Reference no: EM132401867

Assignment - Math questions for finance and economics in calculus derivatives and differentiation.

Question 1 - A firm's total revenue function is given by TR = 2Q, where TR is total revenue and Q is output. What is the value of firm's marginal revenue?

Question 2 - A demand function for a product is given by Q = -2P - P² + 60. At current market price of £6 per unit, what is the elasticity of demand?

Question 3 - Which of the following give the derivative of the expression y = 1/x^½?

(a) -2/x^3/2

(b) -1/2x^½  

(c) -1/2x^3/2

(d) 2/x

Question 4 - Which of the following gives the slope of the expression: y = x³ + 9x² - 8x + 5?

(a) 3x² + 18x - 8

(b) x² + 9x

(c) 3x³ + 18x

(d) 3x + 18x + 5

Question 5 - The derivative with respect to x for the function y = ln(1+x²) is given by?

(a) 2x(1+x²)

(b) (1+x²)/x

(c) (1+2x)/(1+x²)

(d) 2x/(1+x²)

Question 6 - Which of the following gives the derivative with respect to x for the expression y = -e^-2x.

(a) -e^-3x

(b) -2x(e^-2x)

(c) -2x/e^-2x

(d) 2e^-2x

Question 7 - A chocolate manufacturing firm faces a demand function given by Q = 20 -2P where Q is bars of chocolate and P price per bar, while its cost function is given by TC = 50 + 2Q. At its current level of output of 6 bars per day, the firm is maximizing its profit, true or false?

(a) True

(b) False

Question 8 - Which of the following gives the derivative with respect to x for the expression: y = (2x-3)/(x+1).

(a) x-3

(b) 5/(x+1)²

(c) 5/(x+1)

(d) ((x-3)(x+1)-(x-1)(x+3))/(x+1)

Question 9 - A brick manufacturing firm faces demand function given by P = -2Q + 60, while the production function is given by Q = L^½, where , Q is units of brick, P is price per unit and L is the total labour employed. The Marginal Revenue Product of Labour (MRPL) is defined as dR/dL. What is the MRPL is this  case?

(a) -4L+60/2L^½  

(b) -2 + 30/L^½

(c) -4L

(d) (60)/(2L)

Question 10 - National income accounting states that Y = C + I + G; income = consumption plus investment plus government spending. Consumption depends upon after-tax income and hence income depends upon the tax rate t. Solving these equations for particular values of the parameters yields the equation

Y = 300/(0.2+0.8t)

Given this, what us the value of the tax multiplier, i.e. dY/dt?