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WorksheetsMATHEMATICS FOR ECONOMISTS
Total questions: 15
Worksheet time: 45mins
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
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
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
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
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
Find the profit level of a firm in pure competition that has a fixed cost of $950, a variable cost of $70, and a selling price of $85 when it sells (a) 50 units and (b) 80 units.
π = R − C where R = 85x and C = 70x + 950.
Substituting, π = 85x − (70x + 950) π = 15x − 950
-200, 250
150, 200
-150, 200
200, 250
Functions are generally defined by algebraic formulas and functions encountered frequently in
economics. find the name of the function represent below
Linear function
Quadratic function
Polynomial function
Rational function
Find the name of the function represent below
f(x)=ax2+bx+cLinear function
Quadratic function
Polynomial function
Rational function
Find the name of the function represent below
y=ax3+bx2+cx+d,Linear function
Quadratic function
Rational function:
cubic function
Simplify the following exponent
x4 ⋅ x5, x7 ⋅ x−3
x9, x4
x7, x5
x1, x10
x9, x−6
