MATHEMATICS FOR ECONOMISTS

A firm which has fixed costs FC of $560, for rent and executives’ salaries which must be met regardless of output level, and a marginal cost MC of $9, which is the expense incurred for each additional unit of output x, faces a total cost C which can be expressed by a linear equation of the form y = mx + b, where y = C, m = MC = 9, and b = FC = 560. Thus, C = 9x + 560

If 140 units are produced so that x = 140,

• 1820

• 1280

• 1560

• 1400

If the firm operates in pure competition, where it receives a constant price p for each unit of output x, its total revenue R can be expressed by the linear equation R = p · x

If 140 units are sold at p = 25,

• 5300

• 3500

• 2500

• 4500

With profit π being the difference between total revenue and total

cost, the profit level can also be expressed as a linear equation π = R − C

Substituting from above, π = 25(x) − [9x + 560] = 16x − 560

If 140 units are produced and sold,

• 1860

• 1680

• 1080

• 1060

Tags

CCSS.8.EE.C.7B

Use the properties of equality to solve the following linear equations by moving all terms with the unknown variable to the left, all other terms to the right, and then simplifying: (a) 3x + 8 = 5x − 6

• X = 5

• X= 7

• X = 9

• X = 6

Solve: 32 − 3x = 9x − 40

• X = 5

• X = 6

• X = 7

• X = 9

Solve: 6(4x + 5) − 3x = 19 − 2(7x + 82)

• X = 7

• X = 4

• X = -5

• X= -7

Solve: 6x − 13 3(2x − 11) + 20

• 1

• -1

• 0

• 2

Tags

CCSS.8.EE.C.7B

A firm has a fixed cost of $7000 for plant and equipment and a variable cost of $600 for each unit produced. What is the total cost C of producing (a) 15 and (b) 30 units of output? TC = FC + VC (X)

• 16,000, 25,000

• 15,000, 30,000

• 12,000, 18,000

• 25,000, 16,000

Tags

CCSS.HSF.LE.B.5

Find the total cost of producing (a) 20 units and (b) 35 units of output for a firm that has fixed costs of $3500 and a marginal cost of $400 per unit.

• 11,500, 17,500

• 11,000, 17,000

• 11,100, 17,700

• 11,300, 17,200

Tags

CCSS.HSF.BF.A.2

A firm operating in pure competition receives $45 for each unit of output sold. It has a variable cost of $25 per item and a fixed cost of $1600. What is its profit level π if it sells (a) 150 items, (b) 200 items, and (c) 75 items?

π = revenue (R) − cost (C)

where R = 45x and C = 25x + 1600. Substituting, π = 45x − (25x + 1600)

• 1,400, 2400, -100

• 2,200, 4,200, -200

• 1,100, 2,100, -25

• 1,000, 2000, -10