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A profit-maximizing competitive firm uses just one input, x. Its production function is q ? 8x^{1/2}. The price of output is $24 and the factor price is $8. The amount of the factor that the firm demands is
a.11.
b.128.
c.144.
d.27.71.
e.None of the above.
12.A competitive, profit-maximizing firm uses two inputs a and b. Its production function is F(a, b) ? a^{1/2} ? a^{1/2}. Its output sells for $5 per unit. The price of input a is $1 per unit. If the price of output rises to $6 per unit but factor prices do not change.
a.it will increase its purchases of factor a by 11/4 units.
b.it will increase its purchases of factor a by 9/4 units.
c.it will increase its purchases of factor a by 3/4 units.
d.we need to know the price of factor b to be able to determine the change in demand for a.
e.None of the above.
13.A competitive firm’s production function is f(x_{1}, x_{2}) ? 12x^{1/2}_{1} ? 4x^{1/2}_{2}. The price of factor 1 is $1 and the price of factor 2 is $2. The price of output is $4. What is the profit-maximizing quantity of output?
a.304
b.608
c.300
d.612
e.292
14.A competitive firm’s production function is f(x_{1}, x_{2}) ? 6x^{1/2}_{1} ? 8x^{1/2}_{2}. The price of factor 1 is $1 and the price of factor 2 is $4. The price of output is $8. What is the profit-maximizing quantity of output?
a.416
b.208
c.204
d.419
e.196
15.A competitive firm’s production function is f(x_{1}, x_{2}) ? 8x^{1/2}_{1} ? 8x^{1/2}_{2}. The price of factor 1 is $1 and the price of factor 2 is $3. The price of output is $6. What is the profit-maximizing quantity of output?
a.256
b.512
c.252
d.516
e.244
16.Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S ? 100N/(N ? 1), where N is the number of ads. If each ad costs $4,900 approximately how many ads should Jiffy-Pol buy in order to maximize its profits?
a.2,853
b.1,428
c.98
d.1,477
e.714
17.Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S ? 100N/(N ? 1), where N is the number of ads. If each ad costs $10,000 approximately how many ads should Jiffy-Pol buy in order to maximize its profits?
a.200
b.1,995
c.999
d.1,099
e.500
18.Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze’s share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S ? 100N/(N ? 1), where N is the number of ads. If each ad costs $3,600 approximately how many ads should Jiffy-pol buy in order to maximize its profits?
a.3,329
b.72
c.1,666
d.1,702
e.833
19.A competitive firm uses a single input x to produce its output y. The firm’s production function is given by y ? x^{3/2} for quantities of x between 0 and 4. For quantities of a greater than 4, the firm’s output is y ? 4 ? x. If the price of the output y is $1 and the price of the input x is $3, how much x should the firm use to maximize its profit?
a.16/9
b.4
c.0
d.4/9
e.9/2
20.The production function is given by F(L) ? 6L^{2/3}. Suppose that the cost per unit of labor is $16 and the price of output is $8. How many units of labor will the firm hire?
a.16
b.8
c.4
d.24
e.None of the above.
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