Question

can anyone answer this please with workings

[Ec Question 1 Consider the matrix below: T12 6 a) Find A b) What is the rank of matrix A? c) If element a became 4, would this change results to parts (a) and (b), and if so, why? Consider these further matrices: B= d) Describe, using matrix terminology, each of the further matrices above (be sure to also describe the dimensions of each matrix). Perform the following matrix operations, where possible, being clear why this isn't e) possible in any particular case: i. cB ii. dB iv. A+B [12 marks] Question 2 Ringa-Dingding PLC is a monopoly provider of high-tech telephone equipment to the UK call-centre industry. The firm faces the following market demand function for their equipment: y-500-3 P The company knows that it faces fixed costs of production of £15,000 and variable costs of the form: VC(a)-q'-704+18504 a) Write a function for the total profit of the firm, in terms of quantity. q. b) Use your answer from part (a) to establish the profit maximising quantity the firm should produce. What do total profits at this level of output amount to? e) Verify that at the profit maximising level of output found in part (b), marginal cost equals marginal revenue. d) At this profit maximising level of output, what price are Ringa-Dingding selling their equipment? [12 marks) 2 of 5 Question 3, A consumer can buy two goods, x and y. The utility they derive from consuming these has the following functional form: U(x,y)-8ry a) Find expressions for the marginal utility (MU) the consumer derives from consuming each of the two goods. The amount of x and y the consumer can purchase is limited by a budget constraint of the following form 2x+3y 40 b) Establish the maximum utility the consumer can attain and the associated quantities of x and y consumed, subject to the budget constraint, by using the Lagrange Multiplier method c) What do the partial derivatives of the budget constraint with respect to each good implicitly represent? d) If the constraint were relaxed, so the total amount available was 41, by how much, approximately, would total (constrained) utility change? What, approximately, would the new level of utility therefore be? [20 marks] Question 4 Consider a production function of the following form: a) What would you call this particular type of functional form? b) Is there any assumption which you would usually make regarding K and L, and why is this economically sensible? c) Set O equal to 10 and rearrange the function so that it is in the form K-f(L). What does this function represent? Using your answer from (c) find an expression for the marginal rate of substitution (MRS) between K and L, and explicitly state, given the assumptions you made in (b), the sign of the MRS. d) Use your answer from (d) to show whether the MRS is decreasing or increasing over e) possible values for K and L [8 marks) Please turn over) 3 of 5

Answer 1

Uni matrix a) fnd A1 . Adi A | Where IAI ·determinant of mau rix A |A 시 -8 2 12. 36 36 -36 L2 b) What the Yank ol mabix A? Aru: The rank ol matrx A u 2. Sines the matrx A has more than zero elements, the rank of A muat ba qruatr -ihan 0- he madrix has two Unear A] indeterminant ะ 48-48 jxu deterwinant of the malMix A i 0, A & not mvertia. The ajclam uatioru aloeiahd with natrix A u tùnea» equ the 2nd ro 아 nat7)x A u a scalar multiple, of 1st、oo. . As we ean Le« that So, matrix A à a sinqular matrix, which Aat xiro daterminart and has no tnverae. Since the 2nd roo of A a nudipk ot Jat

B u an exampla oF ident, matrix. Jina, ta a Aguare matrix where au-ha onal ani and an other elements are zero.7됴 dinenoum C io an examplu of a rull malix cohire all elemenh of he matrix are xero Tha dimennion quare matx which can be witth as d The matrin le became ths. nuwbe> 닛 celumns me the number of va«u n B 12 8 811,01=112.1+8.0 o6.11.0 R.0+8.1 AB:112 6.0 1 2 8 02 I 8+0

uestion : Ringa fech telephona equipmento *o U uk call canhre inus 2., ,2500 -2p. r 5q.?500 Market dumand otal eDat Fixad cotVartable cast : 15000 + 70941850 l the frm - Tolal Revenue - Toal cat a> The totl 5503-톺イー15000-9 +70ィー1150 + 67.51.600, î-15000 by The profit of lhe frm would be maxinau ox-3+ 67.5x 2-600 C or. 34-1359 600-0 r q-45q +200-0 hat the frm thould 64000 +10 8000-24000-s000 5000

3g、-1404 +1650. d 7R Marginal revenue (MR) = 孟(PK) px 1250 Whun 9, 40, MC-3x4ン40x40 +1850 4800-5600 +185U 1050 1250-5x40 1050 Proved rofit M 1250 -5x40 1250 100 150.