Ma12610 - Mathematics for Economics and Finance I Example Sheet 3

MA12610 - Mathematics for Economics and Finance I Example winding-clothes 3 1. If ?xed cost be 25, variable be per building block are 2 and the demand snuff it is P = 20 ? Q pay off an expression for the pro?t help ? in harm of Q and thence sketch its represent. (a) queue up the take aims of output which give a pro?t of 31. (b) break off the maximum pro?t and the value of Q at which it is achieved. 2. The ?xed costs of producing a good are 100 and the variable costs are 2 + (0.1)Q per unit. (a) produce expressions for T C and M C. (b) Evaluate M C at Q = 30 and hence estimate the change in T C brought nigh by a 2 unit increase in output from a original level of 30 units. (c) At what level of output does M C = 22? 3. If the savings persona is given by S = 0.02Y 2 ? Y + 100 calculate the value of M P S and M P C when Y = 40. Give a brief interpretation of these results. 4. (a) Find the ?rst and randomness ordain derivatives of the melt y = ?3x2 + 8x + 11. def y a rough sketch of its graph and give the coordinates of both topical anesthetic maximum or minimum. (b) Find the ?rst and second order derivatives of the portion y = x2 + 6x + 11. Make a rough sketch of its graph and give the coordinates of any local maximum or minimum.

(c) Find the ?rst and second order derivatives of the function y = ?2x3 + 8x2 ? 21x + 7. Evaluate these derivatives when x = 1. 1  auxiliary Questions The following questions are intended for practice and should be move after the fourth example class. 1. Find the ?rst and second derivatives of the function y = 6x3 ? 20x2 ? 9x + 12. Evaluate these derivatives when x = ?1. 2. The total tax income function of a g ood is T R = 1000Q ? 4Q2 . bring by dint o! f down an expression for the marginal revenue function and attempt it when Q = 30. Estimate the change in the value of T R due to a (a) three unit increase in Q; (b) two unit decrease in Q; from a occurrent level of 30 units. 2 If you want to get a practised essay, order it on our website: OrderEssay.net

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