Isocost line Suppose 9'1, and (1p; represent the quantities of two inputs that a producer uses, PL and PK represent the prices of the two inputs, and E is the producer's expenditure / cost level. A producer's cost function (expenditure on inputs) may be stated as: quL + quK = E. In order to plot the cost function in (91,, 93) space, the function needs to be rearranged so it is in the form Q'K : F(qL, . . .). This allows calculation of 9K (the variable on the yaXis) for a given value of (1;, (the variable on the xasn's)1 and xed values of E, pi, and 19K. The given value of (1;, and corresponding value of 979: are a pair of (XJ) coordinates that can be used to plot a specic point on an isocost line. The cost function can be rearranged to give an equation for an isocost line (for a given level of expenditure /cost1 En). PLQL +PKQ'K = En (1) :> PKQK : En PLQL (2) E 7 => QK = n PHIL (3) PK Recall that the equation for a straight line ma)r be written as: Y : a + bX, where a is the value of the intercept and b is the value of the slope. In the case of the budget line above, a = E\" and b = 3i. PK PK Production function A production function may be represented by of equation of the form: Y : Amiga, where c, d and A are parameters. {Different numeric values of these parameters may be used distinguish one production fucntion/technology from another.) For example, if c : d : 0.5 and A : 4, the production function is:\" Y : 4(). \"Note that 3&5 is equivalent to . Isoquant Similar to the isocost function, the production function can be rearranged as follows to give the equation for an isoquant curve (for a given level of output, Kl). Y. : Mama (4) Y. =7 = (qiqa (5) Y\" _ d :Aq *9K (6) y\" 3 :qx : (M) (7) Note that the isoquant equation calculatm a value of qK for a given value of In. that yields the given level of output (Kl). For example, if c : d : D5 and A : 4, the equation for the isoquant curve is: Y" E Y" 2 '1\" : 49275) j q\" : (ML) ' Questions 1' This question will involve using the equation for the isooost line to calculate a set of plot points for an isocost line. Use the prices [m and pm) and expenditure levels (E1 and E2) from the Parameter table, calculate two sets of points for two isocost lines [in the Table of plot points) for the range of qL shown in the table. Each set of plot points is for an isocost curve (IE1 and IE2). Note, if you calculate a negative number, leave it blank1 2. Add the isocost lines IE1 and IE2 to the chart. Note: qL is on the horizontal axis. (See the article irl Tool #1 on how to add data to an existing chart) 3' This question refers to the production function below the Parameter table in the form K1 : A(qiq}i(). Rearrange this function, using the relevant numbers (A, c, d) from the Parameter table, to get an isoquant curve equation [i.ei qK = . . . ). 4A This question will involve using the equation for the isoquant curve and a given level of output to calculate a set of plot points. Using the given level of output indicated (K), calculate a set of points [in the Table of plot points) for the range of in shown in the table. Note, the formula for the rst point where q]; > 0 for the isoquant curve has been entered in the table. 5. Plot the isoquant curve using the plot points calculated in the question above (as a. scatter chart. with a smooth line). [1.e. update/add the IQ data seriw in your chart.) 6' Based on your table and chart, state the costiminimising production plan, gig]? (i.e. a pair of qL,qK values). Note: the equation for the isoquant can be used to calculate q} as a function of (11. In the spreadsheet, if you enter a value for in in cell B56, the corresponding value for 11K will be calculated automatically in cell B57. 7' Explain why the production plan you have identied above is costminimising. State the rm's level of expenditure/ cost to produce the given level of output indicated (K). (Hint: refer to slide 34, week 4 notes.)