Please answer these 2 questions

6. Based on your table and chart, state the cost-minimising production plan, qL , qK (i.e. a pair of qL,qK values). Note: the equation for the isoquant can be used to calculate qK as a function of qL . In the spreadsheet, if you enter a value for qL in cell B56, the corresponding value for qK will be calculated automatically in cell B57.

7. Explain why the production plan you have identified above is cost-minimising. State the firm's level of expenditure/cost to produce the given level of output indicated (Y1). (Hint: refer to slide 34, week 4 notes.)

Costs in the long run In the long-run the firm can change all of its inputs, unlike the short- run when only some inputs are variable. What scale will minimise the firm's costs? Returns to scale . Long-run average cost curve: A curve showing the lowest cost at which the firm is able to produce a given quantity of output in the long run, when no inputs are fixed. . Economies of scale: Economies of scale exist when a firm's long- run average costs fall as it increases its scale of production and the quantity of output it produces. 24 1. Parameter table 2. Table of plot points Qn 1 Qn 4 0.5 IE1 IE2 1Q1 0.5 0 195.9 293.9 A 60 165.9 263.9 319.7 PL 1 120 135.9 233.9 159.9 pK 21 180 105.9 203.9 106.6 E 1 391.74 240 75.9 173.9 79.9 E2 587.74 300 15.9 143.9 63.9 Y1 554.00 360 15.9 113.9 53.3 420 83.9 45.7 Production function: Y=4(L^0.5 K^0.5) 480 53.9 40.0 540 23.9 35.5 Qn 3 600 32.0 Isoquant curve: qK = Yn^2/(4vqL)^2 Chart for Qn 2 and 5 IQ-IE plot 1350 300 250 |200 1Q1 150 FIE1 100 IE2 50 0 100 200 300 400 500 600 700 Qn 6 qL* Slope of isocost line: 0.50 qk* Slope of 1Q at identified plan: Qn 7Isocost line Suppose qL and qK represent the quantities of two inputs that a producer uses, pg, and pig 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 ((11,, qK) space, the function needs to be rearranged so it is in the form qK : F(qL, . . . ). This allows calculation of (g (the variable on the y-axis) for a given value of qL (the variable on the x-axis), and xed values of E, 30;, and 13K. The given value of qL and corresponding value of qK are a pair of (x,y) 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 / cost, En). PLQL + PKQK = En => PKQK = En PLQL En PLQL PK AHA WWI'- VVV =>QK= Recall that the equation for a straight line may 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 = 4'1. PK PK Production function A production function may be represented by of equation of the form: Y : A(q}:q}f{), 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 = \"x/(TX)- \"Note that 530-5 is equivalent to V5. 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, Yn). Yn = A(qiqk) Yn = (qiqk ) A Yn Aqi R/H Yn =9K = Aqi Note that the isoquant equation calculates a value of qx for a given value of qr that yields the given level of output (Yn). For example, if c = d = 0.5 and A = 4, the equation for the isoquant curve is: 1 2 0.5 qK = ( Yn 0.5 9K = Yn Aq L AVqu