that the production of seat-miles between Dallas and San Jose is characterized by a multiplicative, Cobb–Douglas technology? If not, explain the nature of the production function that might characterize a typical firm producing seat- miles in this city- pair market.

## Answer to relevant Questions

Economists classify production functions as possessing constant, decreasing or increasing returns to scale. Yet, from a cause-and-effect point of view, it is not readily apparent why decreasing returns to scale should ever ...Nineteenth-century British economist Thomas Malthus reasoned that because the amount of land is fixed, as population grows and more labor is applied to land, the productivity of labor in food production would decline, ...Suppose that Marriott’s production function is characterized by constant returns to scale at all output levels. What will the firm’s long- run total, average, and marginal cost curves look like?“IBM should never sell its product for less than it costs to produce.” If “costs to produce” is interpreted to mean IBM’s average total cost, is this correct? If it is interpreted to mean average variable cost, is ...Can all schools in the MBA education market face constant returns to firm scale and yet the industry has an upward-sloping long- run supply curve? If the MBA education industry is constant- cost, what, if anything, does this ...Post your question

0