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Homework answers / question archive / If AVC = Q 2 - 10Q + 120 and MC = 6Q 2 - 40Q + 120, then the quantity at which AVC is minimized is: a

If AVC = Q 2 - 10Q + 120 and MC = 6Q 2 - 40Q + 120, then the quantity at which AVC is minimized is: a

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If AVC = Q 2 - 10Q + 120 and MC = 6Q 2 - 40Q + 120, then the quantity at which AVC is minimized is: a. 11

b. 5

c. 1

d. 6

A firm's production function is Q = 2KL. Its marginal product of capital is 2L, and its marginal product of labor is 2K. The wage rate is $4 per hour, and the rental rate of capital is $5 per hour. If the firm wishes to produce 150 units of output in the long run, how many units of K and L should it employ?

a. K = 7.75; L = 9.68.

b. K = 4.23; L = 5.45.

c. K = 2.5; L = 5.

d. K = 6.33; L = 7.91.

A Toyota Camry costs $19,400 and has an average gas mileage of 24 mpg. A Toyota Prius costs $26,000 and has an average gas mileage of 55 mpg. Assuming gas costs $4 per gallon, generate total cost equations as a function of miles driven for each of these cars and identify the fixed and variable costs. How many miles do you have to drive before the two cars have the same total cost?

a. 10,000

b. 49,891

c. 70,258

d. 25,723

Philo T. Farmsworth is a corn farmer with a 40-acre tract of land. Each acre can produce 100 bushels of corn. The cost of planting the tract in corn is $20,000, and the cost of harvesting the corn is $10,000. In May, when corn is selling for $10 per bushel, Philo plants his crop. In September, the price of corn has fallen to $2 per bushel. What should Philo do, and why?

a. Philo should not harvest the corn, since the cost to harvest exceeds the revenues from selling the corn; he'll have economic losses of $22,000 this way.

b. Philo should harvest the corn, since it's already been planted; he'll have economic profit of $8,000 this way.

c. Philo should harvest the corn, since it's already been planted; he'll have economic losses of $2,000 this way.

d. Philo should not harvest the corn, since the cost to harvest exceeds the revenues from selling the corn; he'll have economic losses of $20,000 this way.

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(1) The correct option is d.

AVC is minimized when MC cuts AVC. To calculate this point, equate both the AVC and MC functions:

AVC=MCQ2−10Q+120=6Q2−40Q+1205Q2−30Q=05Q(Q−6)=0Q=6AVC=MCQ2−10Q+120=6Q2−40Q+1205Q2−30Q=05Q(Q−6)=0Q=6

(2) The correct option is a.

The production function and cost function of the firm are:

Q=2KLC=wL+rKC=4L+5KQ=2KLC=wL+rKC=4L+5K

The number of units that the firm should employ will be given at equilibrium which occurs when the ratio of the marginal product of labor to marginal product of capital is equal to the ratio of price of labor to the price of capital:

MPLMPK=wr2K2L=45K=0.8LMPLMPK=wr2K2L=45K=0.8L

To produce 150 units of output, include in the production function the value of K from the above equation:

Q=2KL150=2(0.8L)L0.8L2=75L=9.68K=0.8×9.68=7.75Q=2KL150=2(0.8L)L0.8L2=75L=9.68K=0.8×9.68=7.75

(3) The correct option is c.

Let the miles be denoted by m.

The cost function for Toyota Camry is:

C(m)=19,400+424mC(m)=19,400+424m

The cost function for Toyota Prius is:

C(m)=26,000+455mC(m)=26,000+455m

The fixed cost for Toyota Camry is $19,400 and for Toyota Prius is $26,000. The variable cost for Toyota Camry is 424m424m and Toyota Prius is455m455m.

The number of miles both the cars will have to drive to have the same total cost can be found by equating the cost functions:

19,400+424m=26,000+455m4m(124−155)=6,6004m×311,320=6,600m=70,258.0619,400+424m=26,000+455m4m(124−155)=6,6004m×311,320=6,600m=70,258.06

(4) The correct option is c.

The total cost that Philo will bear to plant and harvest the corn is a sum of the costs, which is $20,000 and $10,000 equal to $30,000. The revenue that Philo will generate is equal to $2 times 100 bushels per acre (2 * 100 * 40), which is equal to $8,000.

Since Philo has already planted the crop, he should harvest. Since the price of corn has fallen, he will have to bear an economic loss of  $2,000(= 10,000− 8,000) $2,000(= 10,000− 8,000).

Option a and d are incorrect because after the crop has been planted, Philo's only choice is to harvest the crop before it is damaged. Option b is also incorrect because Philo will have an economic loss of 2,000 and not an economic profit.

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